Phys TUs LVL 5

Terms named after this process are traditionally found on the left side of the Navier-Stokesmomentum equations and consist of the partial derivatives of the product of density and one or morevelocity components. The magnitude of the Richardson number determines whether this process isfree or forced. A buoyancy-dependent form of this process causes the formation of hexagonalprism-shaped cells; that is the Rayleigh-Benard type of it. The Prandtl number, or ratio of kinematicviscosity to (*) thermal diffusivity, determines whether this process or conduction dominates. This processcreates thermal columns in the atmosphere and causes the upward creeping of the mantle. For 10 points,name this process in which heat is transferred by the movement of a fluid.

convection [or word forms]

The power that can be extracted from a windmill depends on this function of the wind speed. The self-force on a particle is inversely proportional to this function of the speed of light. Planck's law predicts that the radiance of a blackbody depends on this function of the frequency over the exponential of frequency. At very low temperatures, phonons cause the heat capacity of a solid to vary with this function of temperature. The reciprocal of this function of the radius is proportional to a (*) dipole's electric field. The orbital period is proportional to the square root of this function of the semimajor axis according to Kepler's third law. The universal gravitational constant has units containing this function of length. For 10 points, name this function that is applied to length to get units of volume.

cubed [or third power] <Silverman>

The German word for "single", einzel (YNE-tzell), names a type of one of these devices composed of three cylinders, of which the first and third are held at the same potential. In one theory, these objects effectively take the Fourier transform of a plane wave and map it as a point spread function onto a backplane. An effect named for these devices can form Einstein rings; that effect can be used to map (*) exoplanets. The power of these objects is measured in inverse-meters or diopters, and depends on the reciprocal of two radii, according to an equation named for a "maker" of these things. These devices can produce comas. When rays traced through them do not convene at a single point, they give spherical aberrations. For 10 points, name these devices that refract and focus light.

lenses [or electrostatic lenses; or einzel lenses; or gravitational lenses] <Silverman>

Finding the time-derivative of the expectation value of this quantity gives Ehrenfest's theorem. InLagrangian mechanics, cyclic coordinates can be used if the generalized form of this quantity isinvariant. A relativistic form of this quantity has one component equal to E over c and the otherthree equal to the classical components. This quantity is conserved due to the Lagrangian'stranslational invariance according to (*) Noether's theorem. This quantity divides Planck's constant tofind de Broglie wavelength. The change in this quantity is equal to the impulse. This quantity is conservedin both elastic and inelastic collision. For 10 points, name this quantity equal to mass times velocity.

linear momentum [accept p]

By replacing generalized velocities with the conjugate form of this quantity, one can reformulateLagrangian mechanics as Hamiltonian mechanics. In fluid dynamics, the Cauchy equation isequivalent to the conservation of this quantity. Its operator in quantum mechanics is equal to i h-bartimes the partial derivative with respect to position. The conservation of this quantity proceeds fromtranslational symmetry according to Noether's theorem. According to the de (*) Broglie relation,wavelength is equal to Planck's constant over this quantity. This quantity is conserved by inelasticcollisions. The change in this quantity is defined as the impulse. For 10 points, name this quantityconventionally equal to mass times velocity.

linear momentum [do not accept "angular momentum"]

This person's prediction that displacement squared equals six multiplied by diffusivity multiplied bytime in random walks was used by Jean Perrin to measure Avogadro's number. The proportionalityconstants for the rates of spontaneous and stimulated emission are named for this person. This scientistshowed that, as temperature goes to infinity, heat capacity goes to 3R, if a solid is modeled as a lattice ofindependent (*) springs with quantized vibrations. This physicist also showed that light energy is quantized intophotons in a Nobel Prize-winning description of the photoelectric effect. The fourth of his Annus mirabilis paperspublished in 1905 introduced mass-energy equivalence. For 10 points, name this German physicist who proposedthat E equals m times c squared.

Albert Einstein

This law is used to determine the position of the sample in the WDS technique, which measures trace elements. The phenomenon described by this law breaks down at the Henderson limit. This law is used to determine allowed reflections using the definitions of the h, k, and l planes. One method of deriving it involves setting delta-k equal to G from the von Laue equations, then applying the properties of the reciprocal (*) space. A 54 volt peak confirmed that this law applies to electrons in the Davisson-Germer experiment when using the de Broglie wavelength. This law states that two d times the sine of theta equals n times the wavelength. For 10 points, name this law which gives the angles at which scattered X-rays from a crystal interfere constructively.

Bragg's Law

This force names the cross-terms composed of the product of two different generalized coordinates inthe Euler-Lagrange equations. This force stabilizes the fourth and fifth Lagrange points. It opposespressure in geostrophic flow. Because this force always acts perpendicular to the velocity of the bob at theend of (*) Foucault's pendulum, it does no work on the bob. The magnitude of this force is given as two times thecross product of an angular velocity and a linear velocity. The namesake coefficient of this force is proportional tothe sine of the latitude and the rotation rate of Earth. It explains why a ball thrown from a carousel appears todeflect, depending on the hemisphere. For 10 points, name this fictitious force seen in rotating reference frames.

Coriolis force [or the Coriolis effect]

In spectroscopy, thermal motion of particles causes line broadening via this effect. Within an optical trap, this effect can be used to cool atoms; that setup is used to create Bose-Einstein condensates. At relativistic speeds, this effect's namesake factor is the Lorenz gamma times the quantity one minus v divided by the speed of light. Special relativity predicts a transverse version of it. At lower speeds, the wave (*) velocity is added or subtracted from the receiver or source speed in the numerator and denominator, respectively, of the factor multiplying the frequency. For 10 points, identify this effect in which the relative motion of the emitter and observer causes a shift in the observed frequency of a wave.

Doppler effect

This man names a phenomenon that charged particles undergo when repeatedly reflected by a magnetic mirror, his namesake acceleration. In a semiconductor, he names the energy of the highest occupied quantum state. The probability of a quantum eigenstate transition is given by his "Golden Rule". This man's theory of beta decay posited the creation of a neutrino via the weak force. With (*) Dirac, this scientist names the distribution followed by particles of half-integer spin, which also carry his name. This man discovered several new elements by irradiation with slow neutrons, and he names element number 100. For 10 points, name this Italian physicist who created the first self-sustaining nuclear chain reaction and participated in the Manhattan Project.

Enrico Fermi

Muon lifetime measurements have obtained precise measurements of this scientist's namesake coupling constant, which is proportional to the square of the weak coupling constant and arose when this scientist performed the first mathematically rigorous analysis of beta decay. This scientist measured the displacement of a piece of paper to calculate the blast strength of the Trinity test. This scientist's (*) "paradox" observes that despite the huge number of Sun-like stars in the universe, extraterrestrial life has never been found. Rounding to powers of 10 is commonly done in an "estimation" technique named for this director of the Chicago Pile-1. For 10 points, name this Italian-American physicist who performed the first nuclear chain reaction.

Enrico Fermi [accept Fermi constant or Fermi interaction or Fermi paradox or Fermi estimation] <Busse, Science - Physics>

One technique for measuring the coefficient of this effect for a sample is to use an arrangement with four contacts named for van der Pauw. A type of spacecraft thruster named for this effect ionizes a gaseous propellant and then expels it using an electric field. In a semiconductor, the coefficient of this effect must take the hole mobility into account. In the inversion layer of a field effect transistor, the energy levels induced by this effect are quantized, as predicted by (*) von Klitzing. Its coefficient is inversely proportional to the carrier density, and this effect offers proof that carriers are negatively charged. For 10 points, name this effect in which a transverse voltage appears in a conductor when a magnetic field is applied.

Hall effect [accept more specific answers like quantum Hall effect, fractional quantum Hall effect, integer quantum Hall effect, etc.]

3. Mechanisms producing these particles include gluon fusion or a process with a name punning on bremsstrahlung. The 1964 PLR papers about these scalar particles were written in an effort to work around Goldstone's Theorem. Interaction with these particles is responsible for spontaneous electroweak symmetry breaking. François Englert ("frahn-swah ahn-glair") won part of the (*) 2013 Nobel Prize in physics for his theoretical predictions of these particles. These particles result from a field responsible for the short-range interaction of W and Z bosons. These particles were first observed by the ATLAS and CMS experiments at CERN on July 4th, 2012. For 10 points, name this particle whose namesake field gives mass to subatomic particles and is sometimes called the "God particle".

Higgs boson [accept Higgs particle; prompt on the God particle] <Etzkorn, Science - Physics>

A potential derived from this law predicts energy quantized by half-integer multiples of Planck's constant time frequency. This equation predicts the energy required for an IR-active mode given the reduced mass of a molecule. In the most common test on an Instron device, this aw fails to predict behavior like work hardening or necking as the load increases. This equation models chemical bond vibrations with a quadratic potential energy dependence. A straight line on a (*) stress-strain curve is a consequence of this equation. It uses a proportionality constant which has units of Newtons divided by meters. This law predict a restoring force that is negative and proportional to the distance extended from equilibrium. For 10 points, name this law which applies.

Hooke's Law

This man added an H-squared term to the standard definition of magnetization to describeBarkhausen noise at low field strengths. A value named for this man is the product of the Grashofand Prandtl numbers and tells whether heat transfer is occurring through conduction or convection.This man names a statement that the inverse sine of 1.22 times lambda over diameter is the (*)minimum angle of resolution for diffraction through a circular aperture. Another phenomenon named forthis man has cross section proportional to the sixth power of particle diameter and inverse fourth power ofincident wavelength. For 10 points, name this English scientist who names a form of scattering that turnsthe sky blue.

John Strutt, Third Baron Rayleigh [accept either underlined portion]

One component of this device is tagged with the descriptor "beauty" and utilizes a very narrowforward angular coverage. Another part of this device uses a two-level trigger system to decrease theamount of data it processes. This device suffered a quench shortly after its debut, which damaged theniobium-titanium superconducting magnets needed to create its (*) 8-tesla fields. A test of SUSYinvolving B-meson decay modes was conducted using this device. Its components include ATLAS andCMS, each of which has individually observed evidence of a particle with a mass of about 126 GeV that isbelieved to mediate the acquisition of mass. For 10 points, name this particle accelerator located at CERN,which was originally built to detect the Higgs boson.

Large Hadron Collider [or LHC]

This scientist names a conducting metallic chamber used to measure current in ion implantationand mass spectrometry. This person showed that a charged metal sphere induces an opposite chargeon a metal ice pail, thus discovering the principle behind electrostatic shielding. An equation of thisscientist is incorporated into Maxwell's equation as the curl of electric field equals negative partialtime derivative of magnetic field. The negative sign in that equation is explained by (*) Lenz's law,and it more commonly as electromotive force is proportional to the time derivative of magnetic flux. The SIunit for capacitance is named for this person. For 10 points, identify this namesake of a "law of induction"often used with dynamos.

Michael Faraday

Alfred Potier corrected a calculation made after this experiment that was too large by a factor of two. A variant of this experiment run by Gale and Pearson measured the Sagnac effect, and Hammar conducted a follow-up to this experiment that disproved the drag hypothesis. A self-orienting parallel-plate capacitor and an apparatus with a shortened arm were used in two follow-up experiments based on this experiment; those two experiments are the (*) Trouton-Noble and Kennedy-Thorndike experiments. FitzGerald and Lorentz formulated an explanation for the null result of zero fringe shift observed by this experiment. This experiment utilized equipment such as a half-silvered mirror, a stone slab in a pool of mercury, and a namesake interferometer. For 10 points, name this doubly-eponymous experiment conducted at Case Western Reserve University that disproved the existence of a luminiferous ether.

Michelson-Morley experiment <Hao>

In a classic example of inverse Compton scattering, photons in this region of the spectrum gain energy through the redshift-independent SZ effect. The selection rule delta J equals plus or minus one applies to rotational spectroscopy using this type of radiation. This radiation has frequency slightly greater than ultra-high or super-high frequency radiation. Radiation at (*) 2.7 Kelvin has its maximum intensity wavelength in this region of the spectrum. A cavity magnetron produces this type of radiation. At Bell Labs in New Jersey, Penzias and Wilson discovered a nearly constant spectrum of this radiation in the universe left over from the Big Bang. For 10 points, name this form of radiation which is slightly less energetic than infrared and is often used to cook food.

Microwaves [prompt on radio waves]

A quantity named for this man is the proportionality constant between the product of the total angular momentum, Lande g factor, and one over the reduced Planck constant and the magnetic moment of the atom. De Broglie re-derived this man's restraints on angular momentum as a standing wave with an integer number of periods around a circular orbit. The electron has a magnetic moment of roughly one in units of this man's namesake (*) magneton, which is expressed in terms of electron mass and h-bar. The quantity "a-sub-naught" is part of this man's namesake model, which was able to successfully reproduce the Rydberg formula with transitions between its energy levels. For 10 points, name this early quantum physicist who created a fixed-orbit model of the atom.

Niels Bohr <Wang>

Alfvén's (all-VANE's) theorem uses the idealized form of this law to prove that magnetic field lines exactly coincide with the streamlines in a plasma. In a common analogy, this equation is compared to Fourier's law for heat transport and Fick's law for mass transport. The three different expressions for Joule heating are interchangeable by using this equation. This equation states that the current density is proportional to the gradient of electric potential or, alternatively, the product of (*) conductivity and the electric field. After applying Kirchhoff's loop and junction rules to reduce a circuit, you can use this equation to predict the current through a battery. For 10 points, identify this equation, often written as "V equals IR," whose German namesake also identifies the SI unit of resistance.

Ohm's law <Silverman> Bonuses

The normalization constant for a partition function in n-dimensional phase space is this quantity to the negative n. Precise measurements of this constant in 2017 will enable the kilogram SI unit to be physically defined for the first time. The first energy level of a particle-in-a-box is this quantity squared over eight m L-squared. The Compton wavelength is defined as this quantity over mass times the speed of light. This quantity was plugged into the numerator of an exponential to prevent the Rayleighâ€"Jeans law from diverging at high frequencies. A photon's (*) energy equals its frequency times this constant. The reduced form of this constant gets a bar written across it. For 10 points, identify this value named for the formulator of quantum theory, which is symbolized h.

Planck's constant [accept h until it is read; do not accept or prompt on "h-bar" or "reduced Planck's constant"] <Silverman>

Dividing by this quantity nondimensionalizes many phase space integrals in statistical mechanics.It is multiplied by i to give the commutator between position and momentum. Taking this quantity tozero gives a system's classical limit; accordingly, it appears in the ground state energy of thequantum harmonic oscillator and the numerator of the de Broglie wavelength. This quantity over 4pi gives a lower bound on the products of (*) uncertainties according to the Heisenberg principle, whichis often written using its "reduced" version. For 10 points, identify this quantity symbolized h, named for aGerman originator of quantum physics.

Planck's constant [or h until it is read; or reduced Planck's constant until "4 pi" is read; or h-bar until "4 pi" is read]

In engineering, the Newton number is defined as this quantity over density times rotational speed cubed times stirred diameter to the fifth. The integral of the Poynting vector over an exposed surface has units of this quantity, which can be used to show that it equals two-third times charge squared times acceleration squared over the speed of light cubed. The "reactive" form of this quantity in an AC circuit, caused by a nonzero phase angle, is measured in (*) volt-amps. The pump head times the volumetric flow rate equals this quantity. This quantity is given by the dot product of net torque and the resulting angular velocity, analogous to its definition of force dot velocity. For 10 points, name this quantity, the energy input per unit time in a system.

Power

11. One minus 19.7 divided by this number is proportional to the Strouhal number, which governs the formation of von Karman streets. For a packed bed, its denominator contains one minus the voidage. One version of this value is the ratio of magnetic advection to magnetic diffusion. It appears on the x-axis of a Moody diagram plotted against the Darcy friction factor. This value can be expressed as the ratio of (*) inertial forces to viscous forces, and is equal to the velocity times length scale divided by kinematic viscosity. At high values of it, eddies and vortices appear in the flow. For 10 points, name this dimensionless parameter which determines whether flow is laminar or turbulent.

Reynolds number [or magnetic Reynolds number]

This man and Gell-Mann explained the CP-violation of the weak force using a vector minus axial Lagrangian. Two applications of Ito's lemma are used to derive a formula this man names with Kac, relating parabolic PDEs and stochastic processes. This man assumed infinite momentum in his model of hadron collisions as partons, which later turned out to be quarks. This man created a namesake absorber theory that incorporated time-reversal symmetry by collaborating with his mentor Archibald (*) Wheeler. This man extended Lagrangian mechanics to quantum theory, minimizing action when summing over all histories in his path-integral approach. Along with Schwinger and Tomonga, this man won the Nobel in physics for his work on quantum electrodynamics. For 10 points, name this eccentric Caltech physicist known for modeling particle interactions with his namesake diagrams.

Richard Feynman <Wang>

Before quarks were proposed, this scientist proposed partons to analyze high-energy hadroncollisions. Using a formalism fully developed by this person, the quantum mechanical amplitude canbe found by integrating over all the possible paths with a weighting factor given by the classicalaction, the so-called path integral formulation. Squiggly and straight lines can be used to show theannihilation of an electron and positron to form a photon on his namesake (*) diagrams. Thisphysicist's undergraduate lectures at CalTech were packaged into his namesake Lectures on Physics. For 10points, name this bongo drum enthusiast who shared a Nobel with Julian Schwinger for his work inquantum electrodynamics and demonstrated the effects of cold on an O-ring after the Challenger disaster.

Richard Phillips Feynman

This scientist is the first namesake of a strip reaction in which a deuterium nucleus gives a neutron to aheavier nucleus, causing the release of a proton. A Physical Review paper written by Hartland Snyder andthis physicist provided the modern concept of a black hole. With Tolman and Volkoff, he calculated theupper bound on the mass of a neutron star. He is the second namesake of a statement that permitsfactorization of an atomic (*) wavefunction by fixing the position of the nucleus and factoring out the electronicwavefunction, an approximation he names with Max Born. He quoted from the Bhagavad Gita after the success ofthe Trinity test near Alamogordo, New Mexico in 1945. For 10 points, name this American physicist who directedLos Alamos National Laboratory during the Manhattan Project.

Robert Oppenheimer [or Julius Robert Oppenheimer]

This equation is used to derive the probability continuity equation. The derivation of thisequation relies on plugging a plane wave into the energy-momentum relation. This equation for aconstant V transitions from exponential to oscillatory solutions. Methods of solving this equationinclude one in which a solution near a turning point is solved as an Airy function, and one in which atrial solution is inputted and the variational method is applied. Those are the (*) WKB andHartree-Fock method. Solving this equation for a radially symmetric potential gives the orbitals of theHydrogen atom, and the time-independent version of this equation is written as H psi equals E psi. For 10points, name this central equation of quantum mechanics, named for a German.

Schrodinger equation

This scientist proposed that atoms exist as vortices in the luminiferous aether. A theorem named for this scientist states that, for a barotropic and inviscid fluid, the line integral of the fluid velocity around a closed loop is constant. This scientist is the alphabetically-later namesake of an effect that occurs in throttling valves, in which a gas cools as it expands with no change in (*) enthalpy. This scientist names a unit whose imperial version is the Rankine. His work on laying the transatlantic telegraph cable led him to be knighted. He calculated the point at which molecules have the minimum possible vibrational motion. For 10 points, name this physicist whose temperature scale is set to zero at absolute zero.

William Thomson, 1st Baron Kelvin [accept either underlined name; or Lord Kelvin; or Kelvin circulation theorem; prompt on Jouleâ€"Thomson effect or Jouleâ€"Kelvin effect; do not accept "J. J. Thomson" or "Joseph John Thomson"] <Kalathiveetil, Science - Physics>

This person used relativistic invariance as the basis for his proof of the spin-statistics theorem. Astatement of this man is often proven by considering that the wavefunction for some particles mustbe antisymmetric with respect to the exchange of some variables. The pressure that opposesgravitational collapse in white dwarfs is due to that statement. This scientist proposed that theenergy, momentum, and spin of (*) beta decay could be conserved by the introduction of an additionalparticle: the neutrino. His best known statement does not apply to bosons, but rather particles withhalf-integer spin. For 10 points, name this scientist whose most famous statement requires that electrons inthe same orbital have different spin quantum numbers, which is his "exclusion principle".

Wolfgang Pauli

A version of this experiment showing the principle of complementarity was performed by Afshar. Placing a solenoid on one side of the apparatus in this experiment was used to demonstrate the Aharonov-Bohm effect. In this experiment, time averaging the Poynting vectors shows that the maximum resulting intensity is equal to four times the incident intensity. In this experiment, plane waves turn into cylindrical waves. When the difference in path length is equal to an (*) integer multiple of the wavelength in this experiment, constructive interference occurs. This experiment demonstrated the wave nature of light. For 10 points, name this experiment in which a series of fringes appears on a film after light is shone through a namesake apparatus.

