bluuebunny/crossref_metadata_2025 huggingface dataset:
Relativistic transformation of group velocity via spatial filtering
Authors: Stedman G. E.
Published: September 2005

The group velocity of any wave transforms under Lorentz boosts as a particle velocity, and so by the Einstein velocity addition relations. This is expected for the velocity of energy transport in spite of the presence of a medium and so a preferred frame. The phase velocity has the same transformation property only when the group and phase velocities are parallel and the product of their magnitudes is equal to c2. A proof is given of the relativistic group velocity transformation which is simple and novel, and which uses spatial filtering concepts to derive the formula for group aberration as a consequence of that for phase aberration. This gives some physical insight into the previous proofs based on a four-vector analysis.
Relativistic constitutive relations, differential forms, and the p-compound
Authors: Nguyen D. B.
Published: September 2005

This article introduces the reader to the physical applications of the concept of the p-compound of a linear transformation L. The computation of p-compounds requires nothing more than the computation of p-order determinants and, therefore, has a simple geometric interpretation. While L acts on vectors, the p-compound of L acts on geometric objects made up of p vectors: the two-compound acts on parallelograms, the three-compound acts on parallelopipeds, and so on. The physics is introduced by identifying the electromagnetic field quantities with parallelograms and parallelopipeds in space-time; the p-compound of the Lorentz transformation then yields their (algebraically complicated) relativistic transformations after one matrix multiplication. The relativistic electromagnetic properties of a medium are obtained by two matrix multiplications. In this way, one obtains the expression for the relativistic Biot–Savart law, an explanation for the experimental results of Röntgen and Wilson, an explanation for the null result of Michelson and Morley, and the Cerenkov condition for a charged particle to radiate while moving through a dielectric medium.
Research as a guide for curriculum development: An example from introductory electricity. Part II: Design of instructional strategies
Authors: Shaffer Peter S. , McDermott Lillian C.
Published: September 2005

This is the second of two closely related articles that together describe how results from research can be used as a guide for curriculum development. The first article shows how the investigation of student understanding of electric circuits by the Physics Education Group has contributed to the building of a research base. This second article describes how the group has drawn on this resource both in developing a curriculum for laboratory-based instruction and in adapting this curriculum to fit the constraints of a traditional introductory course. Also discussed is how, in turn, development and implementation of the curriculum have enriched the research base.
Renormalization of a model quantum field theory
Authors: Kraus Per , Griffiths David J.
Published: September 2005

Renormalization is the technique used to eliminate infinities that arise in quantum field theory. This paper shows how to renormalize a particularly simple model, in which a single mass counterterm of second order in the coupling constant suffices to cancel all divergences. The model serves as an accessible introduction to Feynman diagrams, covariant perturbation theory, and dimensional regularization, as well as the renormalization procedure itself.
Scattering from a locally periodic potential
Authors: Griffiths David J. , Taussig Nicholas F.
Published: September 2005

One-dimensional scattering from a series of delta-function barriers is considered, in the context of nonrelativistic quantum mechanics. A surprisingly simple closed-form expression for the transmission probability is obtained, and compared with the earlier result of Kiang [Am. J. Phys. 42, 785–787 (1974)]. The band structure characteristic of periodic potentials emerges even when the number of barriers is quite small. However, the ‘‘saturation’’ phenomenon identified by Lee, Zysnarski, and Kerr [Am. J. Phys. 57, 729–734 (1989)] is found to depend on the energy regime in question.
Path integrals and quantum interference
Authors: Barut A. O. , Basri S.
Published: September 2005

The path integral treatment of the single and double-slit experiments, which illustrates the particle nature of single events and the wave nature of the statistical average of repeated events, is presented.
Experimental study of an inverted pendulum
Authors: Smith H. J. T. , Blackburn J. A.
Published: September 2005

Stable inverted states of a simple pendulum are possible when the pivot is subjected to high-frequency vertical oscillations. Such a pendulum has been constructed, and the ranges of displacement frequency and amplitude for which the inverted state is stable have been experimentally determined and compared to theoretical calculations.
Unified presentation of magnetic and dielectric materials
Authors: Mata-Mendez O.
Published: September 2005

As is well known, time-independent fields generated by dielectric and magnetic materials can be described by real polarization charges and fictitious magnetic charges, respectively. In addition, magnetic materials can also be studied by means of real currents, but no equivalent-current formulation has been given for dielectric materials. In this paper, a compact formulation of Maxwell equations is presented which shows that it is possible to treat time-independent fields generated by dielectric media by using fictitious ‘‘currents’’ related to the electric polarization vector. This compact formulation shows that a complete analogy can be drawn between dielectric and magnetic phenomena.
Rotating waves
Authors: Ceperley Peter H.
Published: September 2005

