bluuebunny/crossref_metadata_2025 huggingface dataset:
Teaching problem solving through cooperative grouping. Part 1: Group versus individual problem solving
Authors: Heller Patricia , Keith Ronald , Anderson Scott
Published: September 2005

An experiment was conducted to investigate the effects of cooperative group learning on the problem solving performance of college students in a large introductory physics course. An explicit problem solving strategy was taught in the course, and students practiced using the strategy to solve problems in mixed-ability cooperative groups. A technique was developed to evaluate students’ problem solving performance and determine the difficulty of context-rich problems. It was found that better problem solutions emerged through collaboration than were achieved by individuals working alone. The instructional approach improved the problem solving performance of students at all ability levels.
Teaching problem solving through cooperative grouping. Part 2: Designing problems and structuring groups
Authors: Heller Patricia , Hollabaugh Mark
Published: September 2005

A supportive environment based on cooperative grouping was developed to foster students’ learning of an effective problem-solving strategy. Experiments to adapt the technique of cooperative grouping to physics problem solving were carried out in two diverse settings: a large introductory course at state university, and a small modern physics class at a community college. Groups were more likely to use an effective problem-solving strategy when given context-rich problems to solve than when given standard textbook problems. Well-functioning cooperative groups were found to result from specific structural and management procedures governing group members’ interactions. Group size, the gender and ability composition of groups, seating arrangement, role assignment, textbook use, and group as well as individual testing were all found to contribute to the problem-solving performance of cooperative groups.
Study of radiation-matter interaction processes below 1 MeV from simulated data
Authors: Arqueros Fernando , Martinez Sergio
Published: September 2005

The passage of 1-MeV photons through thin and thick foils of Al and Pb has been simulated. The results have been used to show the basic properties of the dominant effects in radiation-matter interaction processes at energies just below 1 MeV. For the interpretation of the data it is necessary to handle total and differential cross sections of the involved processes, as well as the conservation laws, mainly of the Compton effect, whose phenomenology is studied in depth. In particular, the effect of multiple interactions in thick foils is studied and some results of the simulation are compared with suggested theoretical approaches.
Optical transformations in three-space: Simulations with a PC
Authors: Wilson Raymond G. , McCreary Sean M. , Thompson Jeffrey L.
Published: September 2005

Using Fourier transform and convolution techniques, it is illustrated how all aspects of Fraunhofer diffraction of virtually any aperture real or complex can be calculated and displayed in two- and three-space using an IBM-compatible PC. Details of program commands using software matlabTM are illustrated as well as results of plotting software, surferTM. Fresnel diffraction is illustrated using Fourier transformation.
The Wheatstone kaleidophone
Authors: Whitaker Robert J.
Published: September 2005

In 1827 Charles Wheatstone described a device he called the ‘‘kaleidophone.’’ Its purpose was to illustrate the persistence of vision of the human eye, but it also provided a means of generating those curves that have come to be known as ‘‘Lissajous curves.’’ Wheatstone’s kaleidophone and related curve tracing apparatus will be described.
Characterization of a bulk semiconductor’s band gap via a near-absorption edge optical transmission experiment
Authors: Essick John M. , Mather Richard T.
Published: September 2005

An experimental setup that employs lock-in detection to measure the optical transmission data on a bulk semiconductor sample is described. A straightforward manipulation of these data yields the semiconductor’s absorption coefficient α in the energy range near its absorption edge (0<α<100 cm−1). The theory of optical transitions in semiconductors required to analyze the resulting absorption spectra is presented. It is shown that a model based on an indirect optical transition involving a single phonon accurately describes data taken on a silicon sample. Based on this analysis, a value of (1.098±0.004) eV for silicon’s indirect band gap and an energy of (51±4) meV for the involved phonon is deduced. Conversely, it is shown that data taken on a gallium–arsenide sample are consistent with a model based on a direct optical transition involving exponential band-tail states. A value for the band-tail’s Urbach slope of E0=(6.7±0.2) meV is found. All of these results accurately agree with published values. This laboratory demonstrates important concepts in solid state physics via universally applicable experimental techniques at a level appropriate for upper-division undergraduates.
Elementary derivation of the advance of the perihelion of a planetary orbit
Authors: Cornbleet S.
Published: September 2005

An elementary derivation of the law for the advance of the perihelion of a planet in orbit about the sun is given. This is obtained by comparing a Kepler ellipse in a Lorentz coordinate system, with one in Schwarzschild coordinates, related by the areal constant, and attributing the variation entirely to an increase in the angular coordinate. The result is shown to be entirely in agreement with the classical value.
A computer-based data acquisition laboratory for undergraduates
Authors: Maps J.
Published: September 2005

An electronics course for physics majors is described that introduces students to modern data acquisition methods using computer-based equipment and high level software. The course comprises lectures and extensive laboratory work with standard personal computers, research quality data acquisition hardware, and programmable instruments. The laboratory work consists of a mixture of standard laboratory exercises and open-ended projects.
The Jahn–Teller effect: An introduction and current review
Authors: O’Brien Mary C. M. , Chancey C. C.
Published: September 2005