Young's double-slit experiment [accept either underlined portion]

This quantity is constant in the canonical ensemble, but it varies in the microcanonical ensemble. The maximum value for a coefficient of performance is a simple ratio in this intensive quantity. The reciprocal of this quantity, which is symbolized beta, appears in the exponential of a Boltzmann factor. The energy contributed by each degree of freedom depends only on this quantity. Carnot (car-NOH) efficiency is one minus the (*) ratio of this quantity for the two reservoirs. The entropy change equals the integral of reversible heat over this quantity. The two containers sorted by Maxwell's demon have different values for this quantity, which scales with average molecular speed. For 10 points, name this quantity measured on an absolute scale by Rankines or kelvins.

absolute temperature [or T] <Silverman>

It has nothing to do with magnetic fields, but the Biotâ€"Savart (byoh-sah-VARR) law can be used to derive this force in a theory derived by Ludwig Prandtl. The "equal transit time" theory is a common wrong explanation for this force. The magnitude of this force equals the bulk density times velocity times the line integral of velocity around a closed circle, or circulation. This force is proportional to the angle of attack for small angles. A flat (*) plate will not experience this force, since it requires streamlines to be compressed, generating a pressure gradient. This force arises not due to Bernoulli's principle, as is commonly thought, but when Newton's Third Law is applied to an airfoil. For 10 points, name this force that counteracts gravity and acts upward on airplane wings.

aerodynamic lift <Silverman>

The measurement of this quantity by radiosonde uses an aneroid cell, which is made of aberyllium-copper alloy, has had part of its air evacuated, and is attached to a stiff spring. Ageopotential height is indexed to a constant value for this quantity. The force due to this quantity'sgradient is balanced by the Coriolis force for geostrophic winds. The eye of a cyclone has a much (*)lower value for this quantity relative to outside of the cyclone and is thus depicted on a weather map with ared L. This quantity is commonly measured in inches of mercury of millibars, and it is measured with abarometer. For 10 points, identify this force that the weight of the atmosphere exerts on objects.

air pressure [or atmospheric pressure]

Twisting of the sun's magnetic field lines due to the sun's rotation is called an "effect" named for this letter. The square of the electron charge divided by h-bar times c gives a quantity denoted by this letter which characterizes the strength of electromagnetic interactions in particle physics. The coefficient of thermal expansion and the fine (*) structure constant are denoted by this letter, which names an effect used in ionization-type smoke detectors. In one experiment, a beam of particles denoted by this letter was shot at a gold foil, and the resulting deflection provided evidence for the atomic nucleus. A helium nucleus is released from an atom in a form of radioactive decay denoted by this letter. For 10 points, name this first letter of the Greek alphabet.

alpha <Busse>

The hindrance factor compares the theoretical and experimental rates of this process. The natural logarithm of the rate of this process is linearly related to Z over the square root of kinetic energy. This process occurs near the upper-right end of the belt of stability. A model of this process, based on quantum tunneling through a potential well from the strong force, replicated the empirical Geiger-Nuttall Law and was proposed by (*) George Gamow. This process is the source of ionizers used in smoke detectors. This phenomenon gives diagonal movement on a plot of A versus Z in the thorium chain. It decreases the mass number by four, the atomic number by two, and releases a helium nucleus. For 10 points, name this form of radioactive decay contrasted with beta decay.

alpha decay [or alpha emission; prompt on radioactive decay or radioactivity]

In quantum mechanics, the square of this quantity is equal to h-bar squared times n times quantity n plus one, and the g-factor gives the ratio of the magnetic moment to this quantity. One form of Kepler's Second Law states that this quantity divided by 2 m is equal to the rate of sweeping out area. In the Bohr model, this quantity for the electron is equal to the principal quantum number times h-bar. The vector of this quantity traces out a circle in (*) precession, and the time derivative of this quantity is equal to the torque. The conservation of this quantity explains why a skater spins faster when pulling their arms in. For 10 points, name this physical quantity equal to the product of the moment of inertia and the angular velocity and symbolized L.

angular momentum [accept L before mention; prompt on "momentum"; do not accept "linear momentum"]

This process produces a 511 kilo-electronvolt peak on gamma spectroscopy readouts. TheANTARES detector attempts to find occurrences of this process between WIMPs. An operatornamed for this process has eigenstates that are coherent states, and is symbolized a; that operator isderived while solving the quantum harmonic oscillator and is also known as the lowering operator.One instance of this process produces a pair of (*) photons totaling 1.022 mega-electron-volts moving inopposite directions. The reverse of this process occurring near a black hole is used as an explanation forHawking radiation; that reverse of this process is called pair production. For 10 points, name this processthat occurs when a particle and its anti-particle collide.

annihilation

These systems are described by the differential equation "r double prime minus h squared over r cubed equals F of r over m." Conservation of energy in these systems is described by the vis-viva equation. These systems can be described by the equation M equals E minus epsilon times the sine of E, where M is the mean anomaly. "Closed" examples of these systems can be modeled via a central force (*) two-body problem. These systems, which conserve angular momentum, are described by the equation "T squared is proportional to a cubed," where a is the semi-major axis and T is the period. This type of motion is characterized by elliptical trajectories according to Kepler's first law. For 10 points, name this type of motion exemplified by the Earth's path around the Sun.

astronomical orbits [accept orbital motion, prompt on planetary motion] <Busse>

The stable radius of one of these structures is equal to 1.25 times their mass to the one-thirdpower. One theory of the structure of these objects describes how those with 2, 8, and 20 substituentsare unusually stable; that model is the shell model. Hyperfine splitting is caused by the magneticmoment of these entities. Deformed and unusually long-lived ones might be found in the Island of (*)Stability, and stable ones are said to have a magic number of constituents. Their binding energy can becalculated by finding the equivalent energy of their mass defects, and they are made of baryons heldtogether by the strong force. For 10 points, identify these structure which contains protons and neutrons andis surrounded by electrons, the center of an atom.

atomic nucleus [prompt on "atoms"]

This value is set proportional to the derivative of n with respect to r in Kato's theorem. Thisquantity is related to the square root of the frequency of an emitted K-alpha line by Moseley's Law.According to the semi-empirical mass formula, binding energy is greatest when this quantityapproximately equals twenty-six. A screening constant is subtracted from this value in order todetermine effective nuclear charge in Slater's rules. For hydrogen-like atoms, the (*) square of thisquantity appears in the numerator of the Rydberg formula. Fission occurs when this quantity is greater thanabout seventy. Mendeleev ordered elements by this parameter in the Periodic Table. For 10 points, namethis quantity symbolized Z, the number of protons an element has.

atomic number [or Z before mention; accept nuclear charge or effective nuclear charge before mention]

Fixler and Kasevich's measurement of this quantity relied on measuring the differentialacceleration of two cesium samples. This quantity appears multiplied by the density and eight-thirdspi in one term of the Friedmann equations. This constant appears over the speed of light to the fourthpower in the coefficient of the stress-energy tensor in Einstein's field equations. A device invented byJohn Michell was used in the first measurement of this quantity; that experiment used a (*) torsionbalance and was done by Henry Cavendish, who originally was trying to measure the density of the earth.For 10 points, name this constant equal to 6.67 times 10 to the negative 11th in SI units, which is multipliedby two masses over r squared in a law named for Newton.

big G [or universal gravitational constant or Newton's constant before mention]

In statistical mechanics, the expected number of these particles in a given state is inverselyproportional to an exponential weight minus one. Composite particles that belong to this general class arethe basis for the BCS theory of superconductivity. These particles leave the sign of the wavefunctionunchanged upon particle exchange and include (*) Cooper pairs. They do not obey the Pauli exclusionprinciple because they obey a set of statistics named for their namesake and Einstein. Photons are an example of the"gauge" type of these particles that have integer spin. For 10 points, name this particle whose Higgs type wasdiscovered at the Large Hadron Collider.

bosons

> In an x-ray tube, the intensity of this phenomenon can be calculated with Kramer’s Law. The power produced by this phenomenon is proportional to the second power of charge and the fourth power of the Lorentz factor, and when this phenomenon is emitted from plasma, it is sometimes called free/free (“free slash freeâ€) radiation. When this phenomenon is non-relativistic, the (*) Larmor formula can be used. The Gaunt factor can be used in calculations for the thermal type of this phenomenon, and this phenomenon causes power loss during nuclear fusion. During this process, a photon is typically emitted. For 10 points, name this phenomenon in which a decelerating charged particle, usually an electron, emits radiation, which is German for “braking radiation.â€

bremsstrahlung <Hao>

The metacentric point is the intersection of two vectors representing this force. This force is represented by the isothermal compressibility times temperature difference between surroundings and surface in the numerator of the Grashof number, which compares it to viscous forces. The magnitude of this force is assumed not to be constant in the Boussinesq approximation. In a gas, the neutral type of this force exactly balances (*) gravity. This force opposes the direction of the hydrostatic pressure gradient, and its magnitude equals the density times gravity times the volume of an object. The center of this force must be close to the center of gravity for a ship to be stable. For 10 points, name this force whose magnitude is equal to the weight of the fluid displaced and which causes objects to float.

buoyancy [or the buoyant force]

The applied strength of this technique is measured in RCFs, and tabletop versions of theseinstruments usually have a "Fast Temp" option. Polyribosome binding to mRNA is commonlymeasured using the isopycnic version of this technique. Using a sucrose gradient with this techniqueallows sedimentation velocity analysis, and in that case the coefficients are measured in Svedbergunits. Cell fractionation uses this technique to extract (*) organelles, and this technique typically formsa pellet with a supernatant on top. It can also be used to remove blood plasma from formed elements. For10 points, name this technique whose power is measured in units of g, which is used to separate mixturesby spinning them around really quickly.

centrifugation [or word forms of centrifuge]

The run-time of this procedure is measured by k, the clearing factor. Cesium chloride is used in theisopycnic form of this procedure, enabling identification of the AT to GC base pair ratio. A buffered tissuesample may be blended to homogenize the solution before performing the "ultra" type of this technique.Ribosomal subunits are distinguished based on their values for a parameter in this technique measured in(*) Svedberg units. This step of the cell fractionation process sediments a solution into a pellet and a supernatantand is often performed at 1200 rpm. For 10 points, name this technique in which a namesake machine separatescellular components by size or density by spinning it at a high angular velocity.

centrifugation [or word forms such as centrifuge; prompt on spinning down; prompt on sedimentation until it is read]

An example of a system that exhibits this behavior is created by mapping a square onto itself by squishing it, stretching it, and folding it back on itself; that is the Smale Horseshoe. Systems of this type have dense periodic orbits and undergo topological mixing. The Henon map and Lorenz map exhibit this behavior, and it commonly arises when the maximal Lyapunov exponent is positive. A simple physical example of a system exhibiting it is the (*) double pendulum. Systems with this behavior often have strange attractors, and they are by definition deterministic and highly sensitive to initial conditions. For 10 points, identify this phenomenon in which a dynamical system exhibits unpredictable behaviors, which is exemplified by the butterfly effect.

chaos [or word forms like chaotic or chaotic behavior; accept chaos theory]

Nusselt film theory describes this process. The working fluid undergoes this process after it is turbined,before it is pumped, in a Rankine cycle. An exit stream undergoes this process, and then a recycle, duringreflux. This process shares its name with a method of polymerization contrasted with addition. Coldfingers are used to effect this process, which often occurs in glassware named for (*) Liebig. Silver iodideserves as a nucleus for this process to occur during cloud seeding. This process begins to happen as temperaturedips below the dew point. This process occurs in the tube leading to the receiving flask in a distillation. Thisexothermic process is the inverse of vaporization. For 10 points, name this process in which a vapor is convertedinto a liquid.

condensation [or condensation polymerization; prompt on cooling or subcooling or supercooling]

In relativity, this statement is equivalent to setting the covariant derivative of the Faraday tensorto zero. This statement follows from the gauge invariance of the electromagnetic field. One method ofderiving this statement is to take the divergence of both sides of Ampere's law. Applying thecontinuity equation to the current density yields this result. Implications of this statement includeKirchhoff's junction (*) rule, which states that the total current flowing into a junction equals the totalcurrent out, and the fact that a neutral atom emitting an electron will become positive. This concept isdemonstrated by rubbing a glass rod with a piece of fur. For 10 points, identify this statement that thenumber of coulombs in a volume remains unchanged.

conservation of electric charge [or equivalent answers like charge conservation; prompt on "continuity equation" before mention]

Every cell generated by a Voronoi diagram is a polytope of this type. If the input to the ArtGallery Problem has this property, then the solution only requires a single guard that may simplyadjust his field of view. For a Euclidean space, a set has this property if the line segment betweenevery pair of points stays within the set. A function has this property if its value at the midpoint ofevery interval does not exceed the (*) arithmetic mean of its value at the endpoints. "Every internal angleis less than or equal to 180 degrees" and "every line segment between two vertices remains within theshape" are two necessary and sufficient conditions for this kind of polygon. For 10 points, name thisproperty that is distinguished from concavity.

convex [accept word form equivalents; accept concave up, but do NOT accept "concave" or "concave down"]

One method of doing this has variations using a Zeeman slower and another which uses a pair oforthogonally polarized beams. This process can be achieved by successive rounds of adiabaticmagnetization and demagnetization. One method of doing this uses two rounds of Joule-Thompsonexpansion and is called the Linde cycle. Claude Cohen-Tannoudji developed a method of doing thisusing lasers and the Doppler effect that was used on a sample of rubidium atoms to form the first (*)Bose-Einstein condensate. This process is necessary to create superfluids and superconductors, and a crudeway of doing it is submersion in liquid nitrogen. For 10 points, name this process in which a system losesheat energy and decreases in temperature.

cooling [or refrigeration; accept laser cooling, magnetic refrigeration, or similarly more specific answers]

A device primarily used for this purpose is an array of alternating p- and n-type semiconductorssandwiched between two conductors, one of which has a current passed through it to use the Peltiereffect. The coefficient of performance for devices that perform this process is the reciprocal of theQ-sub-h over Q-sub-c minus one. Steven Chu's Nobel-winning research was in the use of lasers andthe Doppler effect to perform this process. This happens to the gas during the isentropic expansionstep of the Carnot cycle. A law named for it states that the time derivative of (*) temperature is equalto a negative proportionality constant times the difference in temperature between a body and itssurroundings; said law was derived by Isaac Newton. For 10 points, name this process in which heat istransferred away from a body.

cooling [or refrigeration; or obvious equivalents, such as making things colder by the transfer of heat; prompt on heat transfer]

The ratio between this value and the critical density of the universe is approximately 0.7, and thatvalue corresponds to the dark energy density. It is multiplied by one third of the square of the speedof light in the Friedmann equation. Taking this quantity divided by 8 pi gives the vacuum energydensity. Quantum field theories unusually predict its value to be 120 orders of magnitude greaterthan its real value. This value originally appeared multiplying the metric tensor in the (*) EinsteinField Equations in order to maintain a stationary universe. Einstein referred to its conception as the "biggestblunder" of his life since the universe is expanding. For 10 points, identify this mysterious value in generalrelativity symbolized lambda.

cosmological constant [or lambda till mention]

The translational partition function equals volume over the cube of the thermal form of this quantity, which is proportional to the square root of beta over molar mass. In one experiment, this quantity was estimated as one over 0.815 times the square root of the accelerating voltage. For a ground-state particle in a box, this quantity is the twice the length of the box. This quantity for electrons equals twice the lattice (*) spacing, times the sine of the smallest scattering angle, as measured in the Davisson-Germer experiment. This quantity, first hypothesized in a 1924 PhD thesis, is equal to Planck's constant divided by a particle's momentum. For 10 points, name this quantity possessed by all matter according to de Broglie's wave-particle duality, but which for waves, is the distance from crest-to-crest.

de Broglie wavelength [or lambda]

Applying perturbation theory to states with this property causes the denominator to go to zero. If asystem has this property in the ground state, the entropy is nonzero at absolute zero. For a particle ina multidimensional box, this condition occurs when more than one dimension of the box is the same.This property is removed in octahedral complexes by elongation along the z axis in the Jahn-Tellereffect. The Zeeman and Stark effects (*) break this property via splitting. It occurs when the Hamiltonianof a system has multiple eigenvectors with the same eigenvalue. The pressure arising from thisphenomenon balances gravity in a white dwarf below the Chandrashekar limit. For 10 points, name thiscondition in which a single energy level has more than one state.

degenerate [or degeneracy; accept word forms]

A material demonstrating this phenomenon appears to decrease in weight in a Gouy balance. Anelectron in 2D orbit around a nucleus demonstrates this phenomenon due to Larmor precession, with a magnitude proportional to the radius squared over six times the mass. This phenomenon explains the strong downfield shift of aromatic compounds' ring currents in proton NMR. A normal conductor cooled into superconducting state displays the (*) perfect form of this phenomenon, with a susceptibility of negative one. This phenomenon occurs if all electrons in a material are paired. This behavior could be used to accomplish levitation because it causes materials to repel all B fields. For 10 points, name this type of magnetism contrasted with paramagnetism and ferromagnetism.

diamagnetism

Diatomic boron anomalously lacks this property because the increased penetration of s orbitals leads to s-p mixing. The Landau model explains this property in metals as Lorentz interactions in a free electron gas. Molecules with this property form a single peak when shot through a Stern-Gerlach apparatus, because their net magnetic moment is zero. Graphite strongly possesses the (*) conventional form of this property, allowing it to be easily levitated. All noble gases have this property because their fully filled p orbitals can match together their opposing spins, cancelling them out. For 10 points, name this property of materials which induce a magnetic field opposite to an exterior magnetic field, in contrast to its para counterpart.

diamagnetism [do not accept "paramagnetism"] <Wang>

The power of this phenomenon for a particular order is optimized in a technique known as "blazing," which generally minimizes its zeroth order form. This phenomenon can be used in an experiment in combination with the Scherrer equation to determine the size of particles of a powder. It is common to measure the thickness of a strand of hair using this phenomenon and Babinet's principle. James Gregory theorized a device consisting of periodic (*) "gratings" which would induce this phenomenon. The formula "two times distance times sine of the scattering angle is equal to n times wavelength" describes this phenomenon; that equation, Bragg's law, describes this phenomenon's use in crystallography. For 10 points, name this phenomenon in which a light wave bends around an obstacle.

diffraction [accept diffraction grating] <Jose>

Although having nothing to do with signal processing, solving one version of this phenomenonrelies on finding the Fourier transform of the rect function. A mathematical formalism of it takes theGreen's function of Helmholtz's equation, then substituting into that formalism's namesake integraltheorem; that formalism is Kirchoff's scalar theory of this process. Its knife-edge version is governedby a rule stating that every point of a front is the source of a spherical wave, called (*) Huygensprinciple. This phenomenon creates the Arago spot when occurring through a circular aperture, a setupdescribed by the formula 1.22 times lambda over D, which also gives the Rayleigh criterion for the limit ofresolution imposed by this phenomenon. For 10 points, name this effect in which light bends around anobject.

diffraction [prompt on "interference"]

This process' namesake PDE has the Gaussian Kernel as a solution. The fractional anisotropy iscalculated from the eigenvalues of a tensor named for this process. One quantity describing thisprocess is equal to terminal drift velocity times Boltzmann's constant times temperature. The secondderivative of phi with respect to x is proportional to the first derivative of phi with respect to timeaccording to one law governing it. Another law governing this process says that (*) flux is proportionalto the negative grad of the concentration; those laws are named for Fick. This process occurs through asemipermeable membrane in osmosis. For 10 points, name this phenomenon in which a substance movesfrom an area of high concentration to low concentration.

diffusion [accept osmosis till mention]

In the "laser" type of these devices, the gain medium typically has a P-I-N structure. In the hydraulic analogy, these devices are compared to a check valve, which only opens when the pressure difference is of the right magnitude and sign. These devices are symbolized by a triangle whose tip touches a straight line parallel to the base of the triangle. The 2014 (*) Nobel Prize in Physics was awarded to Akasaki, Amano, and Nakamura for developing a "blue" form of one type of these devices. A single p-n junction serves as one of these devices, which let current through under forward bias. For 10 points, name this circuit element which allows current to flow through in only one direction, whose "light-emitting" variant is used in modern light bulbs.

diodes [accept light-emitting diodes or LEDs, prompt on p-n junctions] <Busse>

Transitions named for these objects are subject to the selection rule that L must change by one.The Synchrotron Radiation Source uses magnets in this configuration to generate synchrotronradiation. This configuration, which corresponds to the l equals one spherical harmonic, is thehighest-order one unable to radiate gravitational waves. An oscillating one of these radiates powerproportional to the fourth power of (*) frequency. The electric field of these entities drops off as the thirdpower of the distance. The torque on one of these in an electric field is equal to the cross product of itsnamesake moment and the electric field. For 10 points, name this arrangement in which one positive andone negative charge are paired together.

dipole

This term refers to an anisotropy of the CMB that is caused by the motion of the earth through space. The power radiated by an oscillating one of these is proportional to the fourth power of the frequency, which is a principle used in television antennas. The atomic model of a dielectric posits it as a collection of several of these, which align and create a field opposing the external field. Their electric field falls off as one over the third power of the (*) distance. Placing one of these in an electric field creates a torque equal to the cross product of the field with these configurations' namesake "moment". For 10 points, identify this configuration consisting of a positive and a negative charge bound together.

dipole [prompt on "polar molecules" due to the dielectric clue]

One form of phenomenon can be reduced by using a graded-index profile instead of a step-index profile; that form of this phenomenon is termed "intermodal" or "multimodal." This phenomenon can be quantified using a number calculated using three Fraunhofer lines and symbolized V-sub-d; that number is named for Abbe. Group velocity can be calculated by differentiating a "relation" named for this phenomenon. This phenomenon occurs when a medium's (*) index of refraction is dependent on the wavelength, thus causing a non-coherent light beam to separate since Snell's law implies the different wavelengths refract at different angles. For 10 points, name this optical phenomenon which explains how a prism splits white light into a rainbow.

dispersion [accept more specific answers like "optical dispersion" or "chromatic dispersion" or "intermodal dispersion"; prompt on refraction] <Busse>

The momentum j-factor in the Chilton-Colburn analogy is given by a number describing this phenomenon, divided by two. A constant factor of 1.33, times the square root of the Reynolds number, gives the magnitude of this phenomenon on a flat plane. For high Reynolds numbers, the magnitude of this force is proportional to the velocity squared, but in creeping flow, the dependence is (*) linear, with a coefficient often symbolized b. This force is proportional to the radius and viscosity according to Stokes' Law for spherical particles. The "form" contribution to this force is greater when a surface is perpendicular to the oncoming streamlines. For 10 points, name this force that balances gravity at the terminal velocity, and opposes thrust in fluids.

drag force [or air resistance; prompt on air friction

In 2006, Boyle and Smith were awarded the Nobel Prize in Physics for the creation of a device,used in astronomical imaging, that uses photons to build up this quantity. Structures with a non-zerovalue for this quantity that are driven along magnetic field lines in the atmosphere are named afterBirkeland. Many particle species with a non-zero value for this quantity combined to form hydrogenduring the epoch of (*) recombination. According to the no-hair theorem, this quantity, mass and angularmomentum are the only properties that characterize a black hole. During the epoch of reionization,baryonic matter typically acquired a non-zero value for this quantity. For 10 points, name this quantitywhich is non-zero for ionic species.

