bluuebunny/crossref_metadata_2025 huggingface dataset:
The role of amplitude and phase of the Fourier transform in the digital image processing
Authors: Juvells I. , Vallmitjana S. , Carnicer A. , Campos J.
Published: September 2005

The analysis of the importance of the amplitude and the phase of Fourier transform has been carried out by means of combining these functions between two images and observing the reconstructed image after a second transform. This processing has been studied by taking into account several possibilities, especially for very structurally different images. It is proved that the phase carries the most relevant information, but when common images are combined with images constituted by strongly marked geometric forms it is not so evident and the amplitude could play a more important role.
The relativistic transformations of velocity, acceleration, and higher derivatives as differentials of nonlinear extensions of the Lorentz transformation
Authors: Nguyen D. B.
Published: September 2005

The formulas for the relativistic transformation of velocity, acceleration, and higher derivatives are obtained in a simple way using the concept of the differential of a function. Let F0 be a Lorentz transformation. Given the transformation Fn, this paper describes a process by which one can construct the transformation Fn+1. Starting with the given Lorentz transformation F0, this process yields a sequence of transformations F1, F2, F3,... . Although the Lorentz transformation F0 is linear, Fn, for all n>0, are nonlinear. The differentials of these nonlinear transformations give the correct transformation formulas for velocity, acceleration, and all higher-order derivatives.
Simply no hidden variables
Authors: Jordan Thomas F. , Sudarshan E. C. G.
Published: September 2005

It is shown very simply that for any two observables represented by Hermitian operators that do not commute, there is a state for which there is no joint probability distribution for the two observables.
Assumptions implying the Schrödinger equation
Authors: Jordan Thomas F.
Published: September 2005

A program of proofs is outlined to show how the linear structure of quantum mechanics can be derived from basic principles. For the dynamics part, three alternatives are reviewed briefly. They include the Kadison theorem for evolution of density matrices and the Segal–Simon theorem for evolution of observables in the Heisenberg picture. The focus is on Wigner’s theorem that gives linear operators for evolution of state vectors. New insights are described that motivate the key assumption about probabilities in that theorem. One is that it is implied by the second law of thermodynamics. Another is that it follows from assumptions that evolution in time preserves mixtures of states and preserves probabilities for what is in the mixture.
A tutorial approach to the thermal noise in metals
Authors: Dekker A. J. , Hickman H. , Chen T. M.
Published: September 2005

The Johnson–Nyquist formula for spontaneous voltage fluctuations across a conductor is rederived for metals at a tutorial level within the framework of the free-electron approximation. The spontaneous current fluctuations are linked directly to the occupancy fluctuations in the Fermi–Dirac distribution function for the conduction electrons and to the electron-scattering processes that are responsible for the electrical resistivity. It is also shown that an externally applied Ohmic current through a metal does not affect its thermal noise. The quantum limit of thermal noise is discussed briefly.
Measurements of the transient motion of a simple nonlinear system
Authors: Ojha Archana , Moon Stephen , Hoeling Barbara , Siegel P. B.
Published: September 2005

A freely rotating magnet placed above a solenoid and between a set of Helmholtz coils is used to examine properties of a nonlinear system. Accurate measurements of the angular velocity are made with a photogate timing device. The period-doubling route to chaos, multiple periodicities, and the behavior of transient motion are observed and measured.
Charged particle trajectories in simple nonuniform magnetic fields
Authors: Repko Jane M. , Repko Wayne W. , Saaf Allan
Published: September 2005

The motion of charged particles in magnetic fields whose magnitude varies as a power of one of the coordinates in the plane of the motion is investigated. For interesting power laws, the parametric equations for the trajectory are expressible in terms of Jacobi elliptic functions. These represent a rather natural generalization of the elementary trigonometric solutions that are encountered in the case of a constant magnetic field.
Demonstration of helicity conservation during magnetic reconnection using Christmas ribbons
Authors: Pfister Hans , Gekelman Walter
Published: September 2005

This article shows how a simple Christmas ribbon can be used to demonstrate a relatively complex physical phenomenon: the conservation of helicity during magnetic reconnection. The physical term, helicity, and the process of magnetic reconnection will be introduced and explained in detail. The ‘‘helicity meter,’’ a very simple device that will help in the determination of the helicity of certain topological configurations, will also be introduced.
Improved numerical solutions of Laplace’s equation
Authors: Gash Philip W.
Published: September 2005

Three different methods for generating numerical solutions of Laplace’s equation are derived using a differential operator formalism for a Taylor series expansion of the electric potential about a point. The expansions are evaluated on three different two-dimensional grids in the x-y plane to yield algorithms good up to, but not including, fourth order. The accuracy and convergence of the algorithms are compared by applying them to a rectangular boundary value problem. Second, it is shown that the convergence criterion for numerical solutions can be interpreted as a charge density; and, therefore, the numerical solutions are, in fact, solutions of Poisson’s equation. Further, it is demonstrated that the numerical solutions of Laplace’s equation are bounded above and below by the solutions of Poisson’s equation corresponding to a maximum uniform charge density derived from the convergence criterion. For this reason, it is recommended that numerical solutions of Laplace’s equation should be accompanied by a statement of the maximum uniform charge density.
Laboratory studies of air flow visualization using holographic interferometry
Authors: Peiponen K.-E. , Hämäläinen R. M. K. , Asakura Toshimitsu
Published: September 2005