In cylindrical and spherical geometries, the proper linear combination of standing waves results in a rotating wave field. Such a field looks like a traveling wave chasing its tail: a constant field rotating in space. These rotating wave fields can be considered to be a third major category of waves, similar to traveling and standing waves. While all three types of waves are interrelated, rotating waves offer the clearest insight into angular momentum and rotary motion in wave fields. This paper summarizes the field equations and physics for various rotating wave fields and goes on to discuss simple demonstrations of rotating waves on the surface of water.
Not quite so simply no hidden variables
Authors: Mermin N. David
Published: September 2005

A recent very simple no-hidden-variables theorem is shown to be instructively incorrect.
Doctoral oral examination of Heinrich Kayser, Berlin, 1879
Authors: Mulligan Joseph F.
Published: September 2005

Presented here is a translation of an unpublished account by Heinrich Kayser of his doctoral oral examination at the University of Berlin in 1879. It throws considerable light on doctoral education in Germany at a time when German universities led the world in physics research and the education of physicists. Background information on Kayser’s career and on higher education in Germany at the time is also included.
Magnetostatic field of an axially symmetric electric multipole rotating about its symmetry axis
Authors: Datta Somnath
Published: September 2005

It has been shown that when an axially symmetric localized charge distribution carrying a single electric multipole moment Ql0 is rotated about its symmetry axis, it developes magnetic multipole moments Ml−1,0,Ml+1,0 of orders l−1 and l+1 only. The lower order l−1 does not contribute for l=0, 1. The resulting magnetic field is a superposition of two pure multipole fields.
Frictional forces on an inclined plane
Authors: Wehrbein William M.
Published: September 2005

A box of mass m1 rests on a rough plane elevated through an angle φ. The box is connected to a counterweight of mass m2 by an inextensible rope which passes over an ideal pulley at the higher end of the plane. The box may stick only if μs2≥M2−1, where μs is the coefficient of friction and M≡m2/m1. If, in addition, μs<M, then there are two critical angles φs1 and φs2, such that the resting box sticks for any φ satisfying φs1<φ<φs2. And if the coefficient of kinetic friction μk<μs, then there are two other critical angles φk1 and φk2 such that the resting system is in stable equilibrium for any elevation angle satisfying φk1≤φ≤φk2, and in conditionally (depending on direction of perturbation) stable equilibrium for φs1<φ<φk1 or φk2<φ<φs2.
Using 3-cm microwaves for optics laboratory experiments
Authors: Blair J. Morris
Published: September 2005

Commercially available 3-cm microwave equipment can produce predictable diffraction patterns if precautions are taken to eliminate standing waves resulting from reflections from various surfaces. Equipment modifications and operating procedures are described for a student laboratory experiment involving single-slit diffraction in the transition range between Fraunhofer and Fresnel patterns. Polarization measurements are also described.
Deterministic chaos in the elastic pendulum: A simple laboratory for nonlinear dynamics
Authors: Cuerno R. , Rañada A. F. , Ruiz-Lorenzo J. J.
Published: September 2005

The chaotic motion of the elastic pendulum is studied by means of four indicators, the Poincaré section, the maximum Lyapunov exponent, the correlation function, and the power spectrum. It is shown that for very low and very large energies the motion is regular while it is very irregular for intermediate energies. Analytical considerations and graphical representations concerning the applicability of KAM theorem are also presented. This system and the type of description used are very suitable to introduce undergraduate students to nonlinear dynamics.
Effect of cyclotron resonance on the microwave detection properties of a glow discharge plasma
Authors: Arbel D. , Bar-Lev Z. , Felsteiner J. , Genossar J. , Peled A. , Rosenberg A.
Published: September 2005

The effect of cyclotron resonance on the detection of microwave radiation by a glow discharge tube has been investigated. This effect was reported about a decade ago for the detection of 70-GHz millimeter-wave radiation using a magnetic field of 26 kG. In the present work a similar experiment has been carried out with 9.1-GHz microwave radiation a resonance in the detection signal at a magnetic field of 3.1 kG has been found. This experiment, which involves the use of an X-band microwave source, a moderate magnetic field, and the plasma of a simple glow discharge tube, can easily be adopted in a physics student laboratory.
The Chinese South-Seeking chariot: A simple mechanical device for visualizing curvature and parallel transport
Authors: Santander M.
Published: September 2005

An old mechanical device, the Chinese South-Seeking chariot, presumably designed to work on a flat plane, is shown to perform parallel transport on arbitrary surfaces. Its use affords experimental demonstration and even numerical checking (within a reasonable accuracy) of all the features of curvature and parallel transport of vectors in a two-dimensional surface.
Temperature servomechanisms using thermoelectric modules
Authors: Van Baak D. A.
Published: September 2005

This paper describes the usefulness of commercially available thermoelectric modules for building systems that control the temperature of experimental samples. It discusses how such ‘‘solid-state heat pumps’’ can be incorporated into temperature servomechanisms whose behavior can be fully modeled and predicted. It is shown that quite modest systems can offer temperature control over the range 230–330 K, and that milliKelvin temperature stability can be obtained. Finally, in showing that servomechanisms of interest can be modeled by very familiar differential equations, this paper also provides a tutorial introduction to servomechanisms in general.
Colliding waves on a relativistic string
Authors: Brundobler Stefan , Elser Veit
Published: September 2005