electric charge [accept charged coupled devices on the first sentence; accept current until "no-hair" is read]

In a 1-D or 2-D crystal below the Peierls temperature, standing waves named for density and this quantity are formed. This quantity's density is multiplied by the speed of light in the time-like component of a four-vector which is symbolized J. The flux of the polarization density through a surface equals the "bound" value of this quantity enclosed within the surface. This quantity's conservation is expressed by a continuity equation derived by applying the divergence theorem to (*) Ampere's Law. The quantization of this quantity was demonstrated in an experiment where Robert Millikan studied the motion of oil droplets. The force between "point" examples of this quantity is given by Coulomb's Law. For 10 points, what electrical quantity is thus measured in Coulombs?

electric charge [prompt on Q, accept charge density waves before "four-vector"] <Busse>

When this quantity is divided by cross-sectional area and multiplied by the magnetic permeability, it is equal to the Laplacian of the magnetic vector potential. This quantity is proportional to the product of drift velocity, area, and carrier density, and it is multiplied by the differential length in the BiotÂâ€"Savart law. The line integral of a magnetic field around a loop is proportional to the amount of this quantity (*) enclosed according to Ampere's Law. Kirchoff's junction rule states that the amount of it leaving a junction is equal to the amount entering, and it is multiplied by resistance in Ohm's law. For 10 points, name this quantity equal to the rate of flow of electric charge that is symbolized I and measured in amperes.

electric current

A quantity named for one of these objects can be expressed as a sum over copies of the L equalsone solid harmonic. A time-varying one of these objects emits radiative power proportional to thefourth power of its frequency. The torque on one of them is perpendicular to an applied electric field,and the strength of one of them is equal to a volume integral of charge density times position. Thisobject gives its name to the one over (*) r-squared term in a power series for electric potential, and itselectric field falls off as one over r cubed. For 10 points, name these objects whose "moments" aremeasured in debyes, charge configurations consisting of two equal and opposite charges separated by asmall distance.

electric dipole

The expectation value of an operator named for these objects equals the transition moment integral, which is used to derive most selection rules. The Keesom force is between these objects. The only vibrations detectable in IR spectroscopy require a change in a namesake quantity of these objects. Torque is maximized when they are oriented perpendicular to an applied field. The potential from these objects varies with the negative (*) third power of distance. In chemistry, they are represented by an arrow with a plus sign on one end. Their moments are measured in debyes (duh-byes) or coulomb-meters. Induced ones cause London dispersion forces. For 10 points, name these objects formed from differences in electronegativity in a bond, which consist of two separated, opposite charges.

electric dipole [or magnetic dipole] <Wang>

Davydov splitting is caused by excitations of these systems within individual unit cells. The energy of two of these systems is proportional to 1 minus 3 times cosine squared of the angle between them, giving a critical value at 54.74 degrees. In linear optics, one of these things is created by an external field, with a magnitude proportional to the polarizability. The potential from this arrangement drops off with the (*) third power of distance. The potential energy of these objects is given by the dot product of the external electric field with their namesake moment, which is the product of charge and distance, and is symbolized mu. For 10 points, name these systems of a positive charge separated from a negative charge.

electric dipoles [or electric dipole moment]

Surface plasmon resonance requires an interface across which this quantity changes sign, like a sheet of gold. In SI units, the reciprocal of this quantity is defined as the speed of light squared, times four pi, divided by ten million. In Maxwell's correction to Ampère's law, this quantity multiplies the time derivative of E but not J, since, without polarization, it is the ratio between the displacement and electric fields. The capacitance of parallel plates depends on the plates' (*) area, their separation distance, the dielectric constant, and this quantity. The flux through a Gaussian surface equals the enclosed charge over this quantity. Coulomb's constant equals one over four pi times this constant's value in a vacuum. For 10 points, name this quantity symbolized epsilon.

electric permittivity [or permittivity of free space; or vacuum permittivity; or epsilon or epsilon-naught until it is read] <Silverman>

In general relativity, there are "weak", "dominant", and "strong" versions of a condition onmatter distribution named for this quantity. This quantity is the second namesake of a tensor whosespacelike diagonal components are pressure components. That tensor, which contains this quantity'sdensity in its upper left entry, is named for stress and this quantity. The amount of this quantity (*)stored in a magnetic field is given by the volume integral of B squared over 2 mu-nought, while for acapacitor it equals one-half Q times V. Voltage equals this quantity per unit charge, so Kirchhoff's looprule can be seen as a statement of its conservation. The rate at which this quantity is consumed to do workis given by power. For 10 points, name this quantity measured in joules.

electric potential energy

In natural units, this quantity equals 0.303, or the square root of four pi times the fine structureconstant. The product of this quantity, the Josephson constant, and the von Klitzing constant equals two.It is raised to the fourth power in the Rydberg formula. An experimental measurement of this quantity,which differed from the true value by five standard deviations, was described as "Cargo Cult Science" byRichard Feynman. For quarks, this constant is prefixed by either (*) two-thirds or negative-one-third. Thisconstant was determined by manipulating voltage until the terminal velocity of falling oil droplets was reached. For10 points, name this constant measured by Millikan, whose magnitude is around 1.6 times ten to the negativenineteen, and which is symbolized e.

elementary charge [or e until it is read; or fundamental charge; or charge on a proton; or charge on an electron]

In reduced units, the operator for this quantity for the hydrogen atom is often expressed as one over the radius minus one half del-squared. For a particle in a box, the average value of this quantity is the integral of psi-star times the Hamiltonian of psi, and is minimized at h squared over eight times the mass times the length squared. This quantity does not commute with time, in a common expression of the uncertainty principle. (*) Degeneracy occurs for two states where this quantity is the same. H psi equals this quantity times psi, according to the time-independent Schrodinger equation. For 10 points, name this quantity that is quantized by Planck's constant, and which is measured in electron-volts or Joules.

energy [or total energy; or E; or kinetic energy; or Hamiltonian until it is read]

The derivative of Gibbs free energy over RT with respect to T equals the negative of this quantity over R times T squared. Both terms of this quantity's total differential are positive. This quantity is usually assumed constant when a gas expands through a valve. For an ideal gas, the change in this quantity just equals C-sub-p times the change in (*) temperature. If the change in this quantity is negative, then the equilibrium constant goes down as temperature goes up. For an open system, this quantity replaces the internal energy in the First Law. The change in this quantity exactly equals the heat in a coffee-cup calorimeter. Gibbs energy is defined as it minus temperature times entropy. For 10 points, name this thermodynamic quantity symbolized H.

enthalpy [or H until it is read] <Silverman>

A model first developed to describe this phenomenon predicts that the fraction of low energy states equals the negative hyperbolic tangent of beta times the splitting energy. This phenomenon only occurs if the density of states at the Fermi level times the Stoner exchange parameter is greater than one. Heisenberg modified a model of this phenomenon that simply defines points in a lattice to be spin-up or spin-down. A graph of this phenomenon has intercepts labelled coercivity and remanence and forms a (*) hysteresis loop with steps for gaussing and degaussing. Below the Curie temperature, this phenomenon occurs when domains align in the absence of an external field. For 10 points, name this form of permanent magnetism observed in cobalt, nickel, and iron.

ferromagnetism [or word forms; prompt on magnetism] <Silverman>

8. The residence time distribution equals the negative of this mathematical operation applied to the washout function. This operation applied to the amount of any species equals "in minus out, plus generation minus consumption" in a continuous process. Michaelis-Menten kinetics assume that this operation vanishes when applied to the amount of the enzyme-substrate complex at a pseudo-steady state. A species in a reaction is (*) first-order if this operation applied to its concentration is proportional to its concentration. At equilibrium, this operation returns zero when applied to any species. For 10 points, name this operation from calculus which, when applied to product concentration, gives the rate of a reaction.

first time derivative [or first derivative with respect to time; or ordinary time derivative; or partial time derivative; accept differentiation or differentiating in place of “derivativeâ€; do not accept or prompt on "second derivative"] <Silverman, Science - Chemistry>

This phenomenon is used to measure DNA or RNA concentration in ThermoFisher's Qubit apparatus. The energy of this process can be fine-tuned by adjusting the confinement size in a quantum dot. Two systems undergoing this process can exchange energy in Forster resonance transfer, or FRET, which is used to measure (*) distance. Quenching can reduce the quantum yield of this process, a measure of its efficiency. The timescale of this process is faster than a related phenomenon because its electrons start from a singlet state. Mercury vapor is heated inside a container coated in phosphor to generate light via this process. For 10 points, name this radiation process where light is re-emitted at a longer wavelength, which is used in efficient compact light bulbs.

fluorescence [accept word forms; prompt on radiation; do not accept "phosphoresence" or "luminescence"] <Wang>

This quantity must be the same for each component of an apochromatic triplet. In one approximation, the reciprocal of this quantity equals the index of refraction, minus one, times the difference in the reciprocals of two radii. The inverse of this quantity is measured in diopters and is referred to as power. This quantity is divided by the diameter of the pupil in order to calculate a namesake stop. This quantity over this quantity minus the distance to the (*) object, gives the magnification. This quantity equals half the radius of curvature for a concave mirror. An object placed outside this distance for a convex lens produces an inverted, real image. FTP, name this quantity, the distance from the lens to the point where the light rays converge.

focal length [or f; prompt on partial answer]

Whitehead’s theory is an alternative to this theory, published seven years earlier. The Ricci tensor is on one side of an equation governing this theory; 8 pi times big G over the speed of light raised to the fourth power is on its other side. This theory was confirmed by Arthur Eddington’s observation of a (*) solar eclipse, and it explains the precession of Mercury’s perihelion. Gravitational lensing is a consequence of this theory, in which the curvature of spacetime explains gravity. For 10 points, name this 1915 theory by Albert Einstein that is often contrasted with a “special†one.

general relativity [prompt on relativity; do not accept or prompt “special relativityâ€] <BC>

A principle of this theory would be violated by the Nordtvedt effect, which has likely been ruledout by the Lunar Laser Ranging experiment. A consequence of the use of torsion-free linearconnections in this theory is the Bianchi identities. Under certain conditions, this theory predicts thatparticles will precess due to "frame-dragging". The "weak" form of a principle of this theory statesthat freely falling particles move on timelike geodesics. This theory accounted for the anomalousprecession of the (*) perihelion of Mercury. A stronger form of that "weak" principle states that allphysical phenomena appear the same in an accelerating inertial reference frame and a uniform gravitationalfield. For 10 points, name this theory introduced by Einstein in which gravity results from the curvature ofspace-time.

general theory of relativity [or GR; prompt on Einstein's theory relativity; do not accept "special relativity"]

The existence of these phenomena is shown by Bondi and Feynman's "sticky bead argument".The tensor-to-scalar ratio of these phenomena was recently discovered to be 0.2 by the BICEP2collaboration. The existence of these entities was shown indirectly by observations of PSR 1913 + 6,whose orbital decay matched the predictions of the energy of these phenomena; that work was doneby Hulse and Taylor. BICEP2 inferred their existence from B-modes of the (*) CMB. Attempts todetect these entities include an apparatus in Livingston, Louisiana consisting of an interferometer with longFabry-Perot arms, called LIGO. For 10 points, name these phenomena predicted by general relativity,which are ripples in spacetime caused by the weakest of the fundamental force.

gravitational waves [or gravitational radiation; or gravity waves]

A classic textbook titled for this phenomenon is abbreviated MTW for its three authors. In one theory of this phenomenon, integrating the square of Hamiltonian constraints over induced metrics creates a master constraint. Milgrom proposed a theory in which this phenomenon has a force proportional to the square of acceleration. Feynman (FINE-min) hypothesized using beads on a rod to measure the radiation caused by this phenomenon, which today is measured using (*) interferometers with four-mile arms. LQG and MOND ("mond") are theories of this phenomenon. According to the equivalence principle, this phenomenon is indistinguishable from being in a noninertial reference frame. Another theory equates it with spacetime curvature. For 10 points, name this fundamental force described by general relativity.

gravity [or gravitation; or gravitational force; or gravitational radiation; or gravity waves; or gravitational waves] <Silverman>

In this quantum mechanical system, light absorbance strongly occurring at 121.6 nanometers produces the Gunn-Peterson trough. A tiny splitting of energy levels that occurs in this system due to vacuum interactions is called the Lamb shift. Schrödinger's famous 1926 paper (*) solved the Schrödinger equation for this quantum mechanical system. R times the quantity one over the final state of an electron squared minus one over the initial state of the electron squared is equal to the wavenumber for lines in this system's emission spectrum. That equation works since Z equals one for this system, making it the simplest version of the Rydberg formula. For 10 points, identify this system consisting of an electron in orbit around a proton.

hydrogen atom [prompt on atom or atomic model; prompt on two-body system until mentioned; do not prompt on "proton" or "electron"] <Prieto>

On the mass shell, the self-energy has a component proportional to this quantity, which can be inverted to find the lifetime of a particle. One over kT is replaced by time times this quantity over h-bar when performing a Wick rotation from Euclidean space to Minkowski space. The commutator of two conjugate variables equals this quantity times h-bar. This quantity is multiplied by h-bar and the time derivative of the wavefunction in the (*) time-dependent Schrödinger equation. The reactance is multiplied by this quantity in the formula for impedance. The sine function is multiplied by this quantity in Euler's formula. For 10 points, name this quantity equal to the square root of negative one.

i [or j; or the imaginary unit; accept equivalents like the square root of negative one until read] <Mukherjee, Science - Physics>

For an inductor, this quantity is equal to j times the frequency times the inductance. For a losslessline, the characteristic form of this quantity is equal to the square root of L over C. This quantity isused to normalize both axes of a Smith chart. The maximum power transfer theorem states thatmaximum power is transferred when this quantity of a source equals its complex conjugate acrossthe junction. The reflection coefficient is a function of this quantity between (*) two materials. Theinverse of this quantity is the admittance. This quantity is equal to i times the reactance plus the resistance.For 10 points, name this quantity symbolized Z, a generalized form of electrical resistance applied to ACcircuits.

impedance [prompt on Z]

This quantity is related to a specific wavelength, lambda, by A lambda squared plus B plus Clambda to the minus two plus D lambda to the minus four, where A through D are materialconstants, in Cauchy's equation. It is sometimes useful to derive this quantity as the square root ofrelative permittivity times relative permeability. The arcsine of the ratio of this quantity for twomedia gives the critical angle for (*) total internal reflection. The ratio of this quantity for two media isequal to the ratio of the sine of the angle of incidence and sine of the angle of transmittance according toSnell's law. For 10 points, name this quantity symbolized n and equal to the ratio of the speed of light in avacuum to the speed of light in a material.

index of refraction [or n until it is read]

Losses due to a method used to increase this quantity include the hysteresis and eddy current loss.Transformers use the "mutual" form of this quantity to step-up and step-down voltages. Its presencecauses current to lag voltage. This quantity is multiplied by j omega to obtain impedance. The energystored in devices with it is equal to half this quantity times current squared because the voltageacross such devices is equal to this quantity times the time-derivative of current. As it's often equal to(*) permeability times cross-sectional area over length times number of coils squared, it can be increasedby inserting a core, like iron. This quantity determines the ability of an element to generate magnetic fluxlinkage in response to a current. For 10 points, name this quantity whose SI unit is the Henry.

inductance

This is the order of phase transitions that are continuous and break no symmetries. Theionization energy can be derived from Rydberg's formula by setting the principal quantum numberof the final state to this value. In quantum field theory, renormalization is used to remove points withthis value. The Rayleigh-Jeans law predicts that the energy of a blackbody approaches this (*) valueat low wavelengths. When considering the potential energy of a group of point charges, the energy at thispoint is set to zero. This is the density of the singularity at the center of a black hole, because it has a largemass and zero volume. For 10 points, name this value, which can be obtained by dividing by zero.

infinite [accept equivalents]

For the Lane-Emden equation, having a polytropic index take on this value appropriately models a stable, isothermally stratified atmosphere. This is the value in time at which the rate of expansion becomes zero if the density equals the critical density. When considering the Schwarzschild solution to the Field Equations, the curvature takes on this value when there is no radius. When calculating the escape velocity, this is the value that the distance takes on at the (*) final time. The luminosity of any point in a steady-state universe takes on this value according to the scenario analyzed in Olber's Paradox. As one approaches a singularity, this is the amount of force needed to maintain a particle in place. For 10 points, name this value at which things become immeasurably big.

infinite [or infinity]

Hubbard theory is used to describe a type of these materials which have an odd number of electrons per unit cell, which only exist at low temperatures and are named for Neville Mott. One type of these materials have protected spin states on their surface, which allows an exception to their defining characteristic by creating intermediate energy states above the (*) valence band. Many of these materials can increase the capacitance of a system, a consequence of having high dielectric constants. A sufficiently high voltage will cause these materials to break down, allowing electrons to cross to their conduction band. For 10 points, name these materials that resist the flow of current.

insulators [accept Mott insulators or topological insulators; prompt on dielectrics until "dielectric" is read] <Wang>

A very simple one of these devices can be constructed from two pieces of glass separated by a thin "air wedge." A compensator plate can be used to correct for phase differences in these devices. On September 14, 2015, two of these devices located in Hanford, Washington, and Livingston, Louisiana, detected radiation emitted by a black hole merger. In the most common type of these devices, a coherent and monochromatic beam is split into two and (*) recombined after the two beams are sent down two "arms" oriented perpendicular to each other. LIGO uses a type of this device, which was used in an experiment to disprove the existence of the luminiferous ether. "Fringes" due to superposition of waves can be observed with, for 10 points, the Michelson form of what devices?

interferometers [accept more specific answers like "Michelson interferometers"] <Busse>

This quantity is divided by particle number and raised to the three-haves power in one l-n term ofthe Sackur-Tetrode equation. The derivative of the partition function with respect to thethermodynamic beta gives this quantity. For an ideal gas, the derivative of this quantity with respectto entropy gives temperature, and this quantity is three-halves times particle number timesBoltzmann's constant times temperature. This quantity minus temperature times entropy gives the(*) Helmholtz free energy. The change in this quantity is equal to the work done on the system plus the heatadded according to the first law of thermodynamics. For 10 points, name this quantity symbolized U, whichcan also be expressed as the sum of kinetic and potential terms for a gas.

internal energy [or U before mention; prompt on energy or total energy]

The operator for this equals negative the quantity Planck's constant squared divided by twice themass end quantity times del squared. The Hamiltonian is given by twice this quantity minus theLangragian, while the Lagrangian is given by this quantity minus U. In relativistic calculations, it isfound by gamma minus one times mc2. For a molecule of a gas, it is equal to three-halves timesBoltzmann's constant times temperature. According to a namesake theorem, work equals the (*)change in this. This is usually calculated as momentum squared divided by twice the mass, or as one halfmass times speed squared. For 10 points, name this type of energy possessed by objects in motion.

kinetic energy [prompt on partial answer; prompt on "T" or "K"]

A Cooper pair is created to satisfy this statement in Andreev (on-DRAY-eff) reflection. This statement is a consequence of the symmetry of a wavefunction with respect to rotation, since the U(1) gauge (U-one gayj) is invariant upon scalar addition. The continuity equation equivalent to this law says that the current density is divergence-free at steady-state. This law explains why inserting a dielectric into a capacitor changes voltage by the same factor as the capacitance. Kirchhoff's (*) first rule, a consequence of this law, requires that current into a junction equals current out of it. This law explains why two surfaces rubbed together will attract each other. For 10 points, name this law, the basis of static electricity, which states that the total number of Coulombs in a system is constant.

law of conservation of charge [or electric charge conservation; prompt on partial answer] <Silverman>

Poincaré (pwann-kah-RAY) stresses were introduced to explain this phenomenon. Lord Rayleigh failed to see birefringence in light passing through an anisotropic (AN-iso-TROP-ik) tube in a 1902 experiment aiming to disprove this effect. Paradoxes about this effect include one involving three ships held together by a thread, and one where a ladder is carried through a barn. This effect is visualized in Minkowski space as the difference between two sides of a right triangle. It explains why the "square root of one minus (*) v-squared over c-squared" was the ratio of two distances in the Michelsonâ€"Morley experiment. That factor, gamma, shares its name with this effect's formulator. For 10 points, name this effect in special relativity in which objects moving near the speed of light appear to get shorter.

length contraction [or Lorentz contraction; prompt on partial answer] <Silverman>

The sum over all particles in a system of this quantity dotted with position equals the scalar virial. The derivative of the Lagrangian with respect to the time derivative of a generalized coordinate gives this quantity. This quantity is related to position via a Fourier transform. The magnitude of the wavevector is proportional to this quantity, since it equals Planck's constant divided by the (*) de Broglie wavelength of a matter wave. This quantity squared divided by twice the mass gives kinetic energy. Its time derivative equals force by Newton's second law. The change in this quantity equals impulse. For 10 points, all collisions conserve what quantity, which is equal to mass times velocity and denoted p?

linear momentum [prompt on p, do not accept or prompt on "angular momentum" or "L"] <Busse>

The Jefimenko (YEFF-ee-MEN-koh) equation for this quantity does not have a term containing the retarded charge distribution. This quantity is zero in the direction of propagation for a TM mode of an optical cavity. Charge times this quantity over mass equals the cyclotron frequency. This quantity induces a light wave to rotate its plane of polarization in the Faraday effect. This quantity equals the curl of the (*) vector potential. When this quantity is oriented perpendicular to an electric current, a transverse voltage is produced, a result called the Hall effect. Charge times the cross product of velocity with this quantity gives the Lorentz force that this quantity induces on a moving charged particle. For 10 points, B is the symbol for what vector field measured in Teslas?

magnetic field strength [or magnetic flux density; prompt on B; do NOT accept or prompt on "magnetic flux"] <Busse>

The quantization of this quantity was first demonstrated by the Little-Parks effect, andAbrikosov vortices are sometimes named for the fact that they contain a quantum of this quantity.The inverse of the quantum of this quantity is equal to the Josephson constant. This quantity is equalto the line integral of the vector potential around a boundary. Type II superconductors have theability to pin lines of this quantity. The negative time derivative of this quantity is equal to theinduced (*) emf according to Faraday's Law, and this quantity can be given as the dot product of themagnetic field with the surface area. For 10 points, name this quantity which gives the amount of magneticfield passing through a given area.