Holographic interferometry was used to visualize a low-velocity cooled air flow. The physical properties of the heat exchange of the system were investigated using holographic interferometry.
A simple system for radon-in-air concentration determinations
Authors: Howard A. J. , Carroll S. E. , Strange W. P.
Published: September 2005

Electrostatic precipitation within a 20.4-ℓ container onto a solid-state charged-particle detector is employed to simultaneously collect and detect radon-decay daughter ions. Essentially complete isolation of the 6003-keV α particles associated with 21884Po decay, for which the half-life is 3.05 min, allows radon concentrations in clean, dry air of 4 pCi/ℓ to be determined in 15 min of operation with ∼11% statistical uncertainty. A detailed description of this simple system is given, and its absolute detection efficiency is measured as a function of precipitation voltage and relative humidity.
The use of a nearly confocal interferometer for the study of transverse modes of a cavity
Authors: Kane D. M.
Published: September 2005

An experiment has been developed that enables students to use a nearly confocal interferometer to measure and verify the predicted frequency spacing of adjacent transverse modes of the nearly confocal interferometer.
Effusion of a dilute gas revisited: Van Kampen’s expansion
Authors: Schat C. , Abramson G. , Wio H. S.
Published: September 2005

The problem of effusion of a dilute gas through a hole by means of van Kampen’s systematic Ω expansion has been studied. In this way, the macroscopic equation as well as the Fokker–Planck equation for the fluctuations around the macroscopic behavior have been obtained and some dubious points in a recent analysis of the problem clarified.
An inverted liquid demonstration
Authors: Michaelis M. M. , Woodward T.
Published: September 2005

With the help of a hand-held jigsaw and a tin of syrup, the little known dynamically stabilized inverted liquid experiment can be demonstrated to large classes. Lengthy effective potential arguments are short-circuited by a simple inverted U-tube theory accessible to most. The role of viscosity and wall effects is discussed. The first dynamic stabilization experiment with water is reported.
Supersymmetry-inspired WKB approximation in quantum mechanics
Authors: Dutt Ranabir , Khare Avinash , Sukhatme Uday P.
Published: September 2005

The supersymmetry-inspired WKB approximation (SWKB) in quantum mechanics is discussed in detail. The SWKB method can be easily applied to any potential whose ground-state wave function is known. It yields eigenvalues that are exact for large quantum numbers n (as any WKB approximation should in the classical limit). Furthermore, for the important special case of ‘‘shape-invariant’’ potentials, the SWKB approach gives the exact analytic expressions for the entire bound-state spectra. A study of some nonshape-invariant, but solvable, potentials suggests that shape invariance is not only sufficient but perhaps even necessary for the SWKB approximation to be exact. A comparison of the WKB and SWKB predictions for the bound-state spectra of a number of potentials reveals that in many cases the SWKB approach does better than the usual WKB approximation.
Study of the effect of relativistic time dilation on cosmic ray muon flux—An undergraduate modern physics experiment
Authors: Easwar Nalini , MacIntire Douglas A.
Published: September 2005

An experiment to study the effect of relativistic time dilation on secondary muon fluxes observed at different altitudes is described in this article. Muons, produced as secondary particles from the interaction of primary cosmic rays with the upper atmosphere, form a natural and abundant source of subatomic ‘‘clocks’’ moving at very high speeds. The measured muon flux on a mountain relative to that measured at sea level can be compared to predictions from calculations that take into account the relativistic time dilation in the muon frame. Situations under which such an experiment can be successfully performed are explored with a day-long field trip to a nearby mountain. This experiment has been developed at Smith College as a module in the Five College cooperative undergraduate advanced laboratory course (other participating institutions are Amherst College, Mount Holyoke College, and the University of Massachusetts).
Fibonacci sequence, golden ratio, and a network of resistors
Authors: Srinivasan T. P.
Published: September 2005

It is shown that the ratio of the effective resistance of an infinite network of identical resistors to the resistance of a constituent resistor is equal to the golden ratio.
Transition energies for excited states of helium: An evaluation of two simple approximation techniques
Authors: Weida Miles J. , Schroeder Thomas M. , Waxer Leon J. , Whitten Barbara L.
Published: September 2005

Two standard approximation techniques are applied to the problem of calculating the transition energies of the 3-2 lines in the helium spectrum. First-order perturbation theory gives very poor results, in some cases inverting the order. A simple one-parameter variational calculation, on the other hand, gives results that are remarkably accurate. A comparison of these results gives insight into the nature of both approximations. These calculations can be performed mostly analytically, with the help of a symbolic algebra computer program, and are well within the reach of upper-division undergraduates in an elementary quantum mechanics course.
Chaos in a double pendulum
Authors: Shinbrot Troy , Grebogi Celso , Wisdom Jack , Yorke James A.
Published: September 2005