The Jahn–Teller effect (JTE) is defined and the historical background of the Jahn–Teller theorem is briefly discussed. The E⊗β system, an electronic doublet coupled to a single mode of vibration, is introduced as an elementary example and is used to illustrate features characteristic of Jahn–Teller systems. The spin resonance of Cu++ in various materials is considered and the particular case of Cu++ in a cubic crystal field is used to introduce the E⊗ε Jahn–Teller system. The linear and quadratic E⊗ε systems are discussed, and the linear case is used to illustrate the appearance of the Berry phase in a quantum system. The role of the Jahn–Teller effect in high-temperature superconductivity is also discussed. In particular, the JTE-based superconductivity theories of Englman et al. [Physica C 169, 314–324 (1990)] and Weber et al. [Physica C 162/164, 307–312 (1989)] are briefly reviewed. The possible roles of the Jahn–Teller effect in C60 (buckminsterfullerene) and superconducting K3C60 are also considered.
A relativistic-like presentation of optics in stratified planar media
Authors: Vigoureux J. M. , Grossel Ph.
Published: September 2005

A close comparison is presented between special relativity and optics of stratified planar media. This presentation, which may provide some useful tools in optics, can also suggest interesting thoughts and questions both in optics, in special relativity, and in quantum theory.
Dipole radiators in a cavity: A radio frequency analog for the modification of atomic spontaneous emission rates between mirrors
Authors: Seeley Fred B. , Alexander Joseph E. , Connatser Robert W. , Conway Jeanette S. , Dowling Jonathan P.
Published: September 2005

The results of a simple experiment that studies the dipole radiation rate of a radio frequency antenna inside a parallel mirror cavity are presented. Data on the emission rate of the dipole as a function of both mirror spacing and the dipole location between mirrors is taken, and agrees well with a theoretical prediction that holds in both the classical macroscopic and quantum electrodynamical microscopic domains: In particular, theoretically predicted emission suppression and enhancements are observed. This project is then of pedagogical interest in that it is a simple mockup of several famous cavity QED experiments that investigate the change of atomic spontaneous emission rates in such resonators.
Experimental verification of the Heisenberg uncertainty principle—An advanced undergraduate laboratory
Authors: DeYoung P. A. , Jolivette P. L. , Rouze N.
Published: September 2005

The Heisenberg uncertainty principle can be experimentally demonstrated by combining a Mössbauer experiment with a measurement of a nuclear lifetime. The senior undergraduate students perform a Mössbauer experiment to measure the energy width of the 14.4 keV level of 57Fe followed by measurements of coincident γ rays to determine the lifetime of the level. The experiments are designed to emphasize that the uncertainty principle is inherent in the wave function rather than resulting from the measurement process.
Transmission spectroscopy of a thin membrane
Authors: Nachman Paul
Published: September 2005

A few-micron-thick nitrocellulose membrane stretched flat across an open frame (a ‘‘pellicle’’) has gently modulated passbands typically spaced by 20–60 nm across the visible and near-infrared. This makes it an attractive subject for an upper-division laboratory exercise. In our experiment, students determine the membrane’s thickness d and refractive index n from spectra recorded over a range of incidence angles. These spectra illustrate the classical textbook problem of transmission by a parallel plate and yield values of d and n with uncertainties less than 1%.
The geometric phase: A simple optical demonstration
Authors: Hariharan P.
Published: September 2005

The fact that the wave function of a quantum system may not return to its original phase after its parameters are cycled around a circuit is now well known. The resultant change in phase, known as the geometric phase, has its analog in optics. This paper describes a simple interferometric arrangement that provides a direct demonstration of the geometric phase.
Classical symptoms of quantum illnesses
Authors: Zhu Chengjun , Klauder John R.
Published: September 2005

Pathologies of quantum Hamiltonians are reflected in their classical counterparts and in the solution of the associated classical dynamics. This property permits one, on the one hand, to appreciate the role of certain technical requirements acceptable quantum Hamiltonians must satisfy, and, on the other hand, enables one to recognize potentially troublesome quantum systems merely by examining the classical systems.
An alternative approach for the propagator of a charged harmonic oscillator in a magnetic field
Authors: Farina C. , Maneschy M. , Neves C.
Published: September 2005

An alternative way of computing the propagator of a nonrelativistic (spinless) charged harmonic oscillator in a constant magnetic field through an appropriate variable transformation directly in the Schrödinger equation is proposed. Due to the axial symmetry exhibited by this problem, polar coordinates are used. Also given is a physical interpretation for these results on the light of both classical and quantum mechanics.
Wakes and waves in N dimensions
Authors: Soodak Harry , Tiersten Martin S.
Published: September 2005