magnetic flux [or electromagnetic flux]

These particles are created by the breaking of a G gauge group's symmetry in a model developedby 't Hooft and Polyakov, and they are equivalent to a dyon with no charge. The first solution to theYang-Mills field equation was one of these entities named for Wu and Yang. Before joining CDMS,Blas Cabrera used a SQUID to observe one of these particles on Valentine's Day, 1982. The (*)MoEDAL experiment at the LHC looks for these particles. These particles are produced in large quantitiesat the GUT scale, but inflation explains why their density is low. They were first postulated by Paul Diracand would necessitate a modification of Gauss' law of magnetism if discovered. For 10 points, name thesehypothetical particles which only a north or south end.

magnetic monopoles

In a semiconductor, one form of this quantity is raised to the three-halves power in order to findthe density of states. Along with spin, this quantity provides the index of unitary irreduciblerepresentations of the Poincare group. A "gap" named for this quantity is the difference in energybetween the vacuum state and the next lowest energy state. The inertial and gravitational forms ofthis quantity are equal according to the (*) equivalence principle. The binding energy of a nucleus isfound by calculating the defect in this quantity, and it is multiplied by the gravitational acceleration andheight to find gravitational potential energy. For 10 points, name this quantity which is multiplied by thesquare of the speed of light in order to find energy.

mass [or m; accept effective mass or mass gap]

Dividing the dynamic viscosity by this quantity gives the kinematic viscosity. The drag force isproportional to the product of the square of velocity, the drag coefficient, the cross sectional area,and this. One term of Bernoulli's principle has pressure divided by this quantity, and this quantityvaries in (*) compressible flows. Archimedes' principle states that ratio of the weight of an object to theweight of displaced fluid is equal to the ratio of this quantity for the object to this quantity for the fluid. Thegauge pressure is equal to this quantity times little-g times height in accordance with Pascal's law. Thisvalue is symbolized rho. For 10 points, name this quantity of a fluid, equal to the mass per unit volume.

mass density

This quantity is roughly constant along a streamline when the Mach number is less than 0.3. When this quantity doesn't change within a fluid, the continuity equation in the Euler equations has only one term. Dynamic viscosity is divided by this quantity to give the kinematic viscosity. The only term in the Bernoulli equation which is not multiplied by this quantity is the pressure term. When this quantity is constant (*) throughout a fluid, the fluid is incompressible. The buoyant force on an object is proportional to this quantity times the volume the object displaces. The ratio of this quantity for any fluid to this quantity for water is called specific gravity. For 10 points, kilograms per meter cubed are the units of what quantity defined as mass over volume?

mass density <Busse>

The tennis racket theorem describes an asymmetric instability that arises when this quantity's principal components are all distinct. The diagonalization of this quantity yields three values which define the axes of Poinsot's ellipsoid. Its scalar form can be calculated as the integral of r-squared dm, and it is unchanged when the object is stretched parallel to the (*) axis of rotation. Given its value at the center of mass, it can be calculated for the same object about a parallel axis. This quantity equals torque divided by angular acceleration, as well as angular momentum divided by angular velocity. For 10 points, name this quantity symbolized I, the rotational analog of mass.

mass moment of inertia [or rotational inertia; prompt on "moment"; do not prompt on "inertia" ]

A tandem version of this technique uses collision-induced dissociation to find the sequence of a peptide. One version of this technique equalizes the kinetic energy of the analyte fragments and measures their time-of-flight to distinguish them. An ionization process like MALDI or ESI is used to prepare samples undergoing this technique, and basic versions of these devices use perpendicular electric and magnetic fields to select particles by their (*) velocity. This technique's output is a series of peaks, each of which corresponds to a fragment of the compound being analyzed. For 10 points, identify this technique, which identifies compounds in a sample by analyzing their mass-to-charge ratios.

mass spectrometry [accept mass spectroscopy]

The first verification of this principle came from the first human-controlled nucleardisintegration experiment, in which a lithium atom was split into two alpha particles, which wasperformed by Cockcroft and Walton. When converting between "rest" and "total" forms of thequantities in this principle, an additional factor of momentum times speed of light, all squared,appears. Due to this principle, particle physicists often use natural units to express particle (*) massin terms of giga-electronvolts. This principle was first stated in the 1905 Annus Mirabilis paper thatproposed special relativity. For 10 points, identify this principle proposed by Einstein and demonstrated bythe famous equation E equals m c squared.

mass-energy equivalence [or obvious equivalents, such as that mass and energy are equivalent; or E equals m c squared until it is read]

The Lorenz number, equal to 2.4 times ten to the negative eighth, appears in the empirical Wiedemann-Franz Law for these materials. A classical model of these materials proposes a constant drift velocity from a uniform field and elastic electronic collisions. Sommerfeld adapted the Drude model of these materials into his free-electron model. Cold work prevents the movement of dislocations in these materials, resulting in strain hardening. Sequences of (*) quenching, then tempering, are used to strengthen these materials. Crystal lattices model the microstructure of these materials, which have delocalized "seas" of electrons. As a result, they have high conductivity, and are ductile and malleable. For 10 points, name these materials that are mixed in alloys.

metals [prompt on conductors or crystal lattices]

The Fermi pseudopotential describes the scattering of these particles. SU(5) and SO(10) GrandUnified Theories predict a yet-unobserved oscillation between this particle and its antiparticle. Theseparticles can be generated from spallation sources. Matter-antimatter asymmetry would beexplained by a relatively large value of its electron dipole moment, which is also a measure of CPviolation. These particles were originally discovered in an experiment in which they hit a layer ofparaffin wax after being knocked out of (*) beryllium; that experiment was conducted by Chadwick.This particle consists of two down quarks and one up quark, and changing the number of these particlescreates different isotopes. For 10 points, name this neutral particle in the nucleus.

neutron

The absorption cross-section of these entities is inversely proportional to the square root of their energies in the "one over nu" region. The reproduction factor and the probability of these entities escaping resonance capture appear in the four-factor formula for their "multiplication factor." Whether these particles' energies are below 1 eV, between 1 eV and 10 keV, or above 10 keV determines whether they are "thermal," "epithermal," or (*) "fast." Graphite and heavy water-based "moderators" reduce the energies of these particles, three of which are produced when uranium reacts with one of them to form rubidium and cesium, thus causing a chain reaction. Nuclear fission reactions are induced by, for 10 points, what uncharged particles found in atomic nuclei?

neutrons <Busse>

The right part of a B-vs-A curve, which is downwards sloping, is used to find the yield of thisprocess by finding the y-differential. A naturally occurring instance of this process was discovered byFrancis Perrin at Oklo in Gabon. Lise Meitner and Otto Frisch proposed that results of Otto Hahnand Fritz Strassman were a result of this process. This process was successfully initiated by theChicago (*) Pile-1, which was constructed partially of graphite blocks, designed by Enrico Fermi and usedcadmium control rods. Leo Szilard was the first to propose a chain reaction involving this process, andberyllium is commonly used as a neutron source for this process. For 10 points, name this process in whichthe nucleus of an atom is split into smaller parts.

nuclear fission [prompt on self-sustaining nuclear chain reaction]

Some devices for carrying out this process are characterized by the rotational transform, which is the inverse of the safety factor. The efficiency of this process is expressed by the "triple product" of density, temperature, and confinement time. Modern experiments on this process include the Wendelstein 7-X and ITER, which are examples of a stellerator and (*) tokamak, respectively. The CNO cycle and the proton-proton chain are astronomical mechanisms for this process, which generally doesn't produce elements heavier than iron. The world's energy problems could be solved by achieving this process at room temperature, the so-called "cold" variety of this process. The Sun's energy is produced by, for 10 points, what process in which two nuclei merge into one nucleus?

nuclear fusion [do NOT accept or prompt on "fission"] <Busse>

Bryan and Cox conducted influential work in modeling these things. A ground-breaking experiment that studied these things was the TOPEX satellite. Walter Munk's influential circulation model for these things built on the work of Sverdrup. Transgression and regression are eustatic changes for these structures. Curtis Ebbesmeyer, who studies these structures, found that a collection of (*) garbage moves in accordance with their gyres. Fridtjof Nansen discovered that wind stress on these things creates an Ekman spiral. Density gradients in these things are driven by the thermohaline circulation. The bottom of these things is bounded by the abyssal plain. For 10 points, name these bodies of water that include the Atlantic and Pacific.

oceans [or seas; do not accept "lakes"]

The big letter in a term symbol is strictly determined by this quantity. The Laporte selection rule states that the change in this quantity for an allowed transition is plus or minus one. This quantity, times this quantity plus one, times h-bar squared, is the corresponding eigenvalue for spherical harmonic eigenfunctions. When this quantity is zero, the resulting spectral lines appear sharp. The number of angular nodes exactly equals this value. This quantity equals one for an electron whose probability distribution is shaped like a (*) dumbbell. The magnitude of the magnetic quantum number must be less than or equal to this quantity. For 10 points, name this quantum number that dictates the shape of an atomic orbital, which is often symbolized with a lowercase L.

orbital angular momentum quantum number [or azimuthal quantum number; or l until it is read; or total angular momentum quantum number or j; do not accept "spin" or "spin quantum number"] <Silverman>

A tickler coil is used with feedback to create an example of these objects named for Armstrong. An unusual nonconservative one named for van der Pol conserves energy as long as the parameter mu is greater than zero. The equation describing a general one of these systems states that the second derivative of x plus omega sub zero squared x equals zero. RLC circuits function as these systems when the square root of L over C is small. Their behavior can be described by a Q factor when they are (*) driven or damped. One class of them undergoes acceleration proportional to the displacement and is described by Hooke's law; that example is a simple mass on a spring. For 10 points, name these physical systems that periodically moves about an equilibrium point, whose simple harmonic type is exemplified by the pendulum.

oscillators [prompt on "resonator"; accept more specific answers, like simple harmonic oscillator, harmonic oscillator, nonconservative oscillator, damped oscillator, driven oscillator, etc]

Barker's equation is used to describe one phenomenon that occurs in this shape, and a rotatingfluid in a container takes on this shape. In quantum mechanics, a potential of this shape gives rise towavefunctions that are the product of a Gaussian function and a Hermite polynomial. In celestialmechanics, an object moving in this shape has velocity square root of two G M over r, and captureorbits and escape orbits have this shape. A charge moving straight when entering a uniform electric(*) field will travel in this shape. Lenses in this shape so no spherical aberration, since they focus allparallel rays at a point. For 10 points, name this shape, which is also traced out by a projectile fired into theair at an angle with no air resistance.

parabolic [or parabola or paraboloid]

The law governing this phenomenon in one regime has a coefficient equal to C divided by thequantity T minus theta, where theta accounts for the exchange interaction. Gadolinium-containingMRI contrast agents show the "super" version of this phenomenon. It is displayed by all high-spincoordination complexes. This phenomenon arises in materials with positive susceptibility. Thisphenomenon, which is described by the linear Curie-Weiss law, arises in systems with (*) unpairedelectrons and in ferromagnets above the Curie temperature. It arises when dipoles align in the samedirection as an applied field. For 10 points, name this property of some materials in which they are attractedby external magnetic fields, often contrasted with diamagnetism.

paramagnetism [or word forms, like paramagnetic or paramagnets]

One mode of motion for this system was approximated by Chirikov using the Melnikov-Arnoldintegral. The Gudermannian can be used to derive its motion near unstable equilibria. A completedescription of this system requires the use of Jacobi elliptic functions. In phase space, this system hasa separatrix at H equals g over l, within which it has closed cycles and outside of which it issinusoidal. These devices' amplitude is independent of their (*) period. The equation of motion for thissystem is often derived using the small-angle approximation, and shows that its period is proportional to thesquare root of the length of the string. For 10 points, name this simple system consisting of a weight on theend of a string.

pendulum

One quantity important in understanding this effect appears in the numerator of the exponentialof the RichardsonÂâ€"Dushman equation, and is equal to about one-half of the ionization energy of thefree atom. One can place a collecting plate next to a device undergoing this effect to find the stoppingpotential. The maximum kinetic energy of a particle undergoing this effect does not depend on theincident (*) intensity. The minimum energy needed for this effect to occur is equal to Planck's constantmultiplied by the threshold frequency, which is equal to the work function. For 10 points, identify thiseffect discovered by Heinrich Hertz and studied by Albert Einstein, in which light liberates electrons from ametal to create a current.

photoelectric effect [do NOT accept "photovoltaic effect" or other wrong answers]

This phenomenon is used by an h-over-e apparatus, such as the PASCO AP-9368, which can beused to experimentally determine Planck's constant. The probability of this effect is often given asatomic number raised to the n over h nu to the third, where n is between three and five. By exactlyoffsetting the maximum kinetic energy of this process, one can calculate the stopping potential. Thekinetic energy of particles emitted by this process is equal to Planck's constant times frequencyminus the difference in (*) energy level between the vacuum and their Fermi energy, which is the workfunction. A 1905 Annus Mirabilis paper explaining this effect won Einstein his Physics Nobel. For 10points, name this effect in which incident light frees electrons from a metal.

photoelectric effect [or photoemission]

The tendency of these particles to follow super-Poisson statistics rather than Poisson statisticsmanifests in their namesake bunching. QED predicts that all interactions between charged particlesare due to exchange of these. These particles decoupled from baryonic matter during therecombination era, and their bouncing off of the surface of last scattering created the CMB. Theseparticles are emitted when charged particles change (*) trajectory in brehmsstralung. They decrease inenergy when interacting with matter in Compton scattering, and they interfere with each other whenpassing through an aperture, which shows their dual nature. For 10 points, name this spin-1 massless gaugeboson, the carrier of the electromagnetic force and a particle of light.

photon

Six root two, times pi to the three halves, over the natural logarithm of the namesake parameter of these systems is used to calculate the Coulomb collision time. The magnetic diffusivity is used in the Reynolds number for these systems. Filaments in these systems get pinched inward due to external magnetic fields. Although these systems are (*) "quasi-neutral", redistribution of electrons in them forms an electrostatic sheath to screen out electric fields. Toroidal field lines are necessary to confine these substances stably, as in a tokamak. These extremely conductive substances can form when gas is ionized. For 10 points, name this "fourth" state of matter.

plasma [prompt on conductors]

In the original solution of a first-order equation comprised of three alpha matrices and a beta matrix, this particle's wavefunction has a positive imaginary exponential. In a famous photograph, one of these particles travels through a lead plate and loses its radius of curvature as it travels upward. Fluorodeoxyglucose is a source of these particles. Pauli and Weisskopf explained how this particle gives a (*) negative energy density in the Klein-Gordon equation. When a photon of energy greater than 1.02 MeV undergoes pair production, an electron and this particle are formed. The Dirac equation predicted this particle as a "hole" in a sea of electrons. For 10 points, name this particle symbolized e+, which is the antiparticle of the electron.

positron [or antielectron]

For a capacitor, the instantaneous form of this quantity is given by the capacitance multiplied bythe voltage and the time derivative of voltage. The average for this quantity in an AC circuitincorporates the cosine of the phase angle in its definition, which is its namesake "factor". An opticalquantity with this name is measured in diopters. For a circuit component, this quantity is equal to the(*) current through it times the voltage drop across it. By converting energy to force times distance, one canshow that this quantity is also defined as force times velocity. For 10 points, what quantity is the rate atwhich work is done and has units of Watts?

power

Alfred-Marie Liénard (lyay-NARR) derived a nastily complex relativistic formula for this quantity in electromagnetism involving the square of the cross product of beta with the time derivative of beta. The value of this quantity for an accelerating point charge is proportional to charge squared times acceleration squared according to the Larmor formula, which is derived by noting that this quantity equals the flux of the Poynting vector through a surface. The value of this quantity transmitted by a wave equals (*) intensity divided by area. This quantity can be calculated by the dot product of force and velocity, or current times voltage. For 10 points, name this quantity that represents work done per unit time, which is measured in watts.

power <Busse, Science - Physics>

This model's energy is added to the energy of the rigid rotor to model rovibrionic coupling, andusing an exponential Morse potential with this system gives more accurate results in IR spectroscopy.Taking the higher-order terms of the Taylor expansion of the potential of this system allows formodeling anharmonic effects, and this system's wavefunction contains a Hermite polynomial. Theenergy levels of this system are proportional to the (*) quantum number plus one half. Diatomicmolecules are commonly modeled using this system, whose energy levels are evenly spaced and whosepotential is a parabola given by Hooke's Law. For 10 points, name this simple quantum system that is ananalog of the classical masses connected by a spring.

quantum harmonic oscillator [or QHO; accept quantum harmonic oscillator after "quantum" is read]

A negative form of this phenomenon may occur when the Poynting vector dot the wavevector isnegative. One quantity important in describing this phenomenon is squared in both the numeratorand denominator of one side of the Lorentz-Lorenz equation. Ordinary and extraordinary rays areobserved in anisotropic materials like calcite, in which the (*) "double" form of this phenomenonoccurs. One law used to describe this phenomenon is derived using Fermat's principle of least time. Thesines of the angles at which this phenomenon occurs are related by Snell's law to values of its namesakeindex, defined as speed of light in a vacuum divided by speed of light in a medium. For 10 points, namethis phenomenon in which passing between two media causes a wave to bend.

refraction [accept birefringence due to ambiguities]

In solid-state physics, a dimensionally-equivalent "sheet" version of this quantity is oftenreported as its value "per square". Its quantum is equal to h over e squared, and the Drude modelgives this extensive quantity as inversely proportional to the product of carrier number density andmobility. A complex version of this quantity includes a term equal to frequency times inductance.The power dissipated in a circuit equals (*) current squared times this value. Voltmeters work byapplying a very large value for this quantity in parallel. Devices that provide this quantity are marked witha series of colored bands and symbolized with a zig-zag line. For 10 points, name this quantity set equal tovoltage over current in a law named for Ohm, who also names its SI unit.

resistance

Measuring this value for a semiconductor is done with a four-point probe and allows one to determine the concentration of impurities. A device first fabricated at HP Labs using a thin film of titanium dioxide has a value for this quantity that depends on the history of current in the device. After the turn-on voltage, an ideal diode has a value of zero for this quantity. An unknown value of this quantity can be found by setting up a diamond shape and adjusting until there's no voltage drop across the bridge, a method popularized by Charles (*) Wheatstone. This quantity is the real part of impedance. For a wire this quantity equals rho times length over cross-sectional area, where rho is the inverse of the conductivity. This quantity adds when its namesake circuit elements are placed in series. For 10 points, what quantity is equal to voltage divided by current, by Ohm's law?

resistance [or R; or resistivity or rho until "impedance" is read]

Unlike the XOR gate, the quantum computing CNOT gate has this property, and computers withthis property may surpass the Landauer limit. This kind of process must be quasi-static. The factthat chemical reactions display this property microscopically leads to the principle of detailedbalance. For this type of process, the integral of d-Q over T is zero, which is the equality case ofClausius' theorem. A system is in thermodynamic (*) equilibrium throughout processes of this kind,which generate no entropy. A process of this kind produces the maximum amount of work of all processesbetween two given states. The Carnot cycle is a classic example a process with this property. For 10 points,name this kind of thermodynamic process which can be run backwards.

reversible [prompt on "ideal"; accept time-reversible, time-invertible; accept isentropic before "entropy"]

Spectroscopy based on this process can only measure transitions for which delta J equals plus orminus one. Lorentz transformations among spacetime coordinates correspond to processes of thistype. The matrix describing this process has diagonal cosine terms and antisymmetric off-diagonalsine terms. A black hole undergoing this process has a ring-shaped singularity, is surrounded by anoblate ergosphere, and is described by the Kerr metric. Symmetry under this process leads toconservation of (*) angular momentum by Noether's theorem. Its rate is commonly given in radians persecond, the units of angular velocity. For 10 points, name this process of movement by some angle arounda central point.

rotation

One technique that uses this process can indirectly observe the products of quark confinement. The maximum energy transferred by another type of this process is marked by a sharp decrease, or edge, on a spectrograph. The unit "barns" describes the probability of this process occurring, termed cross section, while the Klein-Nishina formula predicts the resulting angular distribution. Whether there is a positive or negative change in energy differentiates the (*) Stokes and anti-Stokes forms of its inelastic Raman type. One form of this process requires particles' sizes to be much smaller than the wavelength and preferentially affects blue light in the sky. For 10 points, name this process in which two objects collide and exchange energy, whose types include Compton and Rayleigh.

scattering [accept deep inelastic scattering, Rutherford scattering, Compton scattering, Raman scattering, or Rayleigh scattering] <Wang>

The Einstein relation's most important application is in these materials because it sets the ratio of diffusivity and mobility equal to k T over q. Wafers of one type of this material are grown with the Czochralski process. III-V ("three five") and II-VI ("two-six") alloys are used to form the binary, ternary, and quaternary "compound" types of this material. Analyzing these materials often involves determining the rate and type of carrier generation and (*) recombination processes. These materials are useful because substitutional impurities can change their Fermi level in a process called doping, which can create its n-type and p- type. The most commonly used example of this material is silicon. For 10 points, name these materials that have a conductivity intermediate between that of conductors and insulators.

semiconductors

One property of these systems can be quantified by the logarithmic decrement. In phase space, these systems trace out an ellipse in a clockwise fashion. Any system can be modeled as one of these systems by Taylor-expanding the potential energy about a minimum and truncating the result at the second term. When these systems lose energy in a "critical" fashion, their (*) Q-factor equals one-half. External forces can "drive" these systems, which can be "damped" when they lose energy over time. A restoring force proportional to minus the displacement describes these systems, according to Hooke's law. For 10 points, sinusoidal motion is characteristic of what systems exemplified by springs and pendulums?

simple harmonic oscillators [or SHO; prompt on oscillators or springs or pendulums]