A novel demonstration of chaos in the double pendulum is discussed. Experiments to evaluate the sensitive dependence on initial conditions of the motion of the double pendulum are described. For typical initial conditions, the proposed experiment exhibits a growth of uncertainties which is exponential with exponent λ=7.5±1.5 s−1. Numerical simulations performed on an idealized model give good agreement, with the value λ=7.9±0.4 s−1. The exponents are positive, as expected for a chaotic system.
Quantum mechanical tunneling in an ohmic contact
Authors: Crofton J. , Barnes P. A. , Bozack M. J.
Published: September 2005

The tunneling probability for majority carriers in an ohmic contact to n-type GaAs has been calculated by directly solving the Schrödinger equation for the wave functions in the semiconductor depletion region. The direct solution is straightforward and relies on fewer assumptions than previous calculations based on the WKB approximation. It also provides a useful application of undergraduate quantum mechanics to an important area of VLSI semiconductor technology. The direct solution can be performed on an 80286 machine in less than a minute and yields tunneling probabilities roughly twice as large as the WKB approximation at most electron energies. The tunneling probability is then used to calculate the contact resistance as a function of doping for the contact. The contact resistances are approximately one-half the resistances calculated using the WKB method.
On the interesting behavior of a gimbal-mounted gyroscope
Authors: Case William B. , Shay Michael A.
Published: September 2005

The behavior of a gyroscope mounted in frictionless gimbal bearings when the outer ring is constrained to rotate at a constant rate is examined. The resulting motion of the rotor axis is described, accounted for by an elementary argument followed by a more complete treatment. The behavior of the rotor in an unusual parameter regime is also discussed. The equations of motion for a motor-driven rotor are obtained and compared with the frictionless case.
Light rays in gradient index media: A laboratory exercise
Authors: Mamola K. C. , Mueller Wilhelm F. , Regittko Bruce J.
Published: September 2005

A simple laboratory experiment is described for tracing light rays in a medium with spatially varying index of refraction. The analysis is at a level appropriate to an introductory optics course.
Reflection, refraction, and transmission of plane electromagnetic waves from a lossless dielectric slab
Authors: Reali G. C.
Published: September 2005

The problem of propagation of plane electromagnetic waves, impinging at a certain angle on a linear, lossless, dielectric slab in vacuum, is solved in the framework of molecular optics. An integral method is used, by which reflection, refraction, and transmission are seen to arise from superposition of the incident field and the wavelets radiated by the induced polarization. The physics of the radiation-matter interaction and the origin of external and internal Brewster angles is emphasized.
Inversion of transmission for the one-dimensional Dirac equation
Authors: Clerk G. J. , Davies A. J.
Published: September 2005

It is shown that the transmission coefficient for the Dirac equation does not depend on the direction in which the barrier is traversed in one-dimensional quantum mechanics. As an explicit example, the case of two consecutive square barriers of unequal height and width are considered.
Classical view of the properties of Rydberg atoms: Application of the correspondence principle
Authors: Hezel T. P. , Burkhardt C. E. , Ciocca M. , He L-W. , Leventhal J. J.
Published: September 2005

The properties of Rydberg atoms are contrasted with those of hydrogen atoms using both classical and quantal points of view. It is shown that, classically, the effects of the ionic core of the Rydberg atom produce a precession of the otherwise Keplerian elliptical orbit of the excited electron, and that this precession is responsible for the nonhydrogenic properties. Using the correspondence principle, classical properties are then related to quantum mechanical properties by correlating the precession frequency with the quantum defect δl. The linear and quadratic Stark effects are also discussed and it is shown that a negative polarizability of the atom is a consequence of a positive ∂δl/∂l. In the Appendix, the ‘‘gravitational defect’’ associated with the precession of the perihelion of the Keplerian orbit of the planet Mercury is presented.
All about work
Authors: Mallinckrodt A. John , Leff Harvey S.
Published: September 2005

A comprehensive ‘‘taxonomy of work’’ is developed to clarify the confusing potpourri of worklike quantities that exists in the literature. Seven types of work that can be done on a system of particles interacting internally and/or with its environment are identified and reviewed. Each work is defined in terms of relevant forces and displacements; mathematical connections between the works are delineated; work-energy relationships are derived; and the Galilean transformation properties of the works and corresponding energy changes are obtained. The results are applied to several examples, illustrating subtle distinctions between the various works and showing how they can be used to bridge the conceptual gap between the ‘‘pure’’ mechanics of point particles and the thermodynamics of macroscopic matter.
Fourier series and the Gibbs phenomenon
Authors: Thompson William J.
Published: September 2005