An impulsive point excitation in a linear, nondispersive wave medium can produce an after-signal, which has been called a ‘‘wake’’ in the mathematical physics literature. Relations are derived between such wakes and the dimensionality of the space by regarding a point source in space of dimensionality N−2 as a line source in N−1 dimensions and as a plane source in N dimensions. The ‘‘magic’’ of one and three dimensions is discussed from a new point of view.
A Galilean experiment to measure a fractal dimension
Authors: Lima F. F. , Oliveira V. M. , Gomes M. A. F.
Published: September 2005

A simple and pedagogical kinematic experiment to measure the mass-size fractal dimension D of crumpled surfaces is presented. The experiment is inspired in the well-known Galilean experiments with bodies rolling on inclined planes. The experimental results for D agree with those obtained from static means.
Newtonian chaos+Heisenberg uncertainty=macroscopic indeterminacy
Authors: Barone S. R. , Kunhardt E. E. , Bentson J. , Syljuasen A.
Published: September 2005

The specific example of an electron orbiting in the field of a charged sphere and a superimposed uniform magnetic field is used to illustrate that in classically chaotic systems, irreducible uncertainties required by the Heisenberg principle are amplified exponentially to the macroscopic level in short times. According to the Copenhagen interpretation of quantum theory irreducible quantum uncertainties have led to quantum indeterminacy on a macroscopic scale in interesting times.
On the fate of stars in high spatial dimensions
Authors: Bechhoefer John , Chabrier Gilles
Published: September 2005

Chandrasekhar showed that above a limiting mass, white dwarf stars will collapse under their own gravitational force. We use dimensional analysis to show that although the limiting mass is finite in three spatial dimensions (d=3), it is zero in higher spatial dimensions. A star placed in a high-dimensional space is unstable and will either collapse to a black hole or disperse and become unbound. Thus, any universe—or part of a universe—with d≥4 will be profoundly different from one with d=3.
An elementary approach to quantum probability
Authors: Farina J. E. G.
Published: September 2005

Compatibility of elementary propositions in quantum mechanics is usually defined as the commutativity of the corresponding projectors. It is shown that this is equivalent to the vanishing of interference, the theorem of total probabilities, Bayes’ theorem, indifference to the order of acquisition of information, and the validity of the rule for marginal probabilities
The Smith chart and quantum mechanics
Authors: Rosner Jonathan L.
Published: September 2005

The Schrödinger equation and the equation describing the behavior of voltage on a transmission line are both linear second-order equations, which may be solved by convenient matrix methods. By drawing analogies between these two problems, it is shown that a method used for antenna impedance matching based on the Smith chart corresponds in quantum mechanics to a simple conformal transformation of the logarithmic derivative of the wave function. One thereby can arrive at an elementary derivation of the Wentzel–Kramers–Brillouin quantization condition.
The Science BagT
M at the University of Wisconsin–Milwaukee: A successful forum for science outreach
Authors: Greenler Robert G. , Lasca Norman P. , Brooks Arthur S. , Shaw C. Frank
Published: September 2005

A series of science programs for the public has been running for 19 years with an accumulated attendance of 95 000 people.
Self-organized criticality: An experiment with sandpiles
Authors: Grumbacher Sara K. , McEwen Karen M. , Halverson Douglas A. , Jacobs D. T. , Lindner John
Published: September 2005

In 1987, Bak, Tang, and Wiesenfeld introduced the notion of self-organized criticality (SOC) in the guise of a computer simulation: a ‘‘sandpile cellular automaton machine.’’ They supposed that a real, many-bodied, physical system in an external field assembles itself into a critical state. The system then relaxes about the critical state creating spatial and temporal self similarities which give rise to fractal objects and 1/f noise. Their computer modeling was of a system like a sandpile at its critical angle of repose. This provided a new paradigm for many-body dynamics. Understanding SOC may well allow substantial strides to occur in the theory of flow and transport. The simplest model system, one for which computer simulations and corresponding real experiments are feasible, is a ‘‘sandpile’’ near its critical angle of repose. The size and duration of avalanches occurring as subsequent ‘‘sand’’ grains are added can provide detailed information about the ‘‘sandpile’’ as a model of SOC, and for SOC as a basis for many-body dynamics. This article describes a fairly simple, junior-level experiment in this new field involving the measurement of the distribution of avalanche sizes which occur as grains of sand are added to a ‘‘sandpile.’’ The universality of the phenomena can be observed and a power law relationship can be deduced.
Confusion by representation: On student’s comprehension of the electric field concept
Authors: Törnkvist S. , Pettersson K.-A. , Tranströmer G.
Published: September 2005

It is argued that university students’ diffuse ideas about the two related concepts of force and force field could be due to lack of mastery of the graphical representation of these and related concepts.
The cosmological spectral shift
Authors: Boyling J. B.
Published: September 2005