Deflection of starlight was observed by William Wallace Campbell while he was observing one of these events at the Lick Observatory. Walter Grotrian and Bengt Edlen found that the green emission line found as a result of these events was not actually a new element, but was instead highly ionized iron. Arthur Eddington experimentally confirmed Einstein's theory of general relativity using one of these events in 1919. While working in Madras, Pierre (*) Hansen used one of these events to discover the element Helium. The "annular" type of this event occurs when a disk surrounds the occuluding body. For 10 points, name these events during which the corona becomes visible because the moon is in front of the sun.

solar eclipse [prompt on eclipses until "sun" is read and accept it afterwards]

William Huggins observed one of these entities while studying the Cat's Eye Nebula, which led him to propose the element "nebulium." The electronic transition of molecular hydrogen in quasars gives rise to a collection of these objects termed the Lyman Alpha Forest. Equal and opposite shifts of these phenomena due to Doppler (*) broadening is used to detect a certain class of binary stars. For the hydrogen atom, two of the "series" consisting of these things are named for Balmer and Paschen. For a blackbody, none of the "emission" type of these are present, but all "absorption" ones are present. For 10 points, name these "lines" that indicate what wavelengths a body emits or absorbs.

spectral line [accept emission line or absorption line before read] <Jose>

Nitroso or nitrone compounds "trap" this quantity by forming an adduct measured in EPRspectroscopy. This quantity is high for octahedral complexes with low splitting energy. Coupling of thisquantity makes doublets and triplets with peak ratios given by Pascal's triangle. This quantity allowsmolecular orbitals to be antisymmetric. In NMR, a magnetic field (*) "flips" this quantity. Hund's rule ofmaximum multiplicity says that atoms maximize the total amount of this quantity. A single-barbed arrow representsthis vector quantity in configuration diagrams. Two electrons in the same orbital must have the opposite value forthis quantity by the Pauli exclusion principle. For 10 points, name this measure of intrinsic angular momentum.

spin [do not accept or prompt on "angular momentum"]

This quantity's tensor and its trace are multiplied by the two Lamé parameters in a 3Dgeneralization of a certain law. An axis on which this quantity is plotted is the starting point of a lineoffset by 0.2% from the origin that is used to find the offset yield point. The ratio of two types of thisquantity is negative in materials that tend to form domed-shapes when put into flexure, instead of asaddle-shape. That value is the ratio of the (*) transverse to longitudinal forms of this quantity, which isPoisson's ratio. The axial form of this quantity is the change in length per unit length. For 10 points, whatquantity divides stress in Young's modulus?

strain

One phenomenon in these materials is explained by a non-zero effective photon mass within them,and one type loses its properties at an upper critical field. One model of them gives free energy interms of an order parameter. Another theory of them reproduces the isotope effect and gives therelationship between the energy gap and temperature. In that model, phonons mediate thecombination of electrons into (*) Cooper pairs. These materials expel magnetic fields in the Meissnereffect, and are divided into Type I and Type II varieties depending on the temperature of their phasetransition. Their uses include maglev trains and lossless power transmission. For 10 points, name thesematerials described by BCS theory, which have zero electrical resistance.

superconductors [or word forms like superconductivity; accept Type I superconductivity, Type II superconductivity, or high-temperature superconductivity throughout]

The Koide formula gave a theoretical estimate for the mass of a particle symbolized by this letter. A particle symbolized by this letter decays into two pi-plus and a pi-minus, giving negative parity, unlike the theta particle, which has decay with positive parity. A particle symbolized by this letter has energy of 1777 MeV and will decay into a hadron because of its enormous mass. The third (*) generation of leptons is named for this letter, which names a much heavier counterpart to the muon and electron. A quantity symbolized by this letter is the inverse of the decay constant and is a measure of the mean lifetime of a particle. For 10 points, name this Greek letter which is also used to symbolized proper time and torque.

tau

This quantity is the only intensive variable that the canonical ensemble is dependent on. This quantity is the independent variable in TGM analysis. The change in entropy is equal to the integrand of the infinitesimal change in heat divided by this quantity, according to the Clausius inequality. The second virial coefficient equals zero at a particular value for this quantity named for (*) Boyle. Helmholtz free energy equals internal energy minus entropy times this quantity, and it is the conjugate variable of entropy. The average kinetic energy for gas molecules is proportional to this quantity. For 10 points, identify this quantity plotted on the x-axis of phase diagrams, against pressure.

temperature [or T; do not accept or prompt on "heat"] <Prieto, Science - Chemistry>

This quantity is represented as the ratio between the linewidths of arrows on Sankey diagrams. The coefficient of performance is approximately the inverse of this quantity. According to the Shockley- Quiesser limit, a bandgap of 1.4 eV corresponds to a maximum of this quantity for a p-n junction in solar cells. This quantity increases slowly as the compression ratio increases, since it is a function only of that ratio and the adiabatic index for many processes. This quantity will be (*) maximized if the hot and cold reservoirs have infinite and zero temperature respectively, and in a Carnot engine, it equals one minus the ratio of those temperatures. For 10 points, name this quantity symbolized eta, which equals the ratio of net work output over heat input, which would ideally be 100% for a thermodynamic cycle.

thermodynamic efficiency [or eta until it is read]

This system is modeled by the Agekyan-Anosova map, which has a strange attractor at x equalspoint five and y equals zero. Jacobi's integral gives a conserved quantity for this system. Thisproblem can be solved by a slowly-converging series in powers of t to the one-third; that result wasby Sundman. The H two plus ion is a quantum version of this problem, which is often solved usingfirst-order perturbation theory. One restricted version of this problem displays five equilibriumpoints named for (*) Lagrange. This non-integrable problem is approximated by assuming one mass ismuch smaller than the others. For 10 points, name this problem about the motion of the requisite number ofmassive objects under gravity, most often applied to the Earth, Moon, and Sun.

three-body problem [accept n-body problem]

Scleronomic constraints do not explicitly depend on this quantity. An arbitrary function's overall change with respect to this quantity equals the function's Poisson bracket with the Hamiltonian plus its explicit change with respect to this quantity. It's not the action, but this quantity is minimized for a particle under the influence of gravity traveling on the surface of a cycloid. The product of resistance and capacitance for an (*) RC circuit equals a quantity denoted by tau, a "constant" named for this quantity which characterizes the circuit. For a system doing work at constant power, power times this quantity equals work. Acceleration equals the derivative of velocity with respect to this quantity. For 10 points, name this quantity whose SI unit is the second.

time [accept "time constant" before its mentioned] <Busse>

For a gauge transformation of the scalar potential, this operation on the gauge function multiplied by negative one over c is added to the old scalar potential. Hamilton's equations set this operation on the generalized coordinates equal to a function of the Hamiltonian. This operation is symbolized by putting a single dot over a function. The curl of the electric field is equal to the negative of this operation of the magnetic field according to Faraday's Law. Taking this operation on momentum gives (*) force. This operation takes velocity to acceleration and position to velocity. For 10 points, name this operation which finds the instantaneous rate of change of a physical quantity.

time derivative [or d/dt (dee-dee-tee); do NOT accept "d/dx" or any letter but "t"]

4. A method developed to solve this equation iterates until the calculated fields are self-consistent. Linear combinations of Gaussians or Laguerre polynomials are used in the radial term for solutions to this equation. Solutions to this equation are eigenfunctions of the operator: "negative h bar squared, over two m, times del squared, plus the potential" and are characterized by three integers symbolized n, l and (*) ml (m sub l). The Born-Oppenheimer approximation is typically made to solve this equation. This equation cannot be exactly solved for complicated atoms, but for hydrogen, its exact solutions include s and p orbitals. For 10 points, what fundamental equation of quantum chemistry used to compute wavefunctions is often written "H psi equals E psi"?

time-independent Schrödinger equation [prompt on wave equation] <Silverman, Science - Physics>

The hybrid pi and T models describe these objects when they receive small signals. Pinch-off in these devices is quantified by a channel-length modulation parameter symbolized lambda and a transconductance symbolized g. An old type of these devices is diagrammed using a circle intersected by three pins labelled C, B, and E. These devices' characteristic curves converge to a steady-state value on an Iâ€"V diagram that is separated into an active region, a cutoff region, and a (*) saturation region. One type of these objects is named because it has two sets of junctions separating the base, collector, and emitter; however, nowadays, the most common type of them are MOSFETs. For 10 points, name these electronic devices that can either amplify currents or act as switches.

transistors [or bipolar junction transistors; or BJTs; or field effect transistors; or FETs; or MOSFETs or metal-oxide-semiconductor field effect transistor until it is read] <Silverman>

The software package COMSOL uses models such as yPlus and k-omega to describe this phenomenon. Momentum and heat transfer effects caused by this phenomenon can be modeled by the "mixing length" model developed by Ludwig Prandtl. Blasius theory does not apply in this type of boundary layer, in which the coefficient of skin friction is large and boundary layer separation caused by adverse (*) pressure gradients becomes delayed. Energy cascades caused by this phenomenon break up large eddies and vortexes into small ones. At Reynolds numbers above 3000, this type of flow occurs, resulting in irregular and chaotic fluctuations in the fluid velocity. Laminar flow is contrasted with, for 10 points, what type of flow which can cause airplane passengers to have a bumpy ride?

turbulence or turbulent flow <Busse>

This quantity divided by lambda yields k, the wavenumber. For a wire-wrapped toroid, themagnetic field is inversely proportional to this factor times the radius of the toroid according toAmpère's law, which also gives the magnetic field of an infinite wire as inversely proportional to thisfactor times radial distance. This entire quantity, all squared, over big G times stellar mass is equalto the square of the planetary orbital period over the cube the semimajor axis of its orbit accordingto Kepler's third law. Twice this value appears multiplied by the permittivity of free space in thedenominator of (*) Coulomb's law. For small angles, the period of a pendulum is equal to this quantitytimes the square root of length over gravitational acceleration. Frequency multiplied by this quantity givesangular frequency. For 10 points, identify this value that is the period of the sine and cosine functions.

two pi

These functions can be defined by considering a scalar function equal to a ket on a Hilbert space. The Born-Oppenheimer approximation decomposes this value as a product of an electronic and a nuclear one. The square of the magnitude of this value gives the probability density function for a given state. Fermions have antisymmetric ones and bosons have symmetric ones. These values are eigenfunctions of the (*) Hamiltonian, meaning that they are solutions to the Schroedinger equation. Each atomic orbital in the hydrogen atom corresponds to one of these, which collapses under measurement. For 10 points, name this value symbolized psi, which encodes the current state of a quantum mechanical system.

wavefunction [or psi before mention]

In Dirac notation, one of these entities evaluated at a point r is equal to "bra-r-times-ket" of that entity. Whether these entities are symmetric or antisymmetric under exchange is the subject of the spin-statistics theorem. When they are time-invariant, these quantities are equal to their complex conjugate. Applying the Hamiltonian operator to these quantities returns them (*) multiplied by a constant representing energy. According to the Copenhagen interpretation, the square of these quantities is the probability density per unit volume, and they can be found by solving the Schrodinger equation. For 10 points, name these quantum mechanical functions which bear the Greek letter psi.

wavefunctions [prompt on psi before mentioned] <Wang> Bonuses

This interaction has both vector and axial vector components, which behave oppositely underimproper Lorentz transformations. By measuring the disparity in distribution between gamma rayand electron emissions in the decay of cobalt-60 to nickel-60, Chien-Shiung Wu experimentallyshowed that this interaction violates parity conservation. The mass of this interaction's gauge bosonsis provided by the Higgs boson upon the symmetry breaking of this interaction's unification with (*)electromagnetism. The W and Z bosons are the force carriers for this interaction, which mediates betadecay. For 10 points, name this fundamental force that occurs at almost the same length scale as Ââ€" butwhose coupling constant is much smaller than Ââ€" the strong force.

weak force

Holonomic constraints take a function of the position variables and the time and set it equal to this number. In special relativity, the center-of-mass frame has the property that the total momentum takes this value. The Lagrangian takes this value when the potential and kinetic energies are equal. For a reversible process, the integral of dQ-over-T equals this value, which is also the internal (*) resistance of an ideal ammeter. The statement that if two bodies are in thermal equilibrium with a third, then they're all in equilibrium, is given this number. Gauss's law can be used to show that the electric field inside a conductor takes on this value. For 10 points, name this value, which also names a temperature at which all thermal motion stops.

zero <Mukherjee>

The ratio of proportionality constants for two different processes with this name are connected bythe Lorenz number according to the Wiedemann-Franz law. In lumped system analyses of thetransient form of this process, a number proportional to the internal resistance to this process, theBiot number, is used. If there is no internal energy conversion, the steady-state form of this process isdescribed by Laplace's equation. The flux due to this process is equal to minus a proportionalityconstant - often abbreviated k - times the gradient of (*) temperature according to Fourier's law. For 10points, name this mode of heat transfer that occurs by microscopic means - without macroscopic motion ofa material - as opposed to convection and radiation.

thermal conduction [or word forms; prompt on heat transfer; prompt on heat transport]

Spin-aligned electrons tunnel into the "free layer" in a form of magnetoresistive RAM named for thisquantity. In a noninertial reference frame, this quantity equals a time derivative in the body frame, plusomega-cross-L in the noninertial frame. The product of current, magnetic field, and the area of the loop ofwire gives this quantity, if the field is oriented perpendicular to the loop. Precession is either (*) "induced"or "free" of this quantity. The sum of this quantity for the system equals moment of inertia times angularacceleration. For a pulley, this quantity equals the tension in the rope times the radius of the disk. For 10 points,name this quantity that equals force cross distance, and which causes rotational motion if it's nonzero.

torque [or tau; or T]

The polar moment of inertia is defined using a ratio of this quantity to the maximum shear stress on a beam. Henry Cavendish calculated big G using a device whose governing equation is that this quantity equals "negative kappa theta." This quantity is nonzero in a couple. For a wire loop placed in a field, this quantity equals the field strength times the dipole moment times the sine of the angle between them. The rate at which a top (*) precesses equals this quantity divided by the top's angular momentum. The net value for this quantity equals the angular acceleration times the moment of inertia, and is calculated by summing the cross product of each force and its distance to the axis. For 10 points, name this quantity that causes objects to rotate.

torque [or tau; or moment of force; prompt on moment] <Silverman>

Alexander Kashlinsky used the term "dark flow" to describe an unexplained for of this quantity in galaxy clusters. The statistical dispersion of this quantity for an elliptical galaxy is related to its luminosity by the Faber-Jackson relation. This quantity's value relative to a rest frame is called the "peculiar type of it, and it is not explained by (*) Hubble's Law. The change in this quantity is related to the logarithm of the initial mass divided by the final mass by the rocket equation. By setting the kinetic energy equal tot he potential energy, one can derive the minimum value for this quantity for an object to escape from a body's gravitational field. For 10 points, name this quantity, the time derivative of position.

velocity [or motion; or speed]

Two versions of this quantity are equal if the dispersion relation is linear. Adding two examples ofthis quantity and dividing by one plus the product of normalized forms of this quantity is thisquantity's namesake "addition formula." The hyperbolic arctangent of this quantity divided by aconstant is additive in special relativity and is symbolized phi. One version of this quantity is given bythe angular frequency divided by the wavenumber. The curl of the vector field of this quantity for afluid gives the (*) vorticity. The dot product of this quantity with the force gives the power, and thederivative of this quantity is the acceleration. For 10 points, give this vector quantity which measures thechange in position per unit time.

velocity [prompt on "v", prompt on "speed"]

In one type of system involving two of these objects, r theta double dot plus 2 r dot theta dot plus g sine theta equals 0. Systems involving multiple of these objects can be described as “rove to advantage†or “rove to disadvantage,†and the “Z-drag†is a specific system involving two of these devices. In Weston’s “differential†type of these devices, 2 over the quantity 1 minus little r over big R is the (*) mechanical advantage. In a system involving this device, acceleration equals m sub 1 minus m sub 2 all over m sub 1 plus m sub two, all multiplied by little g. The mechanical advantage of one of these devices is equal to the number of ropes supporting the load, and the block and tackle, and Atwood’s machine uses these devices. For 10 points, name these simple machines that consist of a wheel supporting movement of a taut rope.

pulleys (anti-prompt on more specific answers such as “Atwood’s machine,†“block and tackle,†etc. before mention with “Can you be less specific?â€) <Hao>

In a pioneering treatise, Robert Grosseteste surmised that these phenomena are caused by "God's first form" interacting with convex, and not concave shapes. A type of these objects formed by fog is often called Ulloa's Ring. They appear superficially similar to circumzenithal arcs, which are caused by ice crystals. Thomas Young used the wave nature of light to explain (*) "supernumerary" types of these things, which can be modeled with Mie scattering. These things often consist of "full circles," though most observers are only posed to see them when the sun's angular elevation is less than 42 degrees. For 10 points, water droplets refracting white light produce what meteorological phenomena, which consist of the spectrum of colors?

rainbows [accept fogbows]

A nine-year survey of this phenomenon conducted by the Center for Astrophysics led to thediscovery of the Great Wall supercluster. One quantity with this name is equal to GM over c squaredtimes R in the gravitational case, and is roughly equal to relativistic beta for low velocities. Thatquantity, symbolized z, has been measured at values as high as (*) 9.4 for gamma ray bursts and 7.1 forquasars. The expansion of the universe means that this effect is universally observed in cosmologicalradiation, because it arises from the Doppler effect for an emitter moving away from an observer. For 10points, name this increase in radiation wavelength, named for a long-wavelength color.

redshift [prompt on Doppler shift or effect before mention]

The coefficient for this process in a transmission line is equal to the standing wave ratio, gamma,minus one over quantity gamma plus one. Thin films designed to avoid this process typically have anindex of refraction equal to the square root of the surface's and a quarter-wavelength thickness. Thedistinction between a "rough" and "smooth" surface separates its (*) "diffuse" and "specular" types. Ifan unpolarized wave undergoes this process at Brewster's angle, it becomes linearly polarized. If thisprocess occurs from a low-n to high-n medium, the light has a phase change of 180 degrees. The law of thisprocess states that only direction is changed, so its angle is equal to the angle of incidence. For 10 points,name this process for which one typically uses a mirror.

reflection [do not accept "refraction"]

A process which possesses this property on the micro-scale can be described by the Crooks fluctuation theorem. One paradox states that a process lacking this property shouldn't be derivable from T-symmetric physics. Detailed balance describes an equilibrium caused by this type of process, which must be quasi-static, such as the continuous and infinitesimal removal of weight from the top of a piston. In this type of process, the line integral of dQ over (*) T equals zero, according to Clausius' theorem. The amount of work done is maximized by a thermodynamic process with this property. Processes which lack this property must produce entropy. For 10 points, name this type of process, which can be run forward and backward without changing the system.

reversible process or reversibility <Busse>

In deriving the equation named for these objects, the second order term consisting of "dm times dv" is usually neglected, since it is the product of two differentials. Gustav de Laval designed an hourglass-shaped tube that is used to improve the efficiency of them. An equation which states the change in velocity of these objects is proportional to the logarithm of the initial mass over the final mass is (*) named for Konstantin Tsiolkovsky. A coaxial pintle injector is sometimes used in these devices to accelerate the combustion of gases when they use liquid fuel. Two boosters of this kind of engine are attached to an orbiter in a space shuttle. For 10 points, name these engines that achieve thrust by expelling fuel, and which may consist of different "stages."

rockets [accept rocket engines] <Jose>

The unitarity of the universe's transition matrix implies this law because this law is a property ofdoubly stochastic Markov chains. This law is apparently in conflict with the Poincare recurrencetheorem. One consequence of this law is that the Onsager matrix is positive semi-definite, and thislaw's apparent violation of T-symmetry can be resolved using (*) Boltzmann's H-theorem. One versionof this law states that the line integral of dQ over T over a closed path is equal to or less than zero; thatstatement is Clausius' inequality. This statement limits the efficiency of the Carnot cycle and is apparentlyviolated by Maxwell's demon. For 10 points, name this statement that says in a closed system the entropymust always increase.

second law of thermodynamics [accept Clausius inequality before mention]

Like pressure, this quantity is plotted on the y-axis of Fletcher-Munson contours after scaling via A- weighting. The net value for this quantity is zero in a diffuse field but is maximized in the active field. This quantity is proportional to both frequency squared and maximum displacement squared, or alternatively, it equals one-half the pressure squared over a non-electrical quantity called impedance. This quantity equals the product of particle velocity and pressure. It drops off with one over radius squared since it equals power over the (*) surface area of an imaginary sphere. The level of this quantity equals ten times the logarithm of it divided by one picowatt per square meterÂâ€"a reference value also known as the threshold of hearing. For 10 points, name this quantity often measured in decibels.

sound intensity [or acoustic intensity; or I; prompt on loudness or volume]

Using a Lucite or Kundt tube, this quantity can be determined experimentally by examining thesequence of Lissajous curves as the measuring apparatus is moved. The Prandtl-Glauerttransformation breaks down at this value as it predicts an object at it would experience infinitepressure. It's often derived as the square root of the adiabatic constant times gas constant timesKelvin temperature over molecular weight, which is why it is commonly approximated for theatmosphere as (*) 331.45 plus 0.61 times Celsius temperature. Often determined in physics labs with aresonance tube or tuning fork, the shock waves formed when this quantity is exceeded give rise to a sonicboom. For 10 points, name this quantity equal to Mach 1, the speed at which acoustic waves travel in agiven medium.

speed of sound

The ratio of this value caused by grain collisions to that caused by a surrounding viscous fluid isthe Bagnold number. Fields of this quantity are created by adding a dislocation to a crystal. Thisquantity's second deviatoric invariant is the subject of von Mises' criterion. Conservation of angularmomentum dictates that the tensor form of this quantity is symmetric, and the terms of that matrixare restricted by Mohr's circles. Bingham plastics begin flowing after a cutoff value of this quantity.The off-diagonal elements of the (*) Cauchy tensor for this quantity are called shear. This quantity isplotted against strain in order to find Young's modulus. For 10 points, name this quantity, a force on acontinuous material that causes deformation.

stress

A group of 8 three-by-three matrices named for Gell-Mann are used to model this interaction. One property of this interaction can be derived by noting that n sub f in the beta function for this interaction is less than 16. That property was discovered by Gross, Wilczek, and Politzer. String-like flux tubes may occur between two particles that mediate this interaction. In the equation for a screened Coulomb potential describing one version of this interaction, the product of radius and (*) pion mass occur in the exponent. That potential was originally formulated by Yukawa for the residual form of this interaction. A gauge theory with symmetry group SU(3) that describes this interaction has the properties of asymptotic freedom and color confinement. Gluons are the gauge bosons of this interaction, and their color charge is described by quantum chromodynamics. For 10 points, name this force, which is much more powerful than the weak force at short distances.

strong nuclear force/interaction <Hao> BONUSES

In a plane-parallel diode, the current density varies as this power of the anode voltage accordingto the Child-Langmuir law. In the Sackur-Tetrode equation, this number appears in the exponentabove the internal energy. A spherical polytropic fluid of this index is used to derive theChandrasekar limit. This is the maximum spin of a delta baryon. For a body in a circular orbit, theperiod is proportional to this power of the (*) radius. In an ideal gas, this value times Boltzmannconstant times temperature, gives the average kinetic energy per particle. The volume varies as this powerof the surface area. For 10 points, give this value, which when multiplied by pi radians gives thesecond-smallest positive zero of the cosine function.