The occurrence in Fourier series of an overshoot effect near function discontinuities, called the Gibbs phenomenon, is discussed from a pedagogical viewpoint. The reader is led along a path to discover why the phenomenon depends only upon the existence of the discontinuity, but not on other properties of the function that is Fourier analyzed.
The pathological kinematics of unphysical force laws
Authors: Mallinckrodt A. John
Published: September 2005

Particles subject to repulsive power-law forces of position and propulsive power-law forces of velocity exhibit dramatically pathological kinematics. Although the behaviors examined in this article are the result of the unphysical nature of these force laws and the surprising results might, as a result, be viewed as merely academic, understanding them is important for resolving the otherwise paradoxical results of some numerical simulations.
Conservation of linear and angular momentum and the interaction of a moving charge with a magnetic dipole
Authors: Hnizdo V.
Published: September 2005

The operation of the laws of momentum and angular momentum conservation in the interactions between current-carrying bodies and charged particles is analyzed using the correct expression for the force on a magnetic dipole, which takes into account the possible presence of hidden momentum in a current-carrying body. At nonrelativistic velocities, Newton’s third law holds for the interactions, and thus the mechanical momentum associated with the motion of current-carrying bodies and charged particles in a closed system is conserved itself in the nonrelativistic limit. There is no conflict with overall linear momentum conservation because the electromagnetic field momentum is equal and opposite to the hidden momentum of the current-carrying bodies. However, the field angular momentum in a system is not compensated by hidden angular momentum, and thus only the sum of mechanical angular momentum, which must include any hidden angular momentum, and field angular momentum is conserved.
Planck’s constant determination from black-body radiation
Authors: Dryzek J. , Ruebenbauer K.
Published: September 2005

A method originally described by Crandall and Delord has been improved to measure the ratio of the Planck to the Boltzmann constant with low cost apparatus. Such a system can be easily implemented in high school or college laboratories. These improvements enable one to attain accuracies of 2% for Planck’s constant.
Shape invariance of Coulomb problems
Authors: de Lange O. L. , Welter A.
Published: September 2005

It is shown that the Coulomb problems associated with the Schrödinger, Klein–Gordon, and Dirac equations are shape invariant. This property is used to obtain the energy eigenvalues and the normalized coordinate-space eigenfunctions for bound states of these problems.
Displacement, velocity, and frames of reference: Phenomenographic studies of students’ understanding and some implications for teaching and assessment
Authors: Bowden J. , Dall’Alba G. , Martin E. , Laurillard D. , Marton F. , Masters G. , Ramsden P. , Stephanou A. , Walsh E.
Published: September 2005

Student understanding of fundamental concepts in kinematics has been explored using the phenomenographic research method. University and high school physics students were interviewed and their understandings of displacement, velocity, and frames of reference have been analyzed in particular problem contexts. Descriptions of the different ways students understand the concepts have been developed and relations between the different levels of understanding have been identified. The data highlight the contextual nature of learning and the need for teachers to focus on the nature of student understanding in specific contexts using questions that require qualitative explanation by students. In particular, it is demonstrated that success in mechanical, quantitative problem solving can mask inadequate understanding of basic concepts that hinders learning in later years of study of the subject. Implications for teaching and assessment are discussed.
Magnetic monopoles, Galilean invariance, and Maxwell’s equations
Authors: Crawford Frank S.
Published: September 2005

Maxwell’s equations have space reserved for magnetic monopoles. Whether or not they exist in our part of the universe, monopoles provide a useful didactic tool to help us recognize relations among Maxwell’s equations less easily apparent in the approach followed by many introductory textbooks, wherein Coulomb’s law, Biot and Savart’s law, Ampere’s law, Faraday’s law, Maxwell’s displacement current, etc., are introduced independently, ‘‘as demanded by experiment.’’ Instead a conceptual path that deduces all of Maxwell’s equations from the near-minimal set of assumptions: (a) Inertial frames exist, in which Newton’s laws hold, to a first approximation; (b) the laws of electrodynamics are Galilean invariant—i.e., they have the same form in every inertial frame, to a first approximation; (c) magnetic poles (as well as the usual electric charges) exist; (d) the complete Lorentz force on an electric charge is known; (e) the force on a monopole at rest is known; (f) the Coulomb-like field produced by a resting electric charge and by a resting monopole are known. Everything else is deduced. History is followed in the assumption that Newtonian mechanics have been discovered, but not special relativity. (Only particle velocities v≪c are considered.) This ends up with Maxwell’s equations (Maxwell did not need special relativity, so why should we,) but facing Einstein’s paradox, the solution of which is encapsulated in the Einstein velocity-addition formula.
Laplace’s equation in freshman physics
Authors: Canova Brent P.
Published: September 2005

Heat-sensitive liquid crystal sheets are used to observe quantitatively the temperature contours on the surface of an aluminum slab subjected to constant-valued boundary conditions. The experiment is then modeled numerically using spreadsheet techniques. The theoretically derived power series solution to the Laplace equation is given and students use the spreadsheet to numerically investigate its convergence. In a single laboratory session, the introductory physics student studies the Laplace equation from experimental, numerical, and theoretical perspectives.
Can galaxies exist within our particle horizon with Hubble recessional velocities greater than c?
Authors: Stuckey W. M.
Published: September 2005