The dynamics of relativistic strings is studied with emphasis on the close analogy with the transverse motion of the conventional stretched string of freshman physics. A constraint-free parametrization of the world sheet in terms of arbitrary wave packets moving along the string is given. In particular, it is found that for the initial condition of right and left moving wave packets in a collision arrangement, there is no scattering−each packet only experiences a delay upon passing through the other. Also discussed is the geometry of the spontaneous singularities generically arising for strings in two spatial dimensions.
Maxwell’s theory of eddy currents in thin conducting sheets, and applications to electromagnetic shielding and MAGLEV
Authors: Saslow W. M.
Published: September 2005

Using the example of a monopole that is spontaneously generated above a thin conducting sheet, the simplicity and power of Maxwell’s 1872 theory of eddy currents in thin conducting sheets is illustrated. This theory employs a receding image construction, with a characteristic recession velocity v0=2/(μ0σd), where the sheet has conductivity σ and thickness d. A modern derivation of the theory, employing the magnetic scalar potential, is also presented, with explicit use of the uniqueness theorem. Also discussed are limitations on the theory of which Maxwell, living in a time before the discovery of the electron, could not have been aware. Previous derivations either have not appealed explicitly to the uniqueness theorem, or have employed the now unfamiliar current function, and are therefore either incomplete or inaccessible to the modern reader. After the derivation, two important examples considered by Maxwell are presented−a monopole moving above a thin conducting sheet, and a monopole above a rotating thin conducting sheet (Arago’s disk)−and it is argued that the lift force thus obtained makes Maxwell the grandfather, if not the father, of eddy current MAGLEV transportation systems. An energy conservation argument is given to derive Davis’s result that, for a magnet of arbitrary size and shape moving parallel to a thin conducting sheet at a characteristic height h, with velocity v, the ratio of drag force to lift force is equal to v0/v, provided that d≪δc, where δc =√2h/(μ0σv).

If d≫δc, the eddy currents are confined to a thickness δc, leading to an increase in the dissipation and the drag by a factor of d/δc, so that the ratio of drag to lift force becomes proportional to √v′0/v, where v′0 = 2/(μ0σh). The case of a monopole fixed in position, but oscillating in strength (such as can be simulated by one end of a long, narrow, ac solenoid), is also treated. This is employed to obtain the results for an oscillating magnetic dipole whose moment is normal to the sheet. A general discussion of electromagnetic induction and electrical conductors, both thick and thin, is given, emphasizing the difference between the high-frequency limit, where flux expulsion occurs and the self-inductance dominates, and the low-frequency limit, where the flux penetrates and the electrical resistance dominates. A discussion of Lenz’s law, as a statement about motion, is given. It is argued that the most general form of such a statement of Lenz’s law is that induced currents tend to accelerate a conductor in the direction that most effectively decreases the rate of Joule heating. A calculation, in the low-frequency limit, of the drag force on a magnetic dipole falling down a long conducting tube, is also given. This last case can be given a striking demonstration with the newly available neodymium–iron–boron magnets.
Elastic particle scattering from two hard disks
Authors: José Jorge V. , Rojas Cristian , Saletan Eugene J.
Published: September 2005

In a scattering problem where an incoming particle interacts elastically with more than one scatterer the trajectories that the particle can follow can be quite complex, even in two dimensions. In this paper the elastic scattering of a particle from a two-disk system is solved explicitly. This is a nontrivial problem that can serve to introduce the concepts needed to understand more complex systems of three or more disks, which defy an explicit analytic treatment. Indeed, a target of more than two disks of equal radius leads to behavior that has recently been termed chaotic scattering.
Electrons in a crystal lattice: A simple computer model
Authors: Johnston I. D. , Segal D.
Published: September 2005

A simple computer program is presented, well within the capability of sophomore students, which solves the Schrödinger equation for a ‘‘lattice’’ of up to 12 potential wells, and which demonstrates many features important in a discussion of semiconductor physics—energy bands, impurity states, amorphous effects, negative effective mass. The ability to present material like this to students computationally may well have a profound effect on what is taught in future physics curriculums.
Optimum rectangular geometry for Hall effect devices and their application in determining properties of electrons in silicon
Authors: Turvey Keith , Dignan James J.
Published: September 2005

The temperature dependence of the Hall emf under conditions of constant drive potential difference and constant magnetic flux density is obtained for a commercial Hall generator (Honeywell 7SS) having an n-type Si channel. From the measurements, the temperature dependence of the electron conductivity mobility (μ) and the Hall factor are obtained, with results in good agreement with those of others. Conditions for optimizing the Hall emf per unit magnetic flux density are considered for rectangular bar geometry and are applied to determine an approximate value of μ for electrons in silicon. Room-temperature transverse magnetoresistance measurements are obtained for the 7SS device and another device having an n-type Si channel (Sprague 3604). These magnetoresistance measurements are also used for an approximate determination of μ.
On the acoustics of tuning forks
Authors: Rossing Thomas D. , Russell Daniel A. , Brown David E.
Published: September 2005