3/2 [or 1.5]

This scientist names a type of idealized object derived by solving the Helmholtz equation under the paraxial approximation. One over 4 pi times the vacuum permittivity equals 1 in the system of non-SI units named for this scientist, which are based off of CGS rather than MKS units. This scientist names a statement used to prove the shell theorem in electrostatics. This scientist names an imaginary (*) surface whose normal vector is parallel to a vector field, allowing for calculation of flux without performing an integral. Magnetic monopoles are forbidden by one of his laws, while his other law equates the electric flux to the enclosed charge divided by the vacuum permittivity. For 10 points, name this German mathematician who names the normal distribution.

Carl Friedrich Gauss <Busse>

The inverse of the Villari effect, in which magnetization causes a ferromagnetic material to change in length, is called this scientist's magnetostriction. This physicist is the first namesake of a coefficient that is anomalously negative for hydrogen gas at room temperature, equal to the derivative of pressure with respect to temperature at constant enthalpy, and symbolized mu. His "first law" gives the heat radiated from a resistor as proportional to the current squared. This scientist attached a falling weight to a series of (*) spinning plates suspended in water, heating up the water, in an experiment that proved conservation of energy. His namesake unit equals a volt times a Coulomb, or a Watt times a second. For 10 points, name this Englishman whose SI unit measures energy.

James Prescott Joule

This man names a type of matter in which ions with circular orbits are suspected in a delocalizedsea of electrons. This man names highly excited, approximately hydrogenic electronic states. He is thefirst namesake of a principle which says that some spectral lines are the sum or difference of others.His constant is equal to one-half of the hartree energy, or about 13.6 electronvolts. One of hisnamesake equations, which can be used to predict the (*) Lyman and Balmer series, sets reciprocalwavelength equal to his constant times the difference in inverse squares of initial and final principalquantum numbers. For 10 points, name this man who developed that equation to validate the Bohr model ofthe atom and explain electronic transitions in hydrogen.

Johannes Rydberg

These interactions are responsible for the sixth power term in the Lennard-Jones potential, andusing a multipole expansion followed by the Unsold approximation allows the introduction ofionization potentials to explain it. The strength of these interactions is proportional to the product ofthe polarizability volumes, and these interactions are the reason that heavier halogens are liquids andsolids and lighter ones are (*) gases. The strength of these interactions increases with the size of the atomsinvolved because larger electron clouds can form dipoles more easily. For 10 points, name this weakintermolecular force, a subset of van Der Waals forces between instantaneous dipoles.

London dispersion forces [accept van Der Waals forces until "liquids", prompt after]

15. This physicist is the first namesake of a method of selecting allowed states by requiring the line integral of position with respect to momentum to be an integer multiple of Planck's constant. A fundamental quantity named for this physicist equals the charge of the electron times h-bar divided by twice the mass of the electron. He debated Einstein at the Fifth Solvay Conference, and co-names an early quantization rule with (*) Arnold Sommerfeld. The magnetic moment of the electron can be written in terms of his namesake magneton. He developed a model which accounted for the spectral lines of hydrogen but was unable to describe multi-electron atoms. For 10 points, name this Danish physicist who proposed that electrons orbit the nucleus in circular paths.

Niels Bohr [or Niels Henrik David Bohr] <Rosenberg, Science - Physics>

Due to material defects, this phenomenon gives the overall lower bound on losses in propagation in optical fibers. The original derivation of this effect failed to predict the Arago point and two other neutral points of zero polarization. The intensity of this phenomenon is proportional to wavenumber to the fourth power and varies inversely with the (*) sixth power of radius. Its cross-section is proportional to the sine- squared of the angle, which creates a polarization pattern that varies with azimuth. This effect, which occurs only if the wavelength is much larger than the particle diameter, does not impact the energy of the incident photon, unlike Raman scattering. For 10 points, name this form of elastic scattering which explains why the sky is blue.

Rayleigh scattering [prompt on Mie scattering]

7. In the Landau theory of phase transitions, this technique is used to express the free energy as a function of the order parameter. The compressibility factor of a real gas can be expressed in terms of the molar volume by using this technique to create the virial equation of state. Any potential well can be approximated as that of a harmonic oscillator by performing this technique on the potential energy. The (*) small angle approximation arises by performing this technique on the sine and cosine functions, then dropping all terms of order higher than "x squared." For 10 points, name this technique from calculus, in which a function is approximated using a polynomial defined by an infinite series.

Taylor series expansion [or Taylor expansion; accept power series expansion] <Busse, Science - Physics>

A simple inverter consists of one of these components with a DC input in one part. The parameters of one of these devices are determined using the open-circuit and short-circuit tests. These devices' energy losses are sub-divided into copper losses and iron losses. The root-mean-square output of these devices equals approximately 4.44 times the frequency times area times magnetic field times N. An example of the resonant kind of these devices is the (*) Tesla coil. The equation governing these components sets the ratio of the number of turns in the two coils equal to the ratio of the voltages in the winding. For 10 points, name these alternating circuit components containing a pair of inductively-coupled coils that steps down or steps up an input voltage.

transformer

Baker clamps are circuits that can reduce the storage time in one type of these devices, while the creation of a low-impedance path may cause latchup in another type of these devices. High current densities may cause the Kirk effect in these devices, and a variation in width of the bases of these devices causes the Early effect. The Gummel-Poon model for these devices can reduce to the simple Ebers-Moll model. Gold foil was put over the vertex of a triangle in the earliest example of these devices called (*) point-contact. These devices may operate in active, cutoff, or saturation modes, and one type of them can be classified as PNP or NPN types. The base, collector, and emitter comprise the bipolar junction type of these devices, which have been replaced with the MOSFET type. The number of these devices on a computer chip doubles about every 2 years by Moore’s Law. For 10 points, name these devices that can be used as amplifiers or switches.

transistors <Hao>

The relative energy shift in the Kundig experiment is proportional to this quantity squared for theabsorber. This quantity was sinusoidally varied by a loudspeaker for the radiation source in the PoundRebka experiment. For a galaxy, the total value for this quantity equals its "peculiar" form plus H-nought times distance. This quantity multiplies the cosine of the angle between the emitter and receiver in a (*) transverse effect predicted by special relativity. The change in frequency equals the emitted frequency times a ratio of this quantity. If the radial form of this quantity is increasing, then a redshift is seen. For 10 points, name this quantity which causes a Doppler shift if it's different for the source and emitter, and equals the product of wavelength and frequency of a wave.

wave velocity [or source velocity; or radial velocity; or speed]

A bar being dragged down a metal rail by a constant external force may have an exponential decreasein its velocity because of this law. This equation explains how skin and proximity effects create eddies thatheat up metals. A commutator and a rotating solenoid are used to generate power in a commonapplication of this equation. This law gives the magnitude of the step-up or step-down in voltage from a(*) transformer. This law has a minus sign as a consequence of Lenz's law. It sets the electromotive force equal tothe negative time derivative of the B flux through a current loop. For 10 points, name this equation giving theinduced voltage from a change in magnetic field, the only one of Maxwell's equations named for an Englishscientist.

Faraday's law of induction

One law named for this man states that mass equals Q over F times molar mass over valency.Optical isolators are based on an effect named for this man governed by a law in which the pathlength and flux density are related to the angle of rotation by the Verdet constant. He stated that themass of substance transformed at an electrode is proportional to the applied charge in one of his twolaws of electrolysis. Another law named for him subsumes (*) Lenz's law due to the presence of aminus sign, and states that the voltage is equal to the time derivative of the magnetic flux. That law is usedto find the EMF around a loop of current-carrying wire. For 10 points, name this English physicist andnamesake of a law of electromagnetic induction.

Michael Faraday

In a fluid at rest, this principle requires that the components on the diagonal of the stress tensorbe equal. This principle is often proven geometrically for a static fluid at rest by considering atriangular prism, or wedge. Due to this principle, the ratio of two forces must equal the ratio of thearea over which they are applied in a hydraulic pump. It was apocryphally demonstrated by pouringwater into a ten meter high tube attached to a barrel already filled with water, causing the barrel topromptly (*) explode. This principle is often stated mathematically as fluid density times acceleration dueto gravity times difference in height equals difference in pressure. For 10 points, name this law which statesthat the pressure exerted anywhere in a fluid is evenly distributed throughout and is named for Frenchman.

Pascal's law [or Pascal's principle; or the isotropy of pressure]

To simplify the notation of this scientist's namesake equation, one uses a set of four four-by-fourgamma matrices. This scientist introduced the bra and ket notation in quantum mechanics. He is thesecond namesake of a distribution function equal to one over the quantity positive one plus someconstant times the exponential of energy over k T. A function that exists only where its input is zero,has infinite height, and has an integral one is his (*) "delta". His namesake equation is a relativistic waveequation describing spin-one-half particles, as does that distribution of which he is the second namesake.That distribution's first namesake also names spin-one-half particles: Enrico Fermi. For 10 points, namethis person whose namesake equation predicted the existence of antimatter.

Paul Dirac

15. A pair of dual juxtaposed objectives characterizes a super-resolved microscope named for this number. When expressed in Gaussian cgs units, the right-hand sides of Gauss's law and Ampere's law are both multiplied by this number. A special function denoted "Y-zero-zero" simply equals one over the square root of this number. When integrating a spherically symmetric function in spherical coordinates, the angular part comes out to this number, which is the number of (*) steradians subtended by a sphere. The Coulomb's law constant equals one over this number times the permittivity of free space. This number equals two times the factor used to convert Planck's constant to its reduced form. For 10 points, give this number of radians corresponding to two revolutions about the unit circle.

4 pi <Busse, Science - Physics>

It’s not Gauss’s Law, but in one situation, applying this law can determine a piecewise function that is linearly proportional to radius before a certain value, then inversely proportional to the radius after that. Combining this law with the London equation allows one to find the London penetration depth in superconductors. This law predicts that the divergence of J is 0, even though in reality, it equals the negative partial derivative of rho with respect to time. Therefore, a term involving the partial derivative of electric field with respect to time must be (*) added to this law to correct it, which was first done using a displacement current. This law has integral and differential forms that can be proved equal using the Kelvin-Stokes theorem. If current density is not constant, then the Biot-Savart Law must be used instead of this one. For 10 points, name this member of the Maxwell equations that states that the line integral of a magnetic field around a closed loop is proportional to the current.

Ampère’s Circuital Law (do not accept or prompt on “Ampère’s Force Lawâ€) <Hao>

The thermal voltage factor is equal to this quantity times temperature divided by the elementary charge; that factor is used to calculate current in the Shockley equation. This quantity is multiplied by the number of moles in a gas in the Sackur-Tetrode equation. This quantity is multiplied by temperature in the denominator of an exponent in Planck’s (*) black-body law, and this quantity can also be found in a similar position in a modified version of the Arrhenius equation. The average translational kinetic energy of a gas is given by temperature times three-halves times this quantity, and entropy equals the number of microstates of a system times this constant. This constant is defined by the gas constant divided by Avogadro’s number. For 10 points, name this constant approximately equal to 1.38 times ten to the negative 23rd Joules per Kelvin, which is symbolized kB.

Boltzmann's constant (prompt on kB) <Hao>

7. Surface inhomogeneities of rotating stars can be identified using imaging named for this effect which sees the motion of dips and bumps on a spectral line profile. This effect may be used to infer the temperature of a plasma due to this effect causing a random motion of atoms that induces thermal broadening of spectral lines. The (*) Ives-Stilwell experiment tested the effects of time dilation on this effect. The relativistic factor for this effect is equal to the square root of the quantity 1 plus the Lorentz factor over 1 minus the Lorentz factor, while classically it produces a change in frequency proportional to delta v over the wave velocity. For 10 points, name this effect explaining changing frequencies due to movement.

Doppler effect [accept Doppler shift; do not accept or prompt on “redshift†or “blueshiftâ€] <Reinstein, Science - Physics>

This scientist made the farthest radio transmission prior to Guglielmo Marconi’s and increased earth’s estimated age by considering radioactive heat. With Frederick Soddy, this scientist defined the half-life and discovered radon. James Chadwick discovered the neutron in the lab of this discoverer of the (*) proton. This New Zealand scientist developed the theory of radioactive decay and discovered alpha and beta radiation. Geiger and Marsden developed and ran this man’s famous gold-foil experiment. For 10 points, name this discoverer of the atomic nucleus.

Ernest Rutherford <DM>

For diatomic ideal gases, a quantity named for this man roughly depends on the impact pressure over the static pressure all raised to the one-seventh power. This scientist's son popularized an interferometer that uses two detectors and is co-named for Ludwig Zehnder. This physicist criticized Newton's thought experiment involving a bucket full of water by arguing that rotation is relative to the entire universe, an idea that influenced (*)Einstein. If a quantity named for this man is less than 0.2, then a flow is incompressible. That constant named for this man determines whether or not pressure increases or decreases down a streamline, and equals one for air moving at 343 meters per second. For 10 points, name this physicist whose number equals velocity divided by the speed of sound.

Ernst Mach<Silverman>

For a collection of particles, this letter denotes a quantity that equals the sum over all particles of the dot product of momentum with position. That quantity is used to derive a theorem that relates the time-averaged kinetic and potential energies and is called the scalar virial. This letter is multiplied by (read slowly) 8Â pi divided by c to the fourth times the stress-energy tensor on the right-hand side of the Einstein (*) field equations. Henry Cavendish used a torsion balance to measure a constant denoted by this letter, which has a value of 6.67 times 10-to-the-negative-11th in SI units and appears in an inverse-square law developed by Isaac Newton. For 10 points, name this letter whose "big" and "little" forms denote two constants describing the strength of gravity.

G [accept big G or little g] <Busse, Science - Physics>

A generalization of one of this man's namesake objects uses a linear combination of orthogonal versions of a Bessel function to solve PDEs in cylindrical coordinates. The Cooleyâ€"Tukey algorithm implements an efficient version of an operation named after this man; the basic form of that operation uses an integral from negative infinity to infinity and contains the term "e to the minus 2 pi IVT." This man's most famous mathematical invention may have coefficients of "4 over n pi" for odd n, and zero for even n, and that (*) expansion decomposes a periodic function into a sum of trigonometric functions, particularly sines and cosines. For 10 points, name this French mathematician, namesake of a transform and series that analyze signals in the time and frequency domains.

Jean-Baptiste Joseph Fourier [or Fourier-Bessel series; or fast Fourier transform; or Fourier transform; or Fourier expansion; or Fourier series] <Aggarwal>

18. This physicist introduced the concept of "whispering gallery waves" to explain echoes that could be heard from across the room at St Paul's Cathedral. This physicist used a quasi-static approximation for the electric field near a radiating dipole much smaller than the wavelength of light to demonstrate that the intensity of light re-radiated by that dipole is proportional to the negative (*) fourth power of wavelength. The resolution of an imaging system is limited by his namesake "criterion," and his approximation to Mie scattering explains why sunlight traveling through lots of air at sunset appears red when it reaches our eyes. For 10 points, name this British physicist whose namesake form of scattering explains why the daytime sky is blue.

Lord Rayleigh ("RAY-lee") [accept either underlined portion of John William Strutt, 3rd Baron Rayleigh] <Rosenberg, Science - Physics>

This algorithm produces nearly the same result as Halley's method when the second derivative of the input function is near zero. The ancient Babylonians used a special case of this algorithm that averages an "overestimate" and an "underestimate" to compute square roots. This algorithm is often favored over both the bisection method and the secant method since it has a quadratic rate of convergence. This algorithm, which was co-discovered by James Raphson, successively generates the (*) nth value of a function by evaluating the expression consisting of the n-minus-one-th value, "negative f of x-sub-n divided by f-prime of x-sub-n." For 10 points, name this root-finding algorithm named for the British co-inventor of calculus.

Newton's method [or Newtonâ€"Raphson method] <Jose, Science - Math>

In his correspondence principle, this man argued that, in certain conditions, quantum mechanics act like classical mechanics. De Broglie justified the quantization of angular momentum postulated by this scientist who also formulated the principle of complementarity. The Rydberg formula was derived from this scientist’s namesake (*) model, where electrons could be found no closer to the nucleus than his namesake radius. For 10 points, name this Danish physicist who theorized a model of the atom where electrons orbit around the nucleus with discrete energy levels.

Niels Bohr <BC>

This man argued that quantum mechanics acts like classical mechanics at large quantum numbers; that is his correspondence principle. Magnetization equals the Brillouin function multiplied by N, J, the g-factor, and a quantity named for this man. This man is the first namesake of a theorem that determines that magnetism cannot be explained by classical mechanics and is purely a quantum phenomenon; the second namesake of that theorem is van Leeuwen. The magnetic moment of an electron is nearly (*) 1 when expressed in units of this man’s magneton. Another constant named after this man is equal to h-bar over electron mass times c times alpha, and is denoted a sub 0. This man derived the Rydberg formula using a model he developed where electrons were most likely to be found at his namesake radius. For 10 points, name this Danish physicist who created a model of the atom where electrons move in circular, quantized orbits.

Niels Bohr <Hao>

This scientist names a set of four matrices that generate the Clifford algebra C-L-sub-1-comma-3-R. During the 1950s, while this man was teaching at Florida State University, his theory of electromagnetic fields composed of quantum harmonic oscillators was finally renormalized into modern QED. An equation developed by this scientist predicts that the electron g-factor is exactly two and recasts the time-dependent (*) Schrodinger equation to account for relativity. He developed a notation in which "left angle bracket, psi, vertical bar" represents the complex conjugate of a wavefunction. This man proposed that a hole in a sea of negative-energy electrons really represents an electron with a positive charge, or positron. For 10 points, name this British physicist who proposed magnetic monopoles and antimatter.

Paul (Adrien Maurice) Dirac <Silverman>

Loop integrals can be evaluated using this man’s namesake parameterization. Itô’s lemma can be used to derive a statement relating stochastic processes and parabolic partial differential equations named after this man and Kac, and he proposed the parton model of hadrons. In one book by this man, he recounts an episode where he discovers that “You just ask them?†and another story where he plays the frigideira in Brazil. This man later wrote of Six (*) Easy Pieces and Six Not-So-Easy Pieces. This physicist demonstrated that the Brownian Ratchet did not actually exhibit perpetual motion, and he used a “sum over histories†to create his path integral formulation. This man’s undergraduate lectures at Caltech were later collected into three volumes, and he also showed the effect of O-rings in cold water on national television. For 10 points, name this American physicist who used wavy lines and arrows in his namesake diagrams.

Richard Feynman <Hao>

This person determined that Gamma Arietis was a double star system, and the Lamé parameters can be found in the three-dimensional expression of a law named for him. This person worked with Christopher Wren to rebuild London after the Great Fire. There is no portrait of this person, perhaps due to his (*) rivalry with Isaac Newton. A famous illustration of a flea occurred in this scientist’s Micrographia, as well as one of a piece of cork. This scientist’s namesake law is written as F equals negative k x. For 10 points, name this scientist who coined the term “cell†and names a law about springs.

Robert Hooke <BC>

An angle-preserving transform named after a scientist from this country sets z equal to zeta plus one over zeta and is used in designing airfoils. The fact that liquid helium-3 will cool if compressed below 0.3 Kelvin is a type of cooling named after another physicist from this country. A law named after a physicist from this country concerns the evolution of the distribution function of (*) plasmas, and another law named after a physicist from this country explains the negative sign in Faraday’s Law. A device that confines plasma within a magnetic field in the shape of a torus, called tokamaks, were first invented this this country. One physicist from this country found that a blue glow was emitted when particles traveled faster than the speed of light in a medium. For 10 points, name this country, home to scientists such as Lenz, Pomeranchuk, Vlasov, and Cherenkov.

Russia or the Union of Soviet Socialist Republics (accept either) <Hao>

This man’s namesake rings occur when light reflects between a spherical and a flat mirror, which he detailed while making reflecting telescopes. One namesake “method†of this man approximates a function’s roots. This man proposed the corpuscular theory of light and was the first to split light using a (*) prism. Along with the previous Lucasian Professor at Cambridge, this man invented the fluxion, creating calculus. The namesake of the SI unit of force, for 10 points, name this scientist with three namesake laws of motion who discovered the Law of Universal Gravitation.