The formula for the cosmological spectral shift in a Robertson–Walker universe is derived by applying the method of separation of variables to the solution of Maxwell’s field equations. A proof is also given of the formula for the variation of the apparent brightness of a source with distance.
Phenomenological quantum models for under and critically damped oscillators
Authors: Anderson Robert L.
Published: September 2005

According to Rayleigh, if one sets a linear oscillator in motion in a viscous fluid, the fluid not only opposes the motion with a velocity-dependent dissipative force, but the fluid accretes to the oscillator changing its effective mass. A perturbation linking a mass accretion operator with the usual complex spontaneous decay operator is applied to a nonrelativistic quantum undamped oscillator. It results in a quantum model of Rayleigh’s oscillator for which the equation of motion for the expectation value of position and the Heisenberg uncertainty relation between the position and linear momentum are the anticipated ones for a quantum mechanical underdamped oscillator. Another model based on a variation of these ideas which allows for all possibilities, no change or diminution or accretion, for the perturbed mass is presented for the critically damped oscillator. In both models, the situation is fixed by the experimental dissipative ‘‘forces.’’
Electrostatic field bounds for model dielectric configurations
Authors: Wilcox Thomas J.
Published: September 2005

The normal component of an electric field near a convex shaped object of zero net charge and dielectric constant ε embedded in a vacuum with an asymptotically uniform electric field has an upper bound (ε/ε0)‖E0‖, where ε0 is the vacuum permittivity, and E0 is the asymptotic field. This limit may be closely approached in the vicinity of regions of high surface curvature.
The charge densities in a current-carrying wire
Authors: Gabuzda Denise C.
Published: September 2005

In the lab frame the total linear charge density of a current-carrying wire must be zero, while in the rest frame of the electrons making up the current the total volume charge density must be zero. These two pieces of information enable the determination of the volume, surface, and linear charge densities of such a wire in both of these frames using only straightforward relativistic length contractions and simple mathematics.
Classical electromagnetism and relativity: A moving magnetic dipole
Authors: Rosser W. G. V.
Published: September 2005

The force on a stationary electric charge due to a moving current carrying coil and the torque on a moving current carrying coil due to the electrostatic field of a stationary electric charge can both be interpreted quantitatively by including the effects due to the second order charge distribution on the moving coil predicted by the charge transformations of special relativity.
Was Marx right? or How efficient are laser driven interstellar spacecraft?
Authors: Simmons J. F. L. , McInnes C. R.
Published: September 2005

The idea of a laser driven space vehicle capable of interinterstellar travel was raised 25 years ago. The original article by Marx [Nature 211, 22–23 (1966)] presented a relativistic calculation that contained conceptual and numerical errors. Here the inconsistencies of the original article are corrected. Marx’s calculations are generalized to the case where the laser is of variable power, and to the interesting case where the laser beam is recycled by means of mirrors. The obstacles to this form of interstellar travel appear insurmountable, but the calculations provide an excellent example of the application of relativistic ideas.
Force exerted on a stationary charge by a moving electric current or by a moving magnet
Authors: Jefimenko Oleg D.
Published: September 2005

Retarded fields are used for deriving the force exerted on a stationary charge by a slowly moving current-carrying conductor or a slowly moving magnet. The derivation makes use of the fact that a neutral current-carrying conductor, when it is moving, creates an external electric field. Although the presence of this field is generally regarded as a strictly relativistic effect, it is shown that this field is deducible from the basic laws of classical electrodynamics, without any recourse to relativity. In terms of classical electrodynamics, a moving neutral current-carrying conductor creates this electric field because of unequal retardation of the electric potentials associated with the positive and negative charges of the conductor. This field must be taken into account for the correct computation of the force exerted by moving current-carrying conductor or a moving magnet on a stationary charge.
Student programming in the introductory physics course: M.U.P.P.E.T.
Authors: Redish Edward F. , Wilson Jack M.
Published: September 2005

Since 1983, the Maryland University Project in Physics and Educational Technology (M.U.P.P.E.T.) has been investigating the implication of including student programming in an introductory physics course for physics majors. Many significant changes can result. One can rearrange some content to be more physically appropriate, include more realistic problems, and introduce some contemporary topics. One can begin training the student in professional research-related skills at an earlier stage than is traditional. An interesting point to note is that the inclusion of carefully considered computer content requires an increased emphasis on qualitative and analytic thinking.
Heisenberg picture in quantum mechanics and linear evolutionary systems
Authors: Nardone Pascal
Published: September 2005

A straightforward procedure is presented to derive the propagator in simple quantum systems. This approach enables us to define a state which behaves as a generalization of the well-known coherent state of the harmonic oscillator.
A simplified physical picture of phase conjugation using k-space formalism and ray optics
Authors: Ghosh Prasanta K. , Banerjee Partha P.
Published: September 2005

Using a simple geometrical construction in k-space and a ray-tracing procedure, the overall nature of the phase conjugation process is examined. The usefulness of the k-space formalism and the ray-tracing procedure as instructional tools is demonstrated by analyzing various cases.
Interference fringes between two separate lasers
Authors: Louradour F. , Reynaud F. , Colombeau B. , Froehly C.
Published: September 2005