Tuning forks can vibrate in many different modes in which the tines move either in the plane or perpendicular to the plane of the fork. Symmetrical modes can be modeled by the motion of two cantilever beams, antisymmetrical modes by the motion of a beam with free ends. A tuning fork vibrating in its fundamental mode is approximately a linear quadrupole sound source whose strength can be increased by use of a baffle or by touching the stem to a soundboard. The motion of the stem includes strong components at both the fundamental frequency and its second harmonic. Slight alterations in a tuning fork can enhance or suppress either of these components. At large amplitudes, the tines vibrate nonsinusoidally, the nth harmonic increasing approximately as the nth power of the fundamental.
Kinematics between comoving photon exchangers in a closed, matter-dominated universe
Authors: Stuckey W. M.
Published: September 2005

Beginning with the general relativistic, parametric equations for radius and proper time, equations are derived which explain the kinematics between a comoving photon emitter and receiver in a three-sphere, matter-dominated universe. These equations can be used by introductory astronomy students to obtain kinematic information about large redshift objects in a closed universe. An example is provided. Some aspects of photon exchange in the closed, matter-dominated universe are discussed. For example, it shown that photons with the largest redshifts can be received from the most rapidly approaching objects in this model.
Nonlocality in frequency measurements of uniformly accelerating observers
Authors: Moreau William
Published: September 2005

Nonlocality in frequency measurements of uniformly accelerating observers is discussed. The concept of time dilation is explored. (AIP)
Floating equilibrium of symmetrical objects and the breaking of symmetry. Part 2: The cube, the octahedron, and the tetrahedron
Authors: Erdös Paul , Schibler Gérard , Herndon Roy C.
Published: September 2005

The analysis of the equilibrium configurations of floating bodies (see part 1) is extended to the cube, for which a complete discussion is given. The symmetric floating configurations of the octahedron and of the tetrahedron are also examined.
Self-similar and erratic transient dynamics for the linearly damped simple pendulum
Authors: Permann Delmar , Hamilton Ian
Published: September 2005

The transient dynamics of the linearly damped simple pendulum is examined in conjunction with the transition from rotation to libration. Higher derivatives of the phase of the pendulum with respect to time are calculated and these are used to obtain higher-order time plots and higher-order phase plots. For both the time and phase plots, in windows of time about the transition point, complicated dynamics is observed. This transient dynamics may exhibit either self-similar or erratic behavior.
Why we use retarded potentials
Authors: Anderson James L.
Published: September 2005

The use of retarded potentials in solving the wave equation is usually justified on physical grounds or else by an appeal to causality. It is shown here that these potentials are asymptotic solutions obtained by solving the wave equation as an initial value problem and imposing only the condition that the initial field energy be finite. The relation of this result to the so-called electromagnetic arrow of time is discussed.
The electronic bouncing ball
Authors: Zimmerman Robert L. , Celaschi Sergio , Neto Luis G.
Published: September 2005

The electronic analog of the bouncing ball is developed as a simple classroom experiment illustrating all the important features of this nonlinear chaotic system. In an operational amplifier circuit conventionally used to simulate the free fall of a ball in constant gravity, current feedback through a precision diode rectifier is used to model free fall when the rectifier is backward biased, and the bounce when the rectifier is conducting. The ease with which parameters are controlled and variables measured permits the investigation in great detail of the specific dynamic behavior of the bouncing ball.
Entropy production and the second law of thermodynamics: An introduction to second law analysis
Authors: Marcella Thomas V.
Published: September 2005

Analyzing a process in terms of entropy production is shown to provide a quantitative approach to the second law of thermodynamics. The second law, ΔS≥0, is applied to the work–entropy relation obtained by rewriting the first law of thermodynamics in terms of the total entropy increase. The significance of entropy in macroscopic thermodynamics is established, and the limitations imposed by the second law are made evident. Irreversibility, entropy production, and the degradation of energy are seen as manifestations of the second law. The work–entropy relation indicates that entropy-producing irreversibilities are always accompanied by an amount of energy Wlost=TΔS that becomes unavailable to do work. The Kelvin–Planck and Clausius forms of the second law, as well as Carnot’s principle and the inequality of Clausius, are obtained from the work–entropy relation. It is shown that the increase in entropy for a system is due both to heat flowing into it, and to internal irreversibilities. Availability and the second-law efficiency are discussed.
Time scales in the dynamics of the Lorentz electron gas
Authors: Piasecki J.
Published: September 2005

The dynamics of the classical Lorentz electron gas acted upon by an external field is studied. The aim of the paper is to provide an instructive example of the application of the multiple time-scale method. The subtlety and the rich physical content of the problem show in the appearance of quite different stages in the evolution of the gas: switching on effects of the field, quasistationary linear response regime, long-time field dominated heating of the gas. The results reported here had been obtained previously in a different way.
Further properties of hydrogenic wave functions
Authors: Hey J. D.
Published: September 2005