Sir Isaac Newton <DM>

1. The ratio of the intensities of anti-Stokes and Stokes lines from the Raman effect is dependent on this quantity. The diffusion equation is similar to an equation modeling the time evolution of this quantity in a homogeneous and isotropic medium, which states that its time derivative is equal to alpha times the Laplacian ("luh-PLAH-see-un") of this quantity. The gradient of this quantity, times a constant, appears on one side of (*) Fourier's law. The product of this quantity with Boltzmann's constant serves as a scale factor for the energy of molecular systems. This quantity is the conjugate variable of entropy, and thus its product with entropy has units of energy. For 10 points, name this quantity, whose absolute variety is measured by the Kelvin scale.

absolute temperature <Mukherjee, Science - Physics>

Laplace fixed Newton's model for the speed of sound by multiplying the pressure by a quantity named for this property to calculate the bulk modulus. This adjective describes a quantum state change in which the probability density evolves with a slowly changing Hamiltonian. In an ideal system with this property, pressure times volume raised to the power of either five-thirds or seven-fifths is constant. On a Pâ€"V diagram, curved lines representing processes with this property are (*) steeper than isotherms, and correspond to isentropic processes, such as the expansion phase in a Carnot (car-NOH) cycle. A process has this property if the work equals the change in internal energy, which generally occurs only if the system is insulated. For 10 points, name this type of process in which the net heat is zero.

adiabatic [or adiabatic index] <Silverman>

The probability of transitions that lack this property are given by the Landauâ€"Zener formula. This adjective describes properties of a system that remain approximately constant when the system is changed slowly; specifically, the change must be so slow that the system remains in the same eigenstate of the Hamiltonian. The ratio of the constant-pressure and constant-volume heat capacities, denoted gamma, is named for this kind of (*) process, in which pressure times volume raised to gamma remains constant. Reversible processes of this type alternate with isothermal processes in a Carnot cycle. In these processes, the work done equals the change in internal energy. For 10 points, name this kind of process that occurs with zero heat transfer.

adiabatic processes [prompt on isentropic] <Mukherjee, Science - Physics>

This quantity is plotted on log scale on the x-axis of a Bode plot, which measures a system's stability to changes in it. Since skin depth of electric current varies with the negative one-half power of permeability times this quantity, at high values of it, a conductor's resistance increases. In RLC circuits, when this quantity is large, the voltage across the inductor is high and across the capacitor is low. Low-pass filters screen out signals with (*) high values of it. This quantity is represented by the speed at which a phasor rotates. Fourier transforms convert a signal from the time domain to this quantity's domain. An alternating current depends on the sine of this quantity multiplied by time. For 10 points, name this quantity, which in conventional American power lines is 60 hertz.

angular frequency [or frequency; prompt on f; prompt on omega] <Silverman>

Moderator Note: Read the first sentence slowly for the teams Kepler’s second law shows that this quantity is inversely proportional to distance from the sun squared, and his third law shows that this quantity’s average is proportional to the -3/2 power of the semimajor axis. For a frictionless banked turn with no slipping, this quantity squared is “g tan theta over r.†The time derivative of this quantity is torque over (*) moment of inertia. A counterclockwise-moving object has a positive value for this quantity. For 10 points, name this quantity measured in radians per second, the rotational analogue of a quantity denoted v.

angular velocity [do not accept or prompt on partial] <DM>

In one construction, this vector quantity traces out circular curves called the polhode and herpolhode, which lie at the ends of the body cone and the space cone. The components of this vector quantity or their time derivatives appear in every term on the left-hand side of the Euler (OY-ler) rigid body equations. The fictitious Euler force is proportional to this quantity's time derivative, while the (*) Coriolis force is proportional to this quantity crossed with the velocity. This quantity is parallel to angular momentum for a principal axis. Angular momentum equals the product of the moment of inertia with this quantity. The letter omega symbolizes, for 10 points, what quantity representing the rate at which an object rotates?

angular velocity [prompt on omega; do not accept or prompt on "velocity" or "linear velocity"] <Busse, Science - Physics>

12. Excitation of these structures may cause them to undergo a giant resonance. James Rainwater, Ben Mottelson, and Aage Bohr shared the 1975 Nobel Prize in Physics for their work with non-spherical models of these structures. The pairing, asymmetry, and Coulomb terms are found in a semi-empirical model of these structures which treats as them like a (*) liquid drop. The shell model of these structures predicts higher stabilities at certain magic numbers. These entities experience a mass defect between their constituent parts because of their binding energy. The residual strong force attracts the baryons in these structures together. For 10 points, name these structures formed of protons and neutrons found at the center of atoms.

atomic nucleus [or atomic nuclei] <Wang, Science - Physics>

The binding energy of one type of these systems has a "quantum defect" term in the denominator. Replacing a particle in these systems with another particle with the same charge yields their "exotic" type. Using first-order perturbation theory to model relativistic effects and spinâ€"orbit coupling in these systems yields their "fine structure." The simplest example of these systems is modeled by solving the Schrödinger equation with a (*) Coulomb potential; that example of these systems has an emission spectrum with Paschen and Balmer lines. J. J. Thomson analogized the distribution of "corpuscles" in these systems to plum pudding. Democritus theorized the existence of, for 10 points, what systems which possess a nucleus and an electron cloud?

atoms [accept Rydberg atoms or exotic atoms or hydrogen atoms] <Busse, Science - Physics>

Brushes and slip rings are used to control this quantity in rotating mechanisms, with split ring commutators used for a non-oscillating type of it. Joule’s first law states that the heat generated by this quantity is proportional to its second power. By Lenz’s Law, this quantity is dampened by inductors due to it creating a (*) magnetic field concentrically around its path. Ohm’s law relates the drop in voltage across a resistor to this quantity. For 10 points, name this quantity symbolized I, with units of amperes, the rate at which charge moves through a material.

electric current [accept I before mention] <DM>

Electroosmotic (electro-oz-MOT-ik) flow occurs during a form of electrophoresis (electro-for-EE-siss) named for these objects. The length scale at which a drop of liquid begins to flatten due to gravity is named for this object. The time needed for a liquid to flow between two points in one of them is used in certain forms of viscometry (viss-KOM-uh-tree). An analyte is placed in one of them before being heated in a (*) MEL-TEMP (mel-temp) device to determine melting point. Due to the shape of these objects, surface tension and adhesive forces cause a namesake effect to form a meniscus. These items name an effect in which liquids may flow into them opposing the force of gravity, which is their namesake "action." For 10 points, name these extremely narrow tubes that share their name with very thin blood vessels.

capillary (CAP-ill-airy) tubes [or capillaries; or capillary electrophoresis; or capillary action; prompt on tubes] <Wang, Science - Chemistry>

This property appears when taking the Poincaré (pwann-kah-RAY) section of the Duffing equation. One system displaying this property can be analyzed using stretch and fold factors, which quantify its growth rate and boundedness, respectively. Robert Devaney redefined this property to include topological transitivity and dense periodic orbits. After long periods of time, some systems with this property can evolve toward a fractal structure called a (*) strange attractor. This property is seen in dynamical systems like the logistic map and double pendulum, whose equations of motion are nonlinear yet deterministic. For 10 points, name this property found in systems that are highly sensitive to initial conditions, exemplified in the butterfly effect.

chaos [or chaotic motion; accept chaos theory] <Kalathiveetil, Science - Physics>

14. This law establishes the existence of the invariable plane onto which the herpolhode ("hur-pul-HODE") is projected. This statement holds for any Lagrangian ("luh-GRAHN-jee-un") where the thetas are cyclic. It sets a variable symbolized lowercase h, equal to the square root of reduced mass times semi·latus rectum, to be constant. This statement proves that the area swept out by a particle moving along a (*) curve, relative to some fixed point, increases linearly in time. Only torque-free precession is explained by this result, which directly implies Kepler's second law and is often demonstrated by a skater who spins faster when she tucks in her arms. For 10 points, name this law stating that a vector symbolized capital L, equal to mass times velocity times radius, does not change.

conservation of angular momentum [accept angular momentum is conserved; prompt on Kepler's second Law; do not accept or prompt on "conservation of momentum" or "conservation of linear momentum"] <Silverman, Science - Physics>

NMR samples with this property have significant anisotropic effects, while in samples without this property, the anisotropies cancel out. Hermannâ€"Mauguin (mo-GAN) notation may be used to characterize samples with this property into one of 230 space groups. Objects with this property were modeled as a network of quantum harmonic oscillators by Albert Einstein. The Laue (LAO-uh) method analyzes samples with this property which have been ground to a powder, after which their (*) Bragg scattering is analyzed. Dislocations and vacancies are defects that may be found in materials with this property. X-ray diffraction analyzes materials with this property that possess long-range order, unlike amorphous materials. For 10 points, name these solids that form a repeating lattice structure.

crystalline [prompt on solid state] <Wang, Science - Physics>

Calcium copper titanate is a particularly strong one of these materials due to a grain boundary. Energy dissipation in these materials is quantified by the loss tangent. Implicit models of solvation treat the solvent as one of these materials, which name a quantity used to measure solvent polarity. The namesake "strength" of these materials is measured in volts per meter and gives the applied field needed to make them conduct above the (*) breakdown voltage. A quantity named for these materials is also called "relative permittivity" and is multiplied by epsilon-naught times area over distance in the parallel-plate model. For 10 points, what insulating materials are placed between the plates of a capacitor to increase capacitance?

dielectrics [accept dielectric constant; prompt on insulator] <Mukherjee, Science - Physics>

The catalytic rate of enzymes limited only by this phenomenon are termed "perfect." After a pulsed field gradient echo in NMR, molecules undergoing this phenomenon will insufficiently refocus, causing loss of signal intensity. Albert Einstein's doctoral thesis calculated Avogadro's number by applying laws describing this phenomenon for sugar molecules. Those laws describe the dependence of this phenomenon on (*) molar flux and were developed by Adolf Fick. This phenomenon can be visualized by dropping food coloring into water and observing the process by which the color spreads. For 10 points, name this phenomenon driven by a concentration gradient, moving molecules from high to low concentration regions.

diffusion [prompt on Brownian motion] <Prieto, Science - Chemistry>

16. Particles with behavior between that of bosons and fermions called anyons (any-ons) can only exist in systems with limited values for this quantity. Systems with differing values for this quantity may be treated equivalently through compactification. Hermann Weyl's treatment of the anthropic principle notes that Maxwell's treatment of electromagnetism would not hold if the universe had a different value for this quantity. Attempts to solve the hierarchy problem often increase this value to account for the (*) graviton. This quantity equals 11 in M-theory. This value for a brane is one larger than that of a string. In Minkowski space, this quantity is 4 due to treating space and time as a continuum. For 10 points, name this quantity, which is typically treated as 3 for space.

dimension [accept number of dimensions] <Wang, Science - Physics>

This phenomenon can be empirically modelled using the Oswald efficiency factor. The strength of this phenomenon increases drastically in the presence of an adverse pressure gradient due to boundary layer separation. Paradoxically, classical analysis indicates that this phenomenon cannot be present in an irrotational, incompressible, and inviscid (in-VISS-id) system. This phenomenon's namesake coefficient is typically plotted as a function of the (*) Reynolds number. The common "quadratic" form of this force is proportional to the square of an object's velocity. This force counterbalances gravity for an object falling at terminal velocity. For 10 points, name this aerodynamic force that acts in opposition to the direction of motion.

drag [or air resistance; prompt on friction] <Busse, Science - Physics>

12. This output quantity decreases with the square root of time upon a step input in the Cottrell equation. The equivalence point of a coulometric ("koo-low-MEH-trik") titration occurs when this quantity is measured to be zero. The response of this quantity, plotted on the y-axis, produces a curve shaped like a duck when the input is a cyclic ramp potential. The sum of the values for this quantity at the anode and the cathode is named for (*) Faraday and is proportional to the reaction rate. The mass of electroplated metal is proportional to this quantity times the duration that the electrolytic cell operates. This quantity scales linearly with the e.m.f. provided by a galvanic cell by one form of Ohm's law. For 10 points, name this quantity measured using amperometry ("am-pair-AH-muh-tree").

electrical current [prompt on i; prompt on j] <Silverman, Science - Chemistry>

20. For thin films, this quantity is measured with a four-point probe and reported in its normal SI unit per square. The force reported by a strain gauge and the temperature reported by an RTD are both inferred from measured changes in this quantity. In the thermal analogy, this quantity is defined as the difference in temperature divided by the heat flux. This quantity can be directly controlled by a (*) rheostat and is measured for an unknown component by placing it on a Wheatstone bridge. For a cylinder, this quantity is proportional to the length over the cross-sectional area times a material-specific property symbolized rho. This quantity adds harmonically in parallel and algebraically in series. For 10 points, name this quantity measured in ohms.

electrical resistance [or sheet resistance; prompt on electrical resistivity] <Silverman, Science - Physics>

A condition named for this quantity is also called the admissibility condition for the Rankineâ€"Hugoniot (RANK-in-oo-gohn-YOH) equations and is violated by rarefaction (rair-uh-faction) shock waves. The rate of production of this quantity per unit volume times absolute temperature is called the dissipation, whose non-zero value results in "lost work." While this quantity is macroscopically a monotonic function, it does not change in a microscopically (*) reversible process. It is equal to Boltzmann's constant times the natural log of the number of microstates. For 10 points, name this quantity that always increases in a closed system according to the second law of thermodynamics, the measure of disorder in a system.

entropy <Mukherjee, Science - Physics>

12. Very small devices of this type are often built in the shape of three-dimensional "fins" to reduce leakage and other short-channel effects. In enhancement mode, applying a sufficiently high bias to these devices will cause charge carriers to accumulate in an inversion layer near the surface, forming a channel through which majority carriers can travel. A current can flow between the source and drain (*) terminals of these devices when a voltage is applied to the gate terminal, which is usually separated from the semiconductor body by an insulating layer of oxide. The basis of most modern digital circuits relies on variants of these devices called a MOSFET. For 10 points, name these devices which serve as amplifiers or switches.

field-effect transistor [or FET; accept metal-oxide-semiconductor field-effect transistor or MOSFET; accept FinFET] <Rosenberg, Science - Physics>

8. Rapid changes in this vector quantity can be measured with a hot wire probe. The material derivative of a field is equal to the partial time derivative of that field, plus the gradient of that field dotted with this quantity. Due to the principle of mass continuity, this quantity for an incompressible fluid in a pipe increases at choked areas. A curve that is instantaneously tangent to this quantity at every point is called a (*) streamline. The curl of this quantity's vector field is the vorticity. If potential energy is held constant, a decrease in pressure leads to an increase in this quantity according to Bernoulli's principle. For 10 points, name this time derivative of position, which is often measured in meters per second.

flow velocity [do not accept or prompt on "speed"] <French, Science - Physics>

It’s not emittance, but the Stefan-Boltzmann Law relates temperature to this quantity’s energy type. Fick’s first law states that the concentration gradient is proportional to this quantity’s diffusion type. The displacement current is the time derivative of this quantity’s (*) electric type. This quantity’s electric and magnetic types are symbolized phi, and this quantity is equal to the density of perpendicular field lines through an area. For 10 points, name this quantity, whose magnetic type Gauss showed sums to 0 over any closed surface and whose name comes from the Latin word for “flow.â€

flux [accept energy flux, diffusion flux, electric flux, or magnetic flux] <DM>

2. This phenomenon is constrained by a quantum analogue of the Plebanski Lagrangian ("luh-GRAHN-jee-un") in the Barrett-Crane state sum model. This phenomenon can be modeled as propagating over a spin network or "spin foam," which is made up of finite loops. The relative weakness of this phenomenon is the subject of the (*) hierarchy problem. Ten equations modelling this phenomenon can be condensed to one tensor equation using the Ricci ("REE-chee"), metric, and stress-energy tensors. Inertial mass is equal to mass felt from this phenomenon according to Einstein's equivalence principle. An undiscovered gauge boson for this force would have a spin of two. For 10 points, name this force with no grounded quantum analogue, which attracts massive objects.

gravity [accept word forms like gravitation; accept loop quantum gravity prompt on spacetime or curvature] <Etzkorn, Science - Physics>

5. Cycloheximide chase experiments are used to measure this quantity for proteins in cells. Plotting the log of this quantity against atomic number over the square root of energy gives a straight line with positive slope. In pharmacokinetics, drugs are typically deuterated or PEGylated to increase the terminal form of this quantity, and therefore, their bioavailability in the body. This quantity decreases over the course of a (*) zeroth-order reaction, but stays constant if the order is one. The product of this quantity and a rate constant symbolized lambda equals the natural log of two. For bismuth-209, this quantity is thought to be over a billion times the age of the universe. For 10 points, name this quantity, the time required for 50% of a radioisotope to decay.

half-life [prompt on lifetime] <Silverman, Science - Chemistry>

11. The virial theorem can be used to show that the time-averaged kinetic and potential energies for these systems are equal. A crystal made entirely of these systems coupled together has infinite thermal conductivity and zero thermal expansion. Quantum systems of this type have constant energy level spacing and have wavefunctions given by a Gaussian term times a (*) Hermite ("air-MEET") polynomial. Classical systems of this type are described by differential equations in which the second time derivative of the displacement is proportional to the displacement. If friction is present, these systems can be categorized as underdamped, overdamped, or critically damped. For 10 points, name these systems which experience a restoring force proportional to their displacement.

harmonic oscillators [prompt on oscillators; accept simple harmonic oscillators or damped harmonic oscillators or quantum harmonic oscillators] <Rosenberg, Science - Physics>

19. Magnetic moments produced by magnetic examples of these entities contribute to resistivity in the Kondo effect by causing electron scattering. When these entities are added to a phosphor they are referred to as activators. These entities serve as sites for heterogeneous nucleation during a phase transition. Neodymium serves as one of these entities in a form of (*) YAG ("yag") laser. Carrier concentration in semiconductors may be changed by introducing these entities in the process of doping. These entities cause substitutional defects in crystals, and their presence causes the varying colors of rubies and sapphires. For 10 points, name these foreign substances with a different composition from the substance they're contained within.

impurities [accept magnetic impurities; accept dopants or doping agent before "doping"] <Wang, Science - Physics>

Equations where the term (read slowly) this quantity squared minus 1 all over this quantity squared plus 2 appear are often derived from the Clausius-Mossotti relation. Beta must be greater than the 1 over this quantity for the Frank-Tamm formula to apply. A debate as to whether momentum is directly or indirectly proportional to this quantity was known as the Abraham-Minkowski controversy. The change in this quantity is proportional to the square of the electric field strength in the (*) Kerr effect, and it is related to polarizability in the Lorentz-Lorenz equation. This quantity, which can be negative in metamaterials, is subtracted by 1 in the Lensmaker’s equation. A ratio of two values of this quantity is the tangent of Brewster’s angle and is also related to a ratio of sines in Snell’s law. For 10 points, name this quantity equal to the speed of light in a vacuum over the speed of light in a medium.

index of refraction (prompt on n) <Hao>

2. For a magnetized plasma, this value is given by the Appleton-Hartree equation. Filament propagation occurs due to an increase in this value. This quantity is given as the sum of 3 terms of the form B times lambda squared over lambda squared minus C in the Sellmeier ("SELL-my-ur") equation, which is more accurate than the Cauchy ("COW-shee") equation at extreme wavelengths. This quantity scales with the square of the electric field in the (*) Kerr effect, which in turn causes self-focusing. Brewster's angle is equal to the arctangent of this quantity. The ratio of two values of this quantity are set equal to a ratio of sines in Snell's law. For 10 points, name this value equal to the ratio of the speed of light to its speed in a given medium.

index of refraction [accept refractive index] <Mitchell, Science - Physics>

A system of particles with this property can experience either attractive or repulsive exchange interactions, which constrain their collective wavefunction to be either symmetric or antisymmetric. In a phone call, John Wheeler humorously suggested to Richard Feynman that all the electrons in the universe have this property. When a system of particles has this property, a factor of (*) n-factorial is added to the denominator of the classical partition function. A pair of fermions with this property cannot exist in the same state according to the Pauli exclusion principle. If you sort n particles with this property into 2 boxes, there are only n unique ways to do it. For 10 points, name this property of particles that act exactly the same.

indistinguishable [accept word forms such as indistinguishability; accept identical particles; accept indiscernable particles; accept the same until "same" is read] <Wang, Science - Physics>

. This quantity in classical mechanics corresponds to “negative h-bar squared over 2m times the second distance derivative of psi†in the Schrodinger equation. One can derive escape velocity by setting this quantity equal to “G big M little m over r.†This quantity is (*) p squared over 2m, and its rotational form is moment of inertia times angular velocity squared over 2. Given the conservation of mechanical energy, the change in this quantity, work, is negative the change in potential energy. For 10 points, name this quantity, the energy of an object from its motion, equal to m v squared over 2.

kinetic energy <DM> BONUSES

Von Weizsäcker (VYTE-secker) developed a functional to describe this quantity that is commonly used in Thomasâ€"Fermi DFT. This quantity is transferred from large-scale to small-scale eddies in a Kolmogorov (kull-ma-GOR-uff) cascade. In time-of-flight mass spectrometry, all ions with the same charge will also have the same value of this quantity. By measuring this quantity for an emitted photoelectron, one can calculate the work function of a metal. This quantity equals "gamma minus one times (*) m c-squared" in special relativity, and "p-squared divided by 2m" in Newtonian mechanics. This quantity is conserved in elastic collisions but not inelastic collisions. For 10 points, name this quantity which equals one-half times mass times velocity squared and represents the energy of motion.

kinetic energy [prompt on K or T; prompt on energy] <Mukherjee, Science - Physics>

Devices used to measure this quantity include one based on high-density alkali vapor that isn't undergoing spin-exchange relaxation, (pause) and one that contains a sense component around a drive component around a core of mu metal. Another device for measuring this quantity arranges two Josephson junctions in a superconducting loop and is called a SQUID. This quantity equals the curl of the vector (*) potential, and changes in it can be detected by a Hall effect sensor. It is proportional to the line integral of "I times the differential length cross r-prime over the magnitude of r cubed" according to the Biotâ€"Savart (byoh-sah-VARR) law, which gives the value of this quantity created by a current-carrying wire. For 10 points, name this vector field measured in teslas.

magnetic field [accept magnetic flux density or B-field; prompt on B; prompt on magnetic flux until "vector potential" is read, but not afterwards] <Mukherjee, Science - Physics>

The common name for this entity historically referred to another one measured by oersteds in cgs units. Electrons move in circles when this entity is perpendicular to their movement. This entity is produced in an inductor due to a wire in a (*) solenoid. The force exerted on a wire is equal to current times length cross this quantity, and more generally, this entity exerts forces on moving charges. This entity’s lines do not end. For 10 points, name this entity which attracts iron filings, which goes from the south to the north pole of its namesake object.

magnetic field [prompt on B or on field; do not accept or prompt on H or on any other terms containing the word “magneticâ€] <DM>