In a modern, generalized version of Young’s two-slit experiment, it is shown that two separate pulsed lasers can generate visually observable, transient interference fringes of high contrast under the simple and obvious condition that the temporal and spectral structures of the interfering pulses overlap. In a second experiment, a picosecond streak camera allows the observation of spatio-temporal interference fringes between two waves having different frequencies.
The hydrogen atom in a semi-infinite space limited by a conical boundary
Authors: Ley-Koo E. , Mateos-Cortés S.
Published: September 2005

It is shown that the Schrödinger equation for the hydrogen atom in a semi-infinite space limited by a conical boundary, with the nucleus at the vertex, has an exact solution in spherical coordinates. The limit in which the conical boundary becomes a tight sheath around its own axis corresponds to a ‘‘one-dimensional’’ hydrogen atom with an infinitely degenerate ground state at the ionization threshold. This model of an atom in a semi-infinite space includes as a special case the pioneering plane-nodal-wave-function model used by Levine in 1965 to describe an isolated donor atom on the surface of a semiconductor.
Aspects of Debye shielding
Authors: Meyer-Vernet Nicole
Published: September 2005

The Debye shielding is derived in a simple way without assuming Boltzmann’s equilibrium. The conditions under which it applies and some of its consequences are discussed at the elementary level.
Motion of a falling spring
Authors: Calkin M. G.
Published: September 2005

The motion of a spring, initially suspended from its top end and hanging in equilibrium in the earth’s field, and then released and allowed to fall, is studied. The difference between the behaviors of loosely wound and tightly wound springs is emphasized.
Classical degeneracy and the existence of additional constants of motion
Authors: Weigert Stefan , Thomas Harry
Published: September 2005

The relation between degeneracy of classical frequencies in integrable systems and additional global constants of motion is investigated from a general point of view. It is shown that in autonomous systems with N degrees of freedom the existence of Λ<N such additional invariants imply Λ global linear relations with commensurate coefficients between the frequencies, and vice versa. Furthermore, such a degeneracy gives rise to a specific structure of the Hamiltonian considered as a function of action variables. The general statements are illustrated by various examples.
CAPA—An integrated computer-assisted personalized assignment system
Authors: Kashy E. , Sherrill B. M. , Tsai Y. , Thaler D. , Weinshank D. , Engelmann M. , Morrissey D. J.
Published: September 2005

A new integrated computer-assisted personalized assignment (CAPA) system that creates individual assignments for each student has been developed and found to be a powerful motivator. The CAPA system allows students to enter their answers to personalized assignments directly via networked terminals, gives immediate feedback and hints (allowing challenging questions), while providing the instructor with on-line performance information. The students are encouraged to study together which is known to be an effective learning strategy, but each must still obtain his/her own correct answers. Students are allowed to re-enter solutions to the problems before the due date without penalty, thus providing students with different skills levels the opportunity and incentive to understand the material without being judged during the learning process. The features and operation of the system are described, observations on its use in an introductory general physics class are reported, and some of the highly favorable student reactions are included.
Proof that the Neumann Green’s function in electrostatics can be symmetrized
Authors: Kim K.-J. , Jackson J. D.
Published: September 2005

We prove by construction that the Green’s function satisfying the Neumann boundary conditions in electrostatic problems can be symmetrized. An illustrative example is given.
A new theory about light and colors
Authors: Newton Isaac
Published: September 2005

Reprint of the first publication of Mr. Isaac Newton, Mathematics Professor in the University of Cambridge, containing his New Theory about Light and Colors. Light is declared to be not Similar or Homogeneal, but consisting of difform rays, some of which are more refrangible than others. Colors are affirmed to be not Qualifications of Light, derived from Refractions of natural Bodies, as was generally believed, but Original and Connate properties, which in diverse rays are diverse. Several Observations and Experiments are alleged to prove the said Theory. Originally published February 19, 1672 in Philos. Trans. R. Soc. London, No. 80, 3075-3087. [This abstract is an edited version of the table of contents thereof.]
Teaching Newton’s color theory firsthand
Authors: Towne Dudley H.
Published: September 2005

Newton’s first published paper, A New Theory About Light and Color, is intelligible to readers with no background in the subject. Described are demonstrations and experiments to accompany the teaching of this material.
Stopping objects with zero external work: Mechanics meets thermodynamics
Authors: Leff Harvey S. , Mallinckrodt A. John
Published: September 2005

Although the work-energy theorem of pure, nondissipative mechanics states that the work done stopping a body equals its kinetic energy change, the work done stopping a body via an inelastic, dissipative collision can be zero. This counter-intuitive result is used to motivate the development of thermodynamic ideas as a direct extension of classical mechanics. The approach leads to a natural introduction of internal energy, the path dependence of work, and dissipation. It also offers an opportunity for early exposure to powerful symmetry and frame-invariance arguments. The main presentation addresses one-dimensional highly symmetric collisions, with a generalization in the Appendix.
Reading the equations and confronting the phenomena—The delights and dilemmas of physics teaching
Authors: Romer Robert H.
Published: September 2005