The generalized and canonical momentum operators in spherical polar coordinates are derived and discussed, and the radial operators applied to the evaluation of the Heisenberg uncertainty relation for bound states of hydrogenic atoms. The two Pasternack relations, which connect the expectation values 〈rk〉 for values of k differing by an integer, are examined, as well as a generalization of the first relation, and the advantages which they hold for computational purposes discussed. An earlier calculation by the present author, of the electron impact ionization cross section for hydrogen atoms in the 2S metastable state, is compared with other experimental data from the literature. The calculation of the wavelengths of transitions between hydrogen-like levels in highly excited ions possessing a few additional, tightly bound, electrons is described and compared with experimental data.
An alternative calculation of light bending and time delay by a gravitational field
Authors: Bruckman W. , Esteban E. P.
Published: September 2005

An alternative method is proposed to calculate light bending and time delay in weak and strong gravitational fields. This approach is elementary, straightforward and uses mathematica, a computer algebra system, to perform the numerical calculations.
Resource Letter ETDSTS-1: Experimental tests of the discrete space-time symmetries
Authors: Commins Eugene D.
Published: September 2005

This Resource Letter provides a guide to the literature on experimental tests of space-inversion symmetry or parity (P), charge conjugation symmetry (C), time reversal symmetry (T), and the combined symmetries CP and CPT. Journal articles and books are cited for the following topics: early history, parity nonconservation in charged weak interactions, parity nonconservation in high-energy polarized-electron scattering, parity nonconservation in atoms, CPT invariance, tests of C-invariance, CP violation in neutral kaon decay, tests of time-reversal invariance, and search for electric dipole moments. [The letter E after an item indicates elementary level or material of general interest to persons becoming informed in the field. The letter I, for intermediate level, indicates material of a somewhat more specialized nature, and the letter A indicates rather specialized or advanced material.]
More than one mystery: Quantum interference with correlated charged particles and magnetic fields
Authors: Silverman M. P.
Published: September 2005

Examples of charged-particle interferometry are descibed whereby isolated magnetic fields—i.e., fields through which the particles do not pass—influence the clustering, as well as spatial distribution, of the particles. The configurations, which combine features characteristic of (i) Aharonov–Bohm and Hanbury Brown–Twiss experiments, and (ii) Aharonov–Bohm and Einstein–Podolsky–Rosen experiments, manifest simultaneously the effects of three distinct kinds of interference: (i) interference, dependent upon optical path length difference, resulting from wavelike propagation of particles; (ii) interference, dependent upon confined magnetic flux, resulting from particle charge and spatial topology; and (iii) interference, dependent upon quantum statistics, resulting from particle indistinguishability under exchange.
Kinetic theory: Understanding nature through collisions
Authors: Cohen E. G. D.
Published: September 2005

The attempts to understand the macroscopic behavior of fluids, in particular their nonequilibrium properties, in terms of the dynamics of the many particles, out of which they consist, are sketched from Clausius, in the middle of the 19th century, to the present day. The fundamental role that collisions play for dilute as well as dense gaseous or liquid systems is emphasized. The main difficulty is to identify the relevant collision sequences in the myriads of collisions that go on in a macroscopic system. While for dilute gases uncorrelated binary collisions dominate, as was already known in the 19th century, relevant correlated collision sequences for dense gases and liquids have only been identified in the last 25 years, leading to vortex and cage diffusion. Applications to transport coefficients are discussed.
Light polarization: A geometric-algebra approach
Authors: Baylis W. E. , Bonenfant J. , Derbyshire J. , Huschilt J.
Published: September 2005

The geometric algebra of three-dimensional space (the ‘‘Pauli algebra’’) is known to provide an efficient geometric description of electromagnetic phenomena. Here, it is applied to the three-dimensional Stokes subspace to describe the polarization of an approximately monochromatic collimated beam of electromagnetic radiation. The coherency density ρ is a real element of the algebra whose components are the four Stokes parameters: a scalar representing the total photon flux density plus a three-dimensional vector whose direction and length in the Poincaré sphere give the type and degree of polarization. The detection of the radiation and the incoherent and coherent modification of the polarization by various optical elements are calculated by algebraic multiplication which has faithful representations in 2×2 matrices. One matrix representation of ρ is the coherency matrix with which Jones and Mueller matrices are related whereas another representation is the spin density matrix. However, the calculations are simplest to perform and interpret in the algebraic form independent of any particular matrix representation. It is shown that any possible change in the Stokes parameters can be treated algebraically by a combination of attenuation, depolarization, polarization, and rotation transformations of ρ. The geometric algebra thus unifies Stokes parameters, the Poincaré sphere, Jones and Mueller matrices, and the coherency and density matrices in a single, simple formalism.
Factors of 2 in magnetic moments, spin–orbit coupling, and Thomas precession
Authors: Corben Herbert C.
Published: September 2005