A simple, global picture of photon exchange in the flat, matter-dominated universe is presented using relativistic cosmology. Equations for the photon’s recessional velocity and position relative to the receiver are derived. The results are discussed in the context of the ‘‘raisin bread universe.’’ Contrary to intuition, it is shown that the Hubble recessional velocity of the emitter can exceed the speed of light for sources within the particle horizon of the receiver. The model used to obtain these results can be used by introductory astronomy students to obtain the proper distance and the time-of-flight distance to sources with large redshifts.
Quantum interference viewed in the framework of probability theory
Authors: Herbut Fedor
Published: September 2005

An additivity equality of probability theory is suggested to define (relative) noninterference. Interference is deviation from this additivity. It is shown that two-slit interference fits into this scheme. It is argued that the physical meaning of quantum interference is an observable deviation of quantum filtering from quantum occurrence of events. The expounded view should restore the essence of textbook treatment of interference in a precise and correct probability-theoretic framework. The approach is essentially a continuation of a critical argument presented by Ballentine.
The Gaussian formula and the elusive fourth principal ray
Authors: Allen Sue
Published: September 2005

The Gaussian formula in geometrical optics can be derived without relying on specific mechanisms such as reflection and refraction. The extensive use of symmetries in this derivation clarifies the deep analogy between mirrors and lenses, and reveals the natural existence of four, not three, principal rays for both mirrors and lenses.
Mutual inductance M12=M21: An elementary derivation
Authors: Crawford Frank S.
Published: September 2005

By using the energy U stored in the magnetic field, we have presented an elementary derivation of the relationship between the mutal inductance M of coils 1 and 2 such that M12=M21. (AIP)
Phase-conjugate Michelson interferometers for all-optical image processing and computing
Authors: Norman Jeffrey B.
Published: September 2005

When the mirrors of a conventional Michelson interferometer are replaced by phase-conjugate mirrors, the resulting interferometer displays dramatically altered behavior which makes it ideally suited to performing important operations in parallel optical image processing and optical computing. The phase-reversing property and real-time response of the phase-conjugate mirrors make this type of interferometer much more immune to spatially uniform and nonuniform phase distortions, both static and dynamic. Phase-conjugate interferometers are remarkably stable, sensitive only to real amplitude disturbances or information in the arms, and they readily display the subtraction, addition, intensity inversion, spatial differentiation and, in certain cases, temporal differentiation of two-dimensional optical images.
‘‘Frames of Reference’’ revisited
Authors: Steyn-Ross Alistair , Ivey Donald G.
Published: September 2005

The PSSC teaching film, ‘‘Frames of Reference,’’ was made in 1960, and was one of the first audio-visual attempts at showing how your physical ‘‘point of view,’’ or frame of reference, necessarily alters both your perceptions and your observations of motion. The gentle humor and original demonstrations made a lasting impact on many audiences, and with its recent re-release as part of the AAPT Cinema Classics videodisc it is timely that we should review both the message and the methods of the film. An annotated script and photographs from the film are presented, followed by extension material on rotating frames which teachers may find appropriate for use in their classrooms: constructions, demonstrations, an example, and theory.
Railgun recoil, ampere tension, and the laws of electrodynamics
Authors: Robson A. E. , Sethian J. D.
Published: September 2005

There has recently been a revival of an old controversy over whether Ampere’s original law of force between current elements is to be preferred over the more familiar and universally used Biot–Savart–Lorentz law. Although it is agreed that the two laws give identical results when used to calculate the force between two circuits, it has been claimed that if Ampere’s law is applied to the action of a circuit upon part of itself it predicts internal longitudinal forces that are excluded by Biot–Savart–Lorentz. The existence of longitudinal forces has been inferred from observations of the buckling of the rails in a railgun, attributed to compressive stress, and the fracture of long wires subjected to pulsed currents, attributed to ‘‘Ampere tension.’’ An experiment has been performed that should provide an unambiguous demonstration of this longitudinal force, if it exists. The apparatus consisted of a rigid coaxial circuit in which an unsymmetrical section of the center conductor was free to move in the axial direction under the influence of the longitudinal force. Pulsed currents of up to 100 kA were passed through the circuit but no evidence of a longitudinal force was found. It is shown that this result is consistent with Ampere’s force law, and that claims that the law predicts longitudinal forces are based on the incomplete application of the law.
Path integral approach to the small polaron model in the atomic limit
Authors: Cruz Miguel G.
Published: September 2005

The formalism of functional integration in the holomorphic representation is illustrated by calculating the partition function for the small polaron Hamiltonian in the atomic limit. As an introduction, the standard construction of the functional integral representation of the partition function for a coupled fermion-boson system is reviewed.
Fall streaks: Parabolic trajectories with a twist
Authors: Bohren Craig F. , Fraser Alistair B.
Published: September 2005