The following essay originally appeared in Teaching What We Do, edited by Peter R. Pouncey (Amherst College Press, 1991), a collection of 13 articles by Amherst College faculty members from a wide variety of disciplines.
Microwave experiments on electromagnetic evanescent waves and tunneling effect
Authors: Albiol Francisco , Navas Sergio , Andres Miguel V.
Published: September 2005

A set of experiments is described to measure the decay of electromagnetic evanescent waves and the tunneling effect through an airgap. The experiments are performed using microwaves and have been designed to be carried out by third year students of physics. The proposed experimental setup can be regarded as a quantum mechanical simulator for the one-dimensional motion of a particle.
The Wall of Death
Authors: Abramowicz Marek A. , Szuszkiewicz Ewa
Published: September 2005

Much to everybody’s surprise, it was recently demonstrated that according to Einstein’s general theory of relativity, very close to a compact star or a black hole the centrifugal force may attract towards the center of a circular motion. We show here that Newtonian theory predicts exactly the same effect, and that the geometrical reason for it is identical in both theories. The centrifugal force always repels in the local outward direction. However, in a curved space (or on a curved surface) in which the perimeter of concentric circles decreases with the increasing diameter, the local outward direction points towards the global center of the circles, and thus the centrifugal force attracts to the center.
Kepler’s third law and the oscillator’s isochronism
Authors: Gorringe V. M. , Leach P. G. L.
Published: September 2005

Two classes of differential equations which have Kepler-like and oscillatorlike elliptical orbits are shown to have generalizations of the conserved angular momentum, energy, and Laplace–Runge–Lenz vector (Jauch–Hill–Fradkin tensor for the oscillator case). Both possess a generator of self-similar transformations and the related period–semimajor axis relation is a generalization of Kepler’s third law in which the constant of proportionality depends explicitly on the eccentricity of the orbit.
Polygons of resistors and convergent series
Authors: March Robert H.
Published: September 2005

Construct a polygon of equal resistors, R, and also connect each vertex to the center with resistance R. It is shown that for a large number of sides, N, the entire network of 2N resistors has a vertex-to-center resistance of R/√5. The convergence of the sequence with increasing N is related to the Fibonacci sequence.
Stabilization of a multimode He–Ne laser: A vivid demonstration of thermal feedback
Authors: Stanek Ferdinand , Tobin R. G. , Foiles C. L.
Published: September 2005

A thermal stabilization technique for multimode He–Ne laser tubes is demonstrated. Intensity stability of ∼1% is achieved, where the intensity of the unstabilized laser varied by more than a factor of 5. The system provides both a dramatic demonstration of the principle of negative feedback and a stimulating introduction to basic electronics, laser physics, and solid state physics. It is simple enough to be constructed as an undergraduate laboratory project.
Experimental determination of normal frequencies in coupled mechanical oscillator systems using fast Fourier transforms: An advanced undergraduate laboratory
Authors: Weigman Bernard J. , Perry Helene F.
Published: September 2005

An experimental method for determining frequencies present in complex oscillating systems is given. When an oscillating system is attached to a force transducer, the time-varying force is converted to a voltage. Using an analog to digital converter, a PC/XT samples 1024 points. A fast Fourier transform is performed which gives the frequency or frequencies present in the signal. Results are reported for several coupled systems of mass and spring combinations. In each case the experimentally measured frequencies agree to within 1% of the theoretically calculated values.
Philosophical midwifery and the birthpangs of modern cosmology
Authors: Gale George , Urani John
Published: September 2005

Philosophical considerations sometimes direct developments in physics. Such influence most frequently operates during the genesis of new fields. The birth of modern cosmology provides clear evidence of the interaction between philosophical issues and the shape and direction of a new physical discipline. Philosophical controversy between E. A. Milne and other astrophysicists, including A. S. Eddington, James Jeans, and H. P. Robertson, directly affected the models, methods, and very nature of cosmological science for future generations. Today’s standard space-time metric, for example, resulted from responses by Robertson and A. G. Walker to philosophical challenges presented in Milne’s proposals to scrap the very idea of expanding ‘‘space.’’ Analysis of published works, unpublished manuscripts and correspondence, and personal interviews illustrates the role philosophical considerations played in development of this new field in physics.
Interactions of magnetic monopoles with electric currents
Authors: Kocher Carl A.
Published: September 2005