The frequency of Thomas precession and the magnitude of spin–orbit coupling are shown to follow directly from conservation laws of momentum, angular momentum, and energy in relativistic classical mechanics, without transforming to axes that are instantaneously at rest with respect to the orbiting spinning particle.
Cooling of a vertical cylinder by natural convection: An undergraduate experiment
Authors: Spuller J. E. , Cobb R. W.
Published: September 2005

The transient cooling of a vertical cylinder by natural convection is studied in a computerized undergraduate laboratory experiment. The dependence of the heat transfer coefficient on temperature is determined using simple data fitting algorithms. The results of the experiment clearly show that the natural convection heat transfer coefficient is proportional to ΔT1/4, in agreement with previously published values.
An exact Markovian analysis of effusion
Authors: Gillespie Daniel T.
Published: September 2005

Effusion in an ideal gas is analyzed stochastically, without imposing any approximations on the governing master equation. The exercise affords a physically motivated survey, at a fairly elementary level, of some key concepts, techniques and results of Markov process theory.
Educating women for success in physics: Lessons from Turkey
Authors: Menard Albert , Uzun Ali
Published: September 2005

A comparison of Turkish and U.S. statistics shows that women in Turkey earn a much larger percentage of physics degrees at all levels than do women in the United States. The Turkish educational system is structured so that female students take the same mathematics and science courses at the same level of skill in high school as do male students. This common background is followed by much greater success for Turkish women university students in all areas of science and engineering.
An integrable classical two-spin system
Authors: Gade S. , Gade E.
Published: September 2005

An integrable classical two-spin system is considered with characteristics which are particularly suited for elucidating the properties of integrable systems with two degrees of freedom. The foliation of phase space by the rational and irrational tori is shown with projections onto a particular phase space plane, an expression for the winding number is obtained, and the dense coverage of the irrational tori by the quasiperiodic trajectories is easily demonstrated for this system.
Visual distortions near a neutron star and black hole
Authors: Nemiroff Robert J.
Published: September 2005

The visual distortion effects visible to an observer traveling around and descending to the surface of an extremely compact star are described. Specifically, trips to a ‘‘normal’’ neutron star, a black hole, and an ultracompact neutron star with extremely high surface gravity, are described. Concepts such as multiple imaging, red- and blue-shifting, conservation of surface brightness, the photon sphere, and the existence of multiple Einstein rings are discussed in terms of what the viewer would see. Computer generated, general relativistically accurate illustrations highlighting the distortion effects are presented and discussed. A short movie (VHS) depicting many of these effects is available to those interested free of charge.
Lyapunov exponents for pedestrians
Authors: Earnshaw J. C. , Haughey D.
Published: September 2005

The exponential divergence of chaotic trajectories of a driven nonlinear oscillator is considered. A particularly simple method of determination of the Lyapunov exponents of experimental data is shown to yield quantitative estimates which scale with the control parameter of the system in accord with expectation. Numerical comparisons with conventional approaches, which are unsuited to pedagogic use, demonstrate the adequacy of the present method in this context.
Chaos in a computer-animated pendulum
Authors: Kautz R. L.
Published: September 2005

A classroom demonstration based on computer animation illustrates chaotic motion in a driven pendulum. Generated by a 76 line BASIC program that runs on PC-compatible computers, the animation shows four simultaneous displays, including the pendulum and its trajectory in state space. The program can be used to illustrate periodic attractors, symmetry breaking, period doubling, and chaos.
Experimental study of the Helmholtz resonance of a violin
Authors: Vandegrift Guy
Published: September 2005

The violin supports a Helmholtz resonance, acting like a driven, damped harmonic oscillator. The amount of damping can be measured from the width of the response curve, and also from the decay of an undriven oscillator. The phase shift between driver and resonator is also consistent with theory. Shifts in resonant frequency due to changing the aspect ratio of the f hole are measured and found to be in qualitative agreement with a convenient formula for the resonant frequency associated with a long thin aperture.
On the ‘‘explanation’’ of the null results of Trouton–Noble experiment
Authors: Singal Ashok K.
Published: September 2005

It is shown that a previous explanation of the null results of the Trouton-Noble experiment, as suggested in the literature in terms of a modified definition of energy-momentum density of electromagnetic fields, is beset with many difficulties. Contrary to what was claimed earlier, a ‘satisfactory’ explanation of the null results of the Trouton-Noble experiment in no way demands a change in the standard definition of the electromagnetic energy-momentum density. The pertinent ‘paradox’ of an electromagnetic torque on a freely suspended, charged parallel plate capacitor, as seen from a relatively moving frame of reference, is resolved using the conventional formulation of the energy and momentum densities of electromagnetic fields.
Delta function expansions, complex delta functions and the steepest descent method
Authors: Lindell Ismo V.
Published: September 2005

Expansion of concentrated functions in terms of a delta function series is discussed with examples. The delta function is extended into the complex plane in the limit of the analytic Gaussian function. It is demonstrated that problems normally handled with the steepest descent method can be simply expressed as an integration of the delta function in the complex plane, which can be more easily grasped by students.
Getting contextual and nonlocal elements-of-reality the easy way
Authors: Clifton Rob
Published: September 2005