Fall streaks are arcs in the sky composed of ice crystals falling from high-altitude cirrus clouds. With the crystals falling at their vertical terminal velocity and their horizontal velocity that of the local wind, the streaks are parabolas if the wind increases linearly with height. The dynamics of fall streaks is formally identical with that of drag-free projectiles−but with a twist: the roles of horizontal and vertical coordinates are reversed.
Two-quantum absorption: An undergraduate’s experiment in nonlinear optics
Authors: Payton B. W. , Sieradzan A.
Published: September 2005

An experimental arrangement suitable for the undergraduate laboratory is described which permits the quantitative study of two-quantum absorption in organic dye solutions. Experimental data for a series of dyes are presented and include spectra of two-quantum-induced fluorescence and evidence of its quadratic dependence on the excitation light intensity.
Where the Sun never sets: Solar insolation at the poles of Mercury
Authors: Suffern Kevin G.
Published: September 2005

Since the planet Mercury’s axis of rotation is perpendicular to the plane of its orbit, there exist regions at the north and south poles that are permanently in sunshine. This paper calculates the shape and size of these regions if Mercury were a perfect sphere. The eccentricity of Mercury’s orbit, combined with its 2:3 spin-orbit coupling result in these regions having a noncircular shape. They have a length of 60 km, a width of 48 km, and an area of 2146 km2.
ZAP! freshman electricity and magnetism using desktop experiments: A progress report
Authors: King John G. , Morrison Philip , Morrison Phylis , Pine Jerome
Published: September 2005

A set of informal experiments done with a safe and inexpensive kit of tools, household materials, and electronic components, meant for freshmen students of introductory electricity and magnetism is described. The students work for a term with electric and magnetic fields and their sources, starting with simple dc circuits and finishing with table-top microwaves. All apparatus is built, calibrated and used, not in on-campus supervised labs, but as a part of regular week by week homework, done usually in partnership. Experiment descriptions and quantitative results are reported in notebook form. A few years of actual teaching experience, both at MIT and at Cal Tech, are reviewed.
Dipoles at rest
Authors: Griffiths David J.
Published: September 2005

In a world populated by magnetic monopoles (as well as ordinary electric charges), there are two kinds of electric dipoles: those due to separated electric charges, and those due to current loops of magnetic charge. Similarly, there are two kinds of magnetic dipoles: those due to separated magnetic monopoles, and those due to electric current loops. This paper derives the potentials and fields of each of the four dipole species, and calculates the force, torque, energy, momentum, and angular momentum of each type, when placed (at rest) in a static external field (which may itself be produced by electric charges and currents, magnetic charges and currents, or all of these). Some implications and applications of the various results are discussed.
On Coulomb’s inverse square law
Authors: Heering Peter
Published: September 2005

The famous inverse square law in electrostatics, first published in 1785 by C. A. Coulomb, was strongly contested during the next 40 years, especially in Germany. Therefore, at the Carl von Ossietzky University Oldenburg a replication of the apparatus described by Coulomb was made, and the reasons were investigated why none of his contemporaries succeeded in reproducing his results. In addition the respective theoretical concepts of Coulomb, his supporters, and his opponents were analyzed.
Maxwell’s demon, rectifiers, and the second law: Computer simulation of Smoluchowski’s trapdoor
Authors: Skordos P. A. , Zurek W. H.
Published: September 2005

An automated version of Maxwell’s demon inspired by Smoluchowski’s ideas of 1912 is simulated numerically. Two gas chambers of equal volume are connected via an opening that is covered by a trapdoor. The trapdoor can open to the left but not to the right, and is intended to rectify naturally occurring fluctuations in density between the two chambers. The simulation results confirm that though the trapdoor behaves as a rectifier when large density differences are imposed by external means, it cannot extract useful work from the thermal motion of the molecules when left on its own.
Solutions of Maxwell’s equations for electric and magnetic fields in arbitrary media
Authors: Jefimenko Oleg D.
Published: September 2005

Solutions of Maxwell’s equations for fields in arbitrary media are derived in terms of charge density ρ, current density J, polarization P, and magnetization M. The solutions express E, D, H, and B as integrals of retarded ρ, J, P, M, and their spatial and temporal derivatives.
Classically forbidden behavior of the quantum harmonic oscillator for large quantum numbers
Authors: Diamond James J.
Published: September 2005

The probability that the quantum harmonic oscillator in quantum level n will penetrate into its classically forbidden region, has been calculated, via an algorithm based on a quadrature formula for the probability density, for values of the quantum number n ranging up to 250. These results have been analyzed numerically. The conjecture is made that the probability P(n) of the position of the oscillator in quantum state n being measured in the classically forbidden region follows the approximate formula P(n)≊A(n+1/2)−1/3+O(n+1/2)−1 where the constant A has the value A=0.1339706...; this asymptotic formula has a relative error of less than 2% for quantum numbers 250≳n≳7. The consequences of this formula in regard to the rate of approach to the classical limit are discussed.
Computer display of chromaticity coordinates with the rainbow as an example
Authors: Kubesh Rodney J.
Published: September 2005