When two magnetic monopole distributions interact, the forces are conservative, and mechanical work is transformed into energy stored in the field, as in electrostatics. However, if a monopole distribution interacts with an electric current distribution, the forces are nonconservative; external work done on a monopole system appears as kinetic energy of the moving electric charges. In this case the magnetic field energy does not change in first order, during a displacement or reorientation of one system relative to the other. Contributions to the energies of interaction are calculated and compared for various combinations of magnetic systems. ‘‘Monopole threading’’ effects are also described, which affect the kinetic energy within an electric current loop when a monopole passes through it.
Lost horizons
Authors: Ellis G. F. R. , Rothman T.
Published: September 2005

Cosmological horizons play an essential role in determining the causal structure of spacetime and are of central importance in the inflationary universe scenario. We review the topic of horizons in simple language, pointing out a number of widespread misconceptions. The use of spacetime diagrams plotted in terms of proper time and proper distance coordinates helps sort out some of these difficulties. They complement the widely used conformal diagrams, which show causal relations clearly but severely distort proper distances.
Square wheel
Authors: Klein Nelson H.
Published: September 2005

A solution to the paradoxical problem of a square wheel is presented. Using kinematics, it is shown that the correct roadbed for a square object rolling without slipping is a series of inverted catenaries. The dynamics of the square are revealed by the conservation of energy method. Remarkably, the square is shown to be capable of winning a downhill race against a sphere on a parallel inclined plane.
Resource Letter RP-1: Radio pulsars
Authors: Weisberg Joel M.
Published: September 2005

This Resource Letter provides a guide to the literature on radio pulsars. Papers at elementary (E), intermediate (I), and advanced (A) levels are cited. Historically important papers, including relevant articles published before the discovery of pulsars in 1967, are listed, as are current areas of pulsar research. This guide also includes a discussion of pulsars’ use in studying a variety of other phenomena ranging from the interstellar medium to relativistic theories of gravitation.
Image theory for electrostatic and magnetostatic problems involving a material sphere
Authors: Lindell Ismo V.
Published: September 2005

The well-known image method for a conducting sphere in front of an electrostatic source, due to Lord Kelvin from 1848, is generalized for electrostatic problems involving a dielectric sphere and for magnetostatic problems involving a permeable sphere. It is seen that the image sources are very simple, for a point source they consist of a point source plus a line source obeying a simple power law. The expressions are checked to satisfy all known limit cases. The image theory can be applied with simple computing devices for static or quasistatic problems involving material spheres.
Hamming sets, Ising sets, cellular automata, neural nets, and the random walk
Authors: Franceschetti Donald R. , Jones D. Wayne , Campbell Bruce W. , Hanneken John W.
Published: September 2005

Cellular automata and neural nets are nonlinear dynamical systems of interest to physicists as models of computational devices and physical processes. The possible states of both N-cell automata and N-binary-neuron networks can be represented by the 2N corners of the unit hypercube (the Hamming set) in N-dimensional space. This representation is transparently related to the representation of the states of N spin-one-half particle systems and of N-step random walks by strings of positive and negative ones (the Ising set). The dynamics of discrete neural networks and cellular automata can be described by the 2N by 2N transition matrices which describe the mappings of the Hamming set and Ising set into themselves. This representation renders some properties of these nonlinear systems readily apparent, and highlights their relation to the lattice gas, systems of interacting spins, and the random walk.
Temperature fluctuations in a heat bath
Authors: Prosper Harrison Bertrand
Published: September 2005

The model of two boxes in thermal contact each filled with an ideal quasiclassical gas is used to treat, in a unified way, temperature fluctuations in both finite and infinite heat baths. One box is regarded as the heat bath and the other serves as the thermometer.
A study of the wave function of a particle striking a crystal interface
Authors: Friedmann Gideon , Little W. A.
Published: September 2005

The one-dimensional behavior of the wave function of a free particle striking a crystal interface is studied. The free particle is described using a wave packet of plane waves, and the crystal is described using the Kronig–Penney model. It is found that when the wave packet is spread over many unit cells, it behaves much like a free particle wave packet striking a small step at the interface. The reflection and transmission coefficients are derived and one finds that these coefficients do not contain the effective mass of the particle in the solid. This result is compared with a standard effective mass approach and it is found that the boundary conditions in the latter need to be modified to make it work. This model is useful in understanding the origin of the ‘‘free electron’’ picture in metals, as it describes from basic quantum mechanics, the exact wave function of the particle in the crystal. A computer visualization of the wave packet is presented.
On Bose–Einstein condensation
Authors: Scharf G.
Published: September 2005

Bose–Einstein condensation is considered by an elementary but rigorous method. The vital point is to control the difference between sums and integrals in the thermodynamic limit.
Free expansion for real gases
Authors: Goussard Jacques-Olivier , Roulet Bernard
Published: September 2005

It is sometimes ‘‘proved’’ by simple physical arguments that real gases get cooler when experiencing a free expansion. These arguments are in some way incorrect since the result is in contradiction with experiment, at least for some gases. We show how these arguments can be corrected and find that there is an ‘‘inversion temperature’’ for all real gases. Values of the inversion temperature can be easily estimated and are compared with experiments.
A persistent error in action-angle treatments of Hamiltonian mechanics
Authors: Khein Alexander , Nelson D. F.
Published: September 2005