What if Einstein, Podolsky, and Rosen were right that quantum mechanics is incomplete, and there do exist ‘‘elements-of-reality’’ corresponding to all observables whether or not they are compatible? The implications are surprising. Not only must the values of these elements-of-reality depend upon what measurements are actually performed on the system, but also upon measurements performed at spacelike separation from it! The former dependence has been dubbed ‘‘contextualism,’’ and the latter ‘‘nonlocality.’’ It is important for students to understand the necessity of these two features, if only to reinforce the point that a straightforward classical recasting of quantum theory in terms of pre-existing measurement independent elements-of-reality is not feasible. Unfortunately the argument for contextualism, in particular, is daunting due to its reliance on an elaborate geometrical argument. I aim here to minimize the geometry needed to argue for contextualism by using some ideas inspired by the original arguments of Bell and of Kochen and Specker. Using similar methods, I simplify the closely related geometrical argument for nonlocality due to Heywood and Redhead and to Stairs.
Simple derivation of a general relationship between imaginary- and real-time Green’s/correlation functions
Authors: Yu-Kuang Hu Ben
Published: September 2005

Using a simple contour deformation method it is shown that there is a very general relationship between imaginary-time correlation functions and real-time commutators. This method is used to show easy derivations of the equivalence between (1) two dissimilar forms of the Kubo formula for the electrical conductivity tensor σμν(ω), and (2) the imaginary-time-ordered Matsubara and the real-time retarded Green’s functions. In deriving example (1), the infra- red divergent paramagnetic and diamagnetic parts of σμν(ω) arise naturally from the imaginary-time formulation, and can be explicitly combined to give a single simple regular expression at ω→0.
Millikan Lecture 1992: Hypermedia and the knowing of physics: Standing upon the shoulders of giants
Authors: Fuller Robert G.
Published: September 2005

Hypermedia is defined and its roots briefly discussed. Models of knowing physics and of intrinsically motivating instruction are presented. Uses of hypermedia to increase the knowing of physics and the motivation of learners are proposed.
A magnetic suspension system for atoms and bar magnets
Authors: Sackett C. , Cornell E. , Monroe C. , Wieman C.
Published: September 2005

A three dimensional magnetic confinement system is presented which will trap both macroscopic and atomic magnetic dipoles. The dipole is confined by dc and oscillating magnetic fields, and its motion is described by the Mathieu equation. Most aspects of the dynamics of the trapped objects depend only on the ratio of the magnetic moment to the mass of the dipole. Similar motion was observed for masses varying over 21 orders of magnitude (from 1 atom to 0.2 g). The trap is constructed from inexpensive permanent magnets and small coils which are driven by 60 Hz line current. The design of the trap as well as the behavior of the trapped particle are discussed herein.
The ray form of Newton’s law of motion
Authors: Evans James
Published: September 2005

Through the use of the optical-mechanical analogy, Newton’s law of motion may be cast into the same form as the equation for the ray in the geometrical optics of gradient-index media. The resulting equation is called the ray form of Newton’s law of motion. The same equation may be derived by taking the geometrical optics limit of quantum mechanics. The ray form of Newton’s law of motion is derived in three different ways and is applied in the solution of several problems.
The computerized student laboratory: Motion in a potential well
Authors: Eckstein Shulamith Graus
Published: September 2005

The motion of a body in a potential well is studied in the computerized undergraduate student laboratory. Both large and small oscillations are studied. Small oscillations are found to be harmonic, and the frequency of the oscillations are found to tend to a constant value as the amplitude tends to zero. The trajectory in phase space is studied for both small and large oscillations. The potential energy is found as a function of position by two methods.
Modelling tidal effects
Authors: White Gary , Mondragon Tony , Slaughter David , Coates Dorothy
Published: September 2005

Two for demonstrating and experimenting with various tidal effects are presented. The first takes advantage of the approximately inverse-square nature of the force law for magnetic poles and exhibits symmetric tidal bulges on opposite sides of the planet, analogous to the of the earth. The second demonstration apparatus is a realization of the ‘‘rubber sheet’’ geometry analogy that is often used to potential wells of massive bodies in space. By rolling various objects on the of a stretched cloth one can effectively demonstrate tidal bulges, the Roche limit, and other well-known astrophysical phenomena.
Measure the earth’s radius while boating on one of its lakes
Authors: Goodman Frank O.
Published: September 2005

A very simple and enjoyable method of measuring the earth’s radius while boating on a lake is described. Apart from equipment that is usually carried while boating, no additional apparatus is required and the cost of the experiments is zero.
The measurement of astronomical parallaxes with CCD imaging cameras on small telescopes
Authors: Ratcliff Stephen J. , Balonek Thomas J. , Marschall Laurence A. , DuPuy David L. , Pennypacker Carlton R. , Verma Ritu , Alexov Anastasia , Bonney Vivian
Published: September 2005