The example of the rainbow is used to illustrate a method for the computer display of an object’s color appearance. Color theory is used to transform the physical description of the light reflected by a water drop into chromaticity coordinates and then into colors visible on a monitor. The technique is applicable to any object for which the reflected or transmitted light intensity can be specified.
Spin conservation in one-particle Dirac theory
Authors: Menon V. J.
Published: September 2005

Although the spin operator S(t) of a free Dirac particle does not commute with the Hamiltonian, the expectation value of S(t) computed with respect to positive (or negative) energy solution is found to be time independent. Therefore, the spin projection, i.e., polarization of a free electron (or positron) measured in the laboratory along an arbitrary z direction remains conserved.
Analog demonstrations of Ampere’s law and magnetic flux
Authors: Heller Peter
Published: September 2005

The Ampere circuital law, that the line integral of the magnetic field around a closed path depends only on the total enclosed current and not on the shape of either the current or the integration path, may be strikingly demonstrated. The setup for this is based on the electromagnetic induction taking place in a fine helical coil wound on a nearly closed iron loop. The construction and theory of this device is discussed. Its operation is similar to that of a standard ac ‘‘clamp-on’’ ammeter. The method is simple and can be carried out very quickly. Some analog demonstrations of magnetic flux are also described. These experiments are related to the circuital law demonstration through the electromagnetic reciprocity theorem.
The specular reflection of light off light
Authors: Dowling Jonathan P. , Gea-Banacloche Julio
Published: September 2005

It is well known that any classical electromagnetic field obeys the superposition principle—a fact that would seem to preclude the interaction and hence the deflection of light with light in free space. Nevertheless, the permissible phenomenon of interference between light waves can be viewed as a type of interaction. It is shown that under certain circumstances it is possible to consistently interpret interference as the specular reflection of two electromagnetic waves off each other in the vacuum.
Generalization of the Biot–Savart law to Maxwell’s equations using special relativity
Authors: Neuenschwander Dwight E. , Turner Brian N.
Published: September 2005

Maxwell’s equations are obtained by generalizing the laws of magnetostatics, which follow from the Biot–Savart law and superposition, to be consistent with special relativity. The Lorentz force on a charged particle and its rate of energy change also follow by making Newton’s second law for a particle in a magnetostatic field consistent with special relativity.
Ball moving on stationary or rotating horizontal surface
Authors: Gersten Joel , Soodak Harry , Tiersten Martin S.
Published: September 2005

Interesting new results are added to the already amazing list of unexpected motions of balls moving on stationary or rotating surfaces. New and old results are discussed in a unified manner.
Linear least-squares fits with errors in both coordinates. II: Comments on parameter variances
Authors: Reed B. Cameron
Published: September 2005

Corrected expressions for parameter variances in linear (straight-line) least-squares fits given in an earlier paper [B. C. Reed, Am. J. Phys. 57, 642–646 (1989)] are presented and discussed. In addition, some simplifications to the solution given in that paper are presented, and some comments made as to the role of weighting.
Least-squares fitting when both variables contain errors: Pitfalls and possibilities
Authors: Macdonald J. Ross , Thompson William J.
Published: September 2005

Least-squares fitting is reviewed, in tutorial form, when both variables contain significant errors. Various error models are described; corresponding appropriate weighting is discussed; and the interpretation of weighting is clarified by a physically intuitive description and by graphical results. Resources in the literature on least-squares fitting that are suitable for physics and astronomy students are reviewed. Algorithms for straight-line fitting, indicate practical solution methods, are summarized and numerical comparisons are given. Also described are several readily available computer programs that allow fitting for both straight-line and nonlinear situations and that are appropriate for both research and teaching applications.
A solid-state low-voltage Tesla coil demonstrator
Authors: Bruns Donald G.
Published: September 2005

A low-voltage demonstration Tesla coil using a solid-state photovoltaic relay to replace the conventional spark gap has been analyzed and then built. This relay incorporates an isolated LED to illuminate a silicon photovoltaic stack which drives a bidirectional FET. Component values for the inductances and capacitances have been determined theoretically from measured parameters. Computer simulation by integrating the coupled circuit equations shows excellent agreement with oscilloscope traces. Energy transfer between the primary and secondary circuits is demonstrated, along with continuous secondary oscillations after the primary circuit is interrupted. This low-voltage design is easier to build and diagnose than high-voltage Tesla coils.
The abstract Lorentz transformation group
Authors: Ungar Abraham A.
Published: September 2005