Klystrons are primarily used as sources of this phenomenon, which is used to stimulate transitions created by the Zeeman effect in electron spin resonance. Cavity magnetrons produce this phenomenon. OH and CH radicals in molecular clouds serve as sources of this kind of radiation from space. Charles Townes invented a device which uses rotational transitions in molecules of ammonia to produce a coherent beam of this kind of radiation via (*) stimulated emission. Molecules with a high dipole moment, such as water, are excellent absorbers of this kind of radiation, allowing this radiation to be used in dielectric heating. For 10 points, name this radiation with wavelengths between infrared and radio waves, which is used to efficiently reheat food.

microwave radiation (The device refers to the ammonia maser.) <Wang, Science - Physics> NSC 2018 - Round 06 - Bonuses

21. This form of matter decoupled from the rest of the universe approximately one second after the Big Bang, resulting in this kind of matter leaving behind a namesake relic radiation with a temperature of about 1.95 Kelvin. The SNEWS ("snooze") project detects supernovas by collecting these entities, which comprise around 99% of the energy released by a supernova. These objects caused chlorine to become argon-37 in Raymond Davis's experiment conducted in the Nebraska (*) underground, which found that the Sun only emitted 1/3 the number of these objects as predicted. Sterile types of these particles are dark matter candidates, would only interact via gravity, and would be affected by the weak force. "Flavor oscillations" are undergone by, for 10 points, what small, uncharged particles?

neutrinos <Jose, Science - Astronomy> NSC 2019 - Round 22 - Bonuses

A parameter named for this process equals one-half the Coulomb energy of a sphere over the surface energy of the sphere. The multiplication factor K describing this process is given by the product of six other dimensionless factors, including epsilon and eta, which describe the "fast" and "thermal" types of it respectively. The semi-empirical mass formula predicts that this process occurs when Z-squared over A is greater than about 40. Heavy (*) water moderates the products of this process. This process was found to be self-sustaining in a 1942 experiment led by Enrico Fermi under a football field. It produces two new neutrons in addition to two daughter nuclides. For 10 points, name this process in which a nucleus splits in half, which powers nuclear reactors.

nuclear fission <Silverman>

The coefficient of restitution for an object is equal to this power of the ratio of the initial potential energy to the final potential energy. In Planck units, electric charge equals Planck charge times the fine-structure constant to this power, and the second of Mersenne’s laws states that the fundamental frequency is proportional to this power of the stretching force. After falling for a height h near the surface of the Earth, an object that fell from rest will have velocity equal to this power of (*) 2gh. At constant inductance, the potential energy stored in an inductor will be equal to this number times inductance times current squared; similarly, the potential energy in a spring equals this number times the spring constant times displacement squared. At small angles, the period of a pendulum is proportional to its length raised to this power. A displacement of 3 meters in 6 seconds gives, for 10 points, what average velocity?

one-half <Hao>

Exposing one part of these devices to a periodic UV laser creates a spectral filtering device called a namesake type of Bragg grating. A parabolic spatial profile characterizes the graded-index type of these devices. The resistance of these devices to bend losses depends on their numerical aperture. Whether or not these devices possess one or multiple transverse modes depends on the relative (*) diameters of the core and cladding. These specialized waveguides utilize repeated total internal reflection to allow light, and thus information, to efficiently travel large distances. For 10 points, name these devices which Google is using to provide high-speed internet around the country.

optical fibers [accept fiber optic devices; prompt on fibers or waveguides] <Busse, Science - Physics>

The time of flight of an object whose trajectory is this shape is related to the true anomaly of an orbit by Barker's Equation. Some telescopes work by storing liquid mercury in a container of Kevlar, and spinning the container so that the mercury takes on this two-dimensional shape. An astronomical body whose orbit is this shape has a characteristic energy of (*) zero. James Gregory realized that spherical and chromatic aberrations in Newtonian telescopes could be reduced by adding "reflectors" named for this two-dimensional shape. Orbits with this shape are always travelling at, but not over, the escape velocity. Long-period comets have an elliptical orbit that can be approximated by, for 10 points, what conic section, whose eccentricity is one?

parabola [or parabolic; accept paraboloid or parabolic reflectors] <Jose, Science - Astronomy>

Pyotr Kapitza names a type of this system in which a certain point moves up and down. A lateral harmonograph consists of two of these devices. These systems are described by the equation “theta double dot equals negative g over L sine thetaâ€; that equation is solved by using the (*) small-angle approximation. The period of these systems, which is independent of mass, is given by 2 pi times the square root of length over gravity. For 10 points, name these oscillators that consist of a mass on a string and are used in clocks.

pendulums [prompt on simple harmonic oscillators or SHOs] <BC>

7. This quantity equals the reciprocal of the derivative of the Hamiltonian with respect to the action when using action-angle variables. This quantity increases exponentially via a cascade of bifurcations when the logistic map's parameter exceeds a critical value. In some dynamical systems, the repeated doubling of this quantity occurs at the onset of (*) chaos. This quantity squared divided by the cube of the semi-major axis is constant in Kepler's third law. For a mass on a spring, this quantity equals 2 pi times the square root of mass over the spring constant. For 10 points, name this reciprocal of frequency, the time required for a system undergoing cyclic repeated motion to return to its original state.

period <Busse, Science - Physics>

It’s not temperature, but due to EIT, this value can be nearly 0 in Bose-Einstein condensate. The reciprocal of this value squared is equal to relative permeability times relative permittivity. By Snell’s Law, the ratio of the sines of the angles of incidence and refraction is equal to the corresponding ratio of this value for the two media, and the index of (*) refraction is c over this quantity. Cherenkov radiation results when this value is passed, which cannot happen in a vacuum. For 10 points, name this value, the speed at which photons move in a material, which in a vacuum is defined as c.

phase velocity of light in a medium [accept speed for velocity; accept any mention of electromagnetic waves or photons instead of light (before mention); do not accept or prompt on “c†or “speed of light in a vacuumâ€; do not accept or prompt on “index of refractionâ€] <DM>

Sakurai developed the theory of vector meson dominance to explain the interaction between hadrons and these particles. Negative i times the metric over momentum squared is this particle’s propagator, and if these particles travel in a straight line through a turbid medium, they are called “ballistic.†1.5 times the Schwarzschild radius is the radius of a “sphere†named for these particles. These particles must be near a neutron and have energy greater than twice the rest mass energy of an electron for (*) pair production to occur. BKS theory concerns the interaction of matter with these particles, which interact in a U(1) gauge symmetry. These particles, along with W and Z bosons and gluons, constitute the gauge bosons. Electrons interact with these compounds in Compton scattering. For 10 points, name these massless quanta of light.

photons <Hao>

Maria Goeppert-Meyer names a unit for the cross-section for absorption of two of these particles at once. Transition-edge sensors were used to close these particles' "detection loophole," which arose when using these particles to test Bell's theorem. The rates of processes which produce or emit these particles are measured by the Einstein coefficients. In quantum electrodynamics, the exchange of (*) "virtual" examples of these particles mediates the electromagnetic force. A population inversion of electrons inside a gain medium inside a cavity resonator enables the stimulated emission of these particles at a single frequency by a laser. For 10 points, name these quanta of light.

photons <Mukherjee, Science - Physics>

8. A crystalline microbalance made of a material that has this property is used to measure binding affinities in QCM. Materials with this property are rated by coefficients labelled d, g, h, or v, and subscripted by a 33 or 333. Since materials with this property act like RLC circuits with extremely high Q factors, they are frequently used to make resonators. AFM cantilever tips and pressure sensors are typically made of materials with this property, such as the (*) perovskite lead titanate zirconate. Crystals that possess this property must not have inversion symmetry and deform under external electric fields. For 10 points, name this property possessed by quartz, in which a mechanical force causes a material to become charged.

piezoelectric [or piezoelectricity; prompt on ferroelectric] <Silverman, Science - Physics>

The stability of these systems can be characterized by the ratio of two forms of pressure; that ratio is symbolized beta. The product of Boltzmann's constant, temperature, and number density gives these systems' namesake pressure. When these systems are subject to a tension force proportional to "B dot grad B," they can be compressed into "pinches," according to ideal (*) MHD. These substances are confined at very high temperatures and densities in a torus-shaped device called a tokamak to perform nuclear fusion. Natural examples of these substances include the aurora borealis, the ionosphere, and lightning. For 10 points, name these ionized gases usually considered the fourth state of matter.

plasmas [prompt on tokamaks or stellerators until "namesake pressure" is read] <Wang, Science - Physics>

Gaussian wave packets are usually represented in spaces where these two quantities form the basis and can be interconverted by a Fourier transform. The raising operator for the harmonic oscillator is a linear combination of these two other operators. Hamiltonians are written as functions of generalized versions of these two variables, which are symbolized p and q. A relationship between these two quantities is often explained with a microscope focused on (*) electrons passing through a slit. Since the canonical commutator of these two quantities equals i times h-bar, the product of their standard deviations must be greater than h-bar over two. For 10 points, name these two conjugate variables that cannot be simultaneously measured according to the Heisenberg uncertainty principle.

position AND linear momentum [or coordinate AND linear momentum; or x AND p; either order acceptable; prompt on partial answer; do not accept or prompt on answers involving "angular momentum"] <Silverman>

In 2017, the PAMELA probe detected an excess of these particles. In the Feynman diagram of this particle’s annihilation, it is shown travelling leftward and producing a sine wave. It’s not the muon, but Carl David Anderson discovered these particles in 1932. Fludeoxyglucose is used in these particles’ namesake (*) “emission tomography,†and when potassium-40 undergoes beta-plus decay, a proton is changed into a neutron, an electron neutrino, and this particle. For 10 points, name this antimatter counterpart of the electron with a positive charge.

positrons <BC>

Lev Landau showed that, under certain conditions, the cyclotron motions of charged particles have this property, a fact which allows resistance to be written in terms of the von Klitzing constant. A sharp peak at 254 nanometers corresponding to 4.9 electron-volts implied this result in an experiment that fired electrons through a vapor of mercury and was run by Franck and Hertz. When deriving his law of blackbody radiation, (*) Max Planck arbitrarily assumed that energy has this property. Einstein explained the photoelectric effect by proposing that light is a particle, and thus has this property. For 10 points, name this property where at small scales, quantities become discretized, which names a subfield of physics involving wavefunctions and randomness.

quantization [accept word forms indicating things are quantized or in quanta or are quantum; accept anything suggesting things are discrete or discretized until "discretized" is read] <Wang, Science - Physics>

Three types of this property are represented by the basis states of the most commonly-used space obeying SU(3) symmetry. The Cabibbo angle is defined relative to two eigenstates of this property. Hypercharge is the sum of the five numbers quantifying this property, one of which is isospin. The CKM matrix gives the probability that this property changes due to the weak force. "Truth" and "beauty" were the (*) original names for two new options for this property introduced in the Standard Model's third generation. Neutrino oscillations change this property. Murray Gell-Mann's Eightfold Way describes how combinations of it can lead to symmetry for mesons. For 10 points, name this property that distinguishes the six known quarks, examples of which include up, charm, and strange.

quark flavor [or flavour] <Silverman>

The Sakata model was discarded after the discovery of a type of these particles in 1974 and the Cabibbo angle is related to the decay of these particles. These are the only elementary particles to interact with all four fundamental forces. These particles exhibit asymptotic freedom and cannot exist alone due to color confinement. One of these particles and its antiparticle form a (*) meson and three of these particles form a baryon. These particles have a charge of plus two-thirds or negative one-third and come in six flavours. For 10 points, name these elementary particles whose “up†and “down†flavours make up protons and neutrons.

quarks <BC>

Differing magnitudes of this effect explains why K corrections are necessary to convert apparent magnitudes to absolute magnitudes. The last scattering surface has the maximum value of 1100 for a parameter describing this effect, which roughly equals a ratio of two scale factors, minus one. In a 1959 experiment, the relativistic contribution to this effect was cancelled out by placing an iron-57 sample inside a loudspeaker on top of a building. A quantity symbolized z named for this effect is a proxy for (*) astronomical distances: that's because Hubble's law predicts most objects display this effect since the universe is expanding. For 10 points, name this result of the Doppler effect, in which a light source moving away from an observer appears to increase in wavelength toward a namesake color.

redshift [or gravitational redshift; or z until it is read; prompt on Doppler effect until it is read] <Silverman>

A system that exceeds the Bekenstein limit can be shown to violate this statement by considering it inside a black hole, and the similar Landauer’s principle can also be derived from this statement. Due to this statement, a matrix of phenomenological coefficients named after Onsager can be shown to be positive semi-definite. The concept of adiabatic accessibility was created by Carathéodory in his axiomatic formulation of this statement, and apparent violations of this statement occur in Poincaré’s (*) recurrence theorem and in Loschmidt’s paradox. The probability that this statement is violated on a microscopic scale is given by the fluctuation theorem. Szilard rebutted a thought experiment contradicting this statement by noting that a certain being must expend energy to acquire information about the speeds of gas molecule; that being is Maxwell’s demon. For 10 points, name this law that states that entropy can never decrease in an isolated system over time.

second law of thermodynamics <Hao>

Einstein found that this mass-related quantity’s vibration form was approximately “partial oscillator partial temperature†over molarity. Many solid crystals have a value of 3R over mass for this quantity, by the Dulong-Petit law. Differences in this mass-related quantity cause sea and land breezes, which occur at (*) day and night respectively. This quantity measured in joules per gram per kelvin is around 4.186 for water. Equal to Q over m delta T, for 10 points, name this intensive property symbolized c that is the ratio of heat and resulting temperature change per unit mass.

specific heat capacity [do not accept or prompt on any answer not containing both underlined words] <DM>

4. A set of basis functions that are solutions to Laplace's equation are so-named since they were generated by extracting out an rl factor under this system. Systems in which there is symmetry around a single point and not a whole line, such as models of the geoid, often use a set of orthogonal harmonic functions named for this system. The formula for this system's volume (*) element is the square of the distance times the sine of an angle times three infinitesimals. Weather systems over a planet may be specified using this coordinate system's radial, azimuthal, and zenith components, represented as r, phi, and rho respectively. For 10 points, what 3-dimensional coordinate system is formed by adding a third angle to the 2D polar coordinate system?

spherical coordinates [accept sphere coordinates] <Jose, Science - Math>

4. The so called "plate trick" is used to demonstrate one property of this quantity. QED explains why the g-factor correlated to this value is not exactly two. Coupling between this quantity and motion causes contributions to the fine structure. EPR spectroscopy observes transitions in which the sign of this quantity changes in the presence of a magnetic field. This value for a particle determines whether or not it is symmetric or asymmetric during (*) exchange, which determines whether it follows Bose-Einstein or Fermi-Dirac statistics. Particles with non-integer values of this quantity must obey the Pauli exchange principle, such as the electron's value of plus or minus 1/2 for this quantity. For 10 points, name this intrinsic angular momentum of a particle.

spin [prompt on intrinsic angular momentum; do not accept or prompt on "angular momentum"] <Wang, Science - Physics>

19. A form of super-resolved microscopy depletes fluorophores by forcing them to undergo this process instead of fluorescence; that technique, STED microscopy, earned Stefan Hell a 2014 Nobel in Chemistry. This process begins at a metastable upper level. 4-level systems are preferable to 3-level systems for producing conditions suitable for this process. Gain media help facilitate this process after undergoing (*) pumping. The rate of this radiative process is described by the Einstein B21 ("b sub 2 1") coefficient. This process occurs faster than absorption when a system experiences population inversion. Unlike a similar "spontaneous" process, photons produced by this process are coherent. For 10 points, name this process central to the function of lasers.

stimulated emission [accept light amplification by stimulated emission of radiation; prompt on laser or word forms such as lasing; prompt on optical amplification; do not accept or prompt on "spontaneous emission"] <Wang, Science - Physics>

This phenomenon produces an exotic state of matter, characterized by jet quenching, studied in the ALICE experiment. The symmetry group of this phenomenon is generated by the Gell-Mann (ghell-MAHN) matrices. By coincidence, not definition, this interaction's coupling constant approximately equals one. Feynman's parton (PAR-tawn) model was an early model of this interaction, which is mediated by a gauge boson that comes in (*) eight different types. The magnitude of this force increases with distance, a phenomenon called confinement, since it implies that one cannot isolate a particle with non-zero color charge. Gluons mediate, for 10 points, what fundamental force which holds protons and neutrons together?

strong nuclear force [prompt on asymptotic freedom before "interaction"] <Busse, Science - Physics>

The resonating valence bond theory explains this property, which occurs in many strongly correlated systems, such as certain "heavy fermion" compounds and cuprate complexes. Commonly used materials with this property include alloys of either tin or titanium with niobium. One theory of this property was confirmed by replacing natural mercury with mercury-198 to demonstrate the isotope effect; that theory posits that (*) phonons mediate the condensation of electrons into bosonic quasiparticles. BCS theory describes materials with this property, whose "high temperature" form involves a critical transition above the boiling point of liquid nitrogen. For 10 points, name this property where a material displays zero electrical resistance.

superconductivity <Mukherjee, Science - Physics>

12. A pattern that appears in these systems was given a whimsical Lewis Carroll-inspired name by David Mermin after a lengthy exchange with the editors of Physical Review Letters. Laszlo Tisza theorized that these systems contain two phases; in that model, one phase is condensed while the other is not and carries the entropy. Tisza also proposed that these systems experience temperature waves that behave like (*) sound waves. Circulation is quantized in these systems as vortices. These systems will form a 30-nm thick layer while creeping around the edges of their containers, and will escape them if unsealed. A prominent example of these substances is formed by cooling liquid helium past the lambda point. For 10 points, name these substances with zero viscosity.

superfluids [accept word forms such as superfluidity; prompt on helium II] <Wang, Science - Physics>

The rate of this process for an infinite plane, infinite cylinder, or sphere can be determined using a Heisler chart. The ability of a material to resist this process is primarily determined by the rate of umklapp (OOM-clop) scattering processes. The denominator of the Biot (bee-OH) number contains a quantity that characterizes this process and is a transport coefficient involving a body's interior. This process can be explained microscopically due to diffusion of free electrons and vibration of (*) phonons. The rate of this process is proportional to the gradient in temperature, according to Fourier's law. This process can be explained by molecular collisions causing transfer of energy. For 10 points, name this form of heat transfer by direct contact, contrasted with radiation and convection.

thermal conduction [or heat conduction; prompt on heat transfer] <Busse, Science - Physics>

The partition function is proportional to the square root of temperature for a potential that depends on this power of a coordinate. Central force problems can be simplified by introducing an "effective potential" that is inversely proportional to this power of distance. Hermite (air-MEET) polynomials or ladder operators can be used to solve the Schrödinger equation in a potential that is proportional to this power of distance. By introducing the "reduced mass" and transforming to the (*) center-of-mass frame, one can easily solve the problem involving this many gravitationally interacting bodies. When potential energy is proportional to distance raised to this power, objects oscillate sinusoidally as they undergo simple harmonic motion. For 10 points, how many masses are connected by a pulley in an Atwood machine?

two [or 2] <Mitchell, Science - Physics>

4. This phenomenon may be represented by disconnected bubbles on a Feynman diagram. This phenomenon names an effect in which virtual particle-antiparticle pairs generated by an electric field weaken the field due to reorienting themselves. The impedance due to this phenomenon can be approximated as 120 pi ohms. Fluctuations in this entity lead to the presence of zero-point energy at the ground state. A pair of (*) neutral conducting plates with this entity in between will still experience attractive or repulsive forces in the Casimir effect. The constants ε0 ("epsilon nought") and μ0 ("mu nought") respectively are the permittivity and permeability of this entity. For 10 points, name this term referring to space with very low pressure due to the absence of matter.

vacuum [accept free space] <Wang, Science - Physics>

The hot spot that created the Hawaiian Islands is the largest discovered example of the zones of the core-mantle boundary named for having "ultra low" values of this quantity. In the ocean, the depth at which one form of this quantity is minimized is known as the SOFAR channel. Andrija MohoroviÄić (MOH-hoh-roh-VEE-cheech) used the discrepancy in two different measures of this quantity to provide evidence for the existence of his namesake discontinuity. For an (*) S-wave, this quantity is equal to the square root of the bulk modulus divided by the density. Because this quantity is higher for P-waves than S-waves, P-waves are always measured first on a seismograph. For 10 points, name this quantity which, for a sound wave in the air, is around 343 meters per second.

velocity [or speed; or speed of sound; prompt on Mach 1] <Minarik, Science - Earth Science>

The Joback method for calculating this quantity includes a term where a sum of this quantity for various groups is subtracted by 597.82. Models relating this quantity to temperature, such as those named after Walther and Wright, often include double logarithms. This quantity is directly proportional to temperature to the three-halves power in Sutherland’s formula. One form of this quantity has units of kilograms over meters times seconds, while this quantity is multiplied the Laplacian of velocity in the (*) Navier-Stokes Equations. The Greek letters nu, eta, and mu are used for various forms of this quantity, which is found squared in the denominator of the Grashof number. This quantity is multiplied by radius, velocity, and 6 pi to yield drag in Stokes’ Law, and it is in the denominator of the Reynolds number. For 10 points, name this quantity with dynamic and kinematic forms, a measure of a fluid’s resistance to flow.

viscosity (accept specific types such as dynamic viscosity, kinematic viscosity, or eddy viscosity) <Hao>

4. Due to its low atomic mass, beryllium is nearly transparent to this phenomenon, which allows it to serve as a "window". Spectroscopic techniques using this radiation cannot effectively detect the presence of hydrogen or helium. Manne Siegbahn introduced the notation used in spectroscopy based on this radiation, which includes the k alpha transition. ESCA uses this phenomenon to induce the (*) photoelectric effect. Because this radiation has wavelengths on the same scale as interatomic spacing, crystal lattices serve as effective diffraction gratings for it. Experiments with Crookes tubes resulted in Wilhelm Roentgen's discovery of this form of radiation. For 10 points name this ionizing radiation with energy higher than UV light and lower than gamma rays.

x-rays [accept Röntgen radiation before he is mentioned] <Wang, Science - Physics>