Small telescopes equipped with charge-coupled device (CCD) imaging cameras are well suited to introductory laboratory exercises in positional astronomy (astrometry). An elegant example is the determination of the parallax of extraterrestrial objects, such as asteroids. For laboratory exercises suitable for introductory students, the astronomical hardware needs are relatively modest, and, under the best circumstances, the analysis requires little more than arithmetic and a microcomputer with image display capabilities. Results from the first such coordinated parallax observations of asteroids ever made are presented. In addition, procedures for several related experiments, involving single-site observations and/or parallaxes of earth-orbiting artificial satellites, are outlined.
Negative mass can be positively amusing
Authors: Price Richard H.
Published: September 2005

Some insights into gravitation and mechanics, as well as some surprises, result from considering the dynamics of negative mass particles.
A bifurcation problem in hydrostatics
Authors: Duffy Brian R.
Published: September 2005

The equilibrium positions of a partially submerged rod supported at one end are considered. Simple examples of bifurcations occur, and the breaking of these bifurcations by an ‘‘imperfection’’ is discussed.
Scattering by a finite periodic potential
Authors: Sprung D. W. L. , Wu Hua , Martorell J.
Published: September 2005

The problem of scattering in one dimension by a potential which consists of N identical cells is solved in a transparent manner. The N-cell transmission and reflection amplitudes are expressed in terms of the single-cell amplitudes and the Bloch phase. As examples the results are applied to a row of delta-function potentials, and to a row of square wells, and it is shown that these expressions provide an immediate understanding of the results of detailed calculations.
Wormhole connecting two Reissner–Nordstrom universes
Authors: Harris Edward G.
Published: September 2005

We find an approximate solution to the Einstein–Maxwell equations that describes two Reissner–Nordstrom universes that are connected by a wormhole. A scalar field with negative energy is necessary to maintain the wormhole.
The unexpected path of the energy in a moving capacitor
Authors: Herrmann F.
Published: September 2005

Most physics students know little about energy flow distributions. The example shows the unexpected path of the energy in a familiar situation.
Anomalies for pedestrians
Authors: Holstein Barry R.
Published: September 2005

The subject of anomalies, i.e., quantum mechanical symmetry breaking, is addressed using only basic quantum mechanics. Examples from different areas of physics are examined.
Cherenkov radiation from a charge of finite size or a bunch of charges
Authors: Smith Glenn S.
Published: September 2005

A point charge moving in a medium with a constant speed greater than the speed of light in the medium produces Cherenkov radiation. When the medium is nondispersive, the potential functions and electromagnetic field for the point charge are singular along the surface of the Mach cone, and the spectrum (Fourier transform) of the field increases indefinitely with frequency. The purpose of this paper is to present a simple extension of the results for the point charge to a charge of finite size or a bunch of charges. The model adopted allows an analytical description of the potential functions and electromagnetic field near the surface of the Mach cone. The aforementioned singularities associated with the point charge are absent, and the spectrum for the field is bounded and given by a simple expression. The graphical displays presented for Cherenkov radiation from a charge of finite size clearly show the similarity to other familiar physical phenomena, e.g., the wake of a boat moving in shallow water. In addition, they provide physical insight into the process of radiation that should be useful for instruction.
Optical path difference measurements with a Michelson interferometer using a frequency modulated continuous wave ranging technique
Authors: Fritz Daniel J. , McLaughlin Daniel J.
Published: September 2005

A measurement technique is described which utilizes a frequency modulated AlGaAs semiconductor laser to measure the optical path difference (OPD) in a combination free space-fiber interferometer. The modulation technique employed here is referred to as frequency modulated continuous wave and has been exploited for many years in radar systems. The intent of this paper is to present the fundamentals of this technique as applied to a specific semiconductor laser, and to give a basic procedure for OPD measurements. In addition, the modulation characteristics of the laser are analyzed in terms of an optical frequency deviation given as both a function of time and driving current.
Measurement of inertial and noninertial properties of an air suspension gyroscope
Authors: de Lange O. L. , Pierrus J.
Published: September 2005

We report results of careful measurements of the periods for clockwise and anticlockwise precession (Tc and Ta) of an air suspension gyroscope. These periods were measured for various values of the frequency of spin f between 10 and 70 Hz. In our experiment Tc and Ta had a small, but significant, dependence on the current I which provides the magnetic field used to sustain the spin of the gyroscope against air friction. The measured periods depend linearly on I. The periods Tc0 and Ta0 obtained by extrapolation to I=0 are in good agreement with theoretical values: in particular, we find (i) Tc0+Ta0 (which is predominantly an inertial property dependent on the earth’s gravitational field) is proportional to f, and (ii) Tc0−Ta0 (which is a noninertial property dependent mainly on the Coriolis force) is proportional to f2, as required by theory. It is suggested that the dependence of Tc and Ta on I is associated with a torque provided by the magnetic drive which constrains the spin axis of the gyroscope to lie in very nearly a horizontal plane.