Treatments of the Lorentz transformation of special relativity at an undergraduate level usually assume that the motion of one observer is along the x axis of another observer, resulting in the (1+1)-dimensional Lorentz transformation group. The (1+n)-dimensional Lorentz group, for n=2 or n=3, is unknown to many physics students because of the simplified (1+1)-dimensional treatments found in most texts. The aim of this article is to simplify the presentation of the (homogeneous, proper, orthochronous) Lorentz group by abstraction to the point where the (1+n)-dimensional Lorentz group can readily be presented to physics students in n space dimensions where n is finite or infinite. The study of the (homogeneous, proper, orthochronous) Lorentz transformation group is simplified and generalized in this article by abstraction, thus obtaining an elegant formalism to deal with the Lorentz group. This new formalism allows one to solve in the abstract Lorentz group previously poorly understood problems in the standard, (1+3)-dimensional Lorentz group. Two such problems, studied in this article, are (i) the problem of determining the Lorentz transformation composition law in a way analogous to the well-understood determination of the Galilean transformation composition law, and (ii) the problem of determining all the Lorentz transformations linking two given points in a Minkowski space. Crucial points in the present study of the abstract Lorentz group are (i) the abstract relativistic velocity addition law; (ii) the abstract Thomas precession, called Thomas gyration; and (iii) the parametrization of the abstract Lorentz transformation by abstract velocity and abstract orientation parameters in such a way that the composition law of abstract Lorentz transformations is given by a corresponding parameter composition law. In the limit of large speed of light c, c→∞, Thomas gyration vanishes, and the Lorentz transformation composition law reduces to the Galilean transformation composition law.
The mapping of the Coulomb problem into the oscillatora)
Authors: Bateman David S. , Boyd Clinton , Dutta-Roy Binayak
Published: September 2005

The mapping of the Schrödinger equation for the ‘‘hydrogen atom’’ in one, two, and three dimensions into that for the oscillator is reviewed, with the purpose of relating two of the most basic, illustrative, and useful problems discussed in introductory quantum mechanics courses.
Computer generated holograms from dot matrix and laser printers
Authors: Macgregor A. E.
Published: September 2005

The production of simple computer generated holograms on personal computer equipment is discussed. The drawing of holograms using dot matrix and laser printers is described and some replay results presented.
Heat conduction in a metallic rod with Newtonian losses
Authors: Ràfols Ismael , Ortín Jordi
Published: September 2005

An experimental realization is presented of the problem of heat conduction along a one-dimensional rod subjected to an externally imposed constant temperature difference and allowing for heat losses to the environment. One end of the rod is at a fixed elevated temperature, while, untypically, both the lateral surface and far end of the rod are considered to be at the same fixed lower temperature. Newton’s Law of Cooling has been invoked as a boundary condition. The experimental results are used to illustrate some fundamental concepts of nonequilibrium thermodynamics such as the meaning and temporal evolution of the different contributions to the entropy balance equation, including entropy production, and the influence of initial and boundary conditions on the steady state.
Calculus and physics: Challenges at the interface
Authors: Yeatts F. Richard , Hundhausen Joan R.
Published: September 2005

After three years of teaching an integrated calculus and physics course, a number of observations on student learning have been made which suggest how teachers of the two subjects might better support and take advantage of the efforts of each other to improve the educational experience for the students. Physics teachers, for example, may well overestimate the depth of understanding their students have of the concepts of calculus, while underestimating their computational skills. Calculus teachers, on the other hand may be unaware of what their students actually need to know to succeed in physics and other quantitative disciplines. In the following, several of the areas of mismatch between calculus and physics will be discussed, as evidenced by student performance in our course, and recommendations will be made as to how the physics teacher might better take advantage of the knowledge of calculus students actually have while striving to improve the compatability of the two subjects.
Resource Letter MI-1: Medical imaging
Authors: Riederer Stephen J.
Published: September 2005

This Resource Letter provides a guide to the literature on medical imaging, with emphasis on magnetic resonance imaging. The letter E after an item indicates elementary level of material of general interest to persons becoming informed in the field. The letter I, for intermediate level, indicates material of somewhat more specialized nature; and the letter A indicates rather specialized or advanced material.
A boiling heat transfer paradox
Authors: Lavalle G. Guido , Carrica P. , Garea V. , Jaime M.
Published: September 2005

An instructive experiment for observing the Leidenfrost phenomenon is presented. The experiment, suitable for an undergraduate experimental course, consists of introducing a copper body at room temperature into liquid nitrogen and observing its temperature history. The experiment is then repeated with the body covered by a thermal insulating material, observing that the body reaches thermal equilibrium much more rapidly in the second case. This apparent paradox greatly motivates the students, who need to understand the different regimes of boiling heat transfer to resolve it. The paper also contains an approximate method to determine the insulator thickness that gives the minimum cooling period.
The Liénard–Wiechert potential and the retarded shape of a moving sphere
Authors: Aguirregabiria J. M. , Hernández A. , Rivas M.
Published: September 2005

The subtleties in the derivation of the retarded Liénard–Wiechert potential for a point charge are stressed by explicitly computing and drawing the retarded shape of a moving sphere. This shape is the effective integration region for the charge density and it is computed, with the aid of the ‘‘information collecting sphere,’’ in the limit of vanishing radius (or, equivalently, from the point of view of a remote observer).