An error is pointed out that appears uniformly in mechanics textbooks in the evaluation of the radial action integral. The error leads to a loss of certain characteristic frequencies.
Korringa–Kohn–Rostoker method for electron band calculation of the Kronig–Penney model
Authors: Leung K. M.
Published: September 2005

The Korringa–Kohn–Rostoker or the Green’s function method for electron band calculation is illustrated using the Kronig–Penney model.
Local currents in magnetic flux tubes and flux ropes
Authors: Lorrain Paul , Salingaros Nikos
Published: September 2005

A magnetic flux tube is a cylindrical region inside which there exists an axial magnetic field that is much larger than the field outside. Magnetic flux tubes exist in nature, for example, in the sun’s photosphere. We show here that magnetic flux tubes can exist as self-excited dynamos within conducting fluids, in regions where the fluid velocity has a negative radial velocity, in cylindrical coordinates. We find expressions for the local current density, the magnetic force density, the gas pressure, the ohmic power dissipation, the stored magnetic energy, the inductance, and the inherent time constant. A flux rope is a flux tube, plus an axial current and its azimuthal magnetic field. The axial current cannot be generated locally, but it could be injected at one end; that will be the object of another paper.
Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses
Authors: Hake Richard R.
Published: September 2005

A survey of pre/post-test data using the Halloun–Hestenes Mechanics Diagnostic test or more recent Force Concept Inventory is reported for 62 introductory physics courses enrolling a total number of students N=6542. A consistent analysis over diverse student populations in high schools, colleges, and universities is obtained if a rough measure of the average effectiveness of a course in promoting conceptual understanding is taken to be the average normalized gain 〈g〉. The latter is defined as the ratio of the actual average gain (%〈post〉−%〈pre〉) to the maximum possible average gain (100−%〈pre〉). Fourteen “traditional” (T) courses (N=2084) which made little or no use of interactive-engagement (IE) methods achieved an average gain 〈g〉T-ave=0.23±0.04 (std dev). In sharp contrast, 48 courses (N=4458) which made substantial use of IE methods achieved an average gain 〈g〉IE-ave=0.48±0.14 (std dev), almost two standard deviations of 〈g〉IE-ave above that of the traditional courses. Results for 30 (N=3259) of the above 62 courses on the problem-solving Mechanics Baseline test of Hestenes–Wells imply that IE strategies enhance problem-solving ability. The conceptual and problem-solving test results strongly suggest that the classroom use of IE methods can increase mechanics-course effectiveness well beyond that obtained in traditional practice.
Rotating rigid rods or incompressible fluids: How to determine the stress?
Authors: Roulet B. , Viennot L.
Published: September 2005

When a fluid fills up a rotating box, the pressure inside the fluid is easily obtained by solving a closed set of equations. However, if the fluid is incompressible, the mass conservation equation is trivially satisfied and the pressure remains undetermined. After a preliminary analysis of the similar problem of a rotating rigid rod, this paradox is removed by giving the fluid a small value of the compressibility χ and taking χ→0 at the end of the calculation.
Where are the physics majors?
Authors: Ehrlich Robert
Published: September 2005

This article analyzes statistics on physics bachelor degree production at four-year institutions throughout the U.S., and possible factors responsible for high and low output.
Introductory crystallography for solid-state physics: Computer simulations in two dimensions
Authors: Hall B. D.
Published: September 2005

Student understanding and intuition for direct and reciprocal lattices can be enhanced using computer simulations of two-dimensional crystal structures and their diffraction patterns. Many important relationships can be presented very clearly in two dimensions, thus avoiding the added difficulty of visualizing structures in three dimensions. A number of examples are presented and the extension from two dimensions to three is discussed. The implementation of a program used for teaching is outlined.
Bound orbits with positive energy
Authors: West J. , Dassanayake S. , Daniel A.
Published: September 2005

A study of the gravitational interaction of a unit point mass moving external to (r>R) but under the influence of a fixed very thin ring of radius R and mass of M (M≫m) is presented. We consider the case when the motion of the point mass is restricted to the plane of the ring. With this restriction, it is possible to find trajectories for which the system has a positive total energy, and yet the point mass is bound to, and doomed to collide with, the ring. An example of a numerically iterated trajectory is included to support and illustrate this conclusion.
Equivalent resistors of polyhedral resistive structures
Authors: van Steenwijk F. J.
Published: September 2005

The equivalent resistors of regular polyhedral resistive structures between any two of the vertices are calculated in terms of the characteristic properties of the structures. Some special cases are considered.
Would a topology change allow Ms. Bright to travel backward in time?
Authors: Blau Steven K.
Published: September 2005

Many who have studied special relativity have pondered the question, can a person traveling faster than light take a round-trip journey and return earlier than they set off? The answer could go either way, but for any given journey all observers will agree on whether the return was earlier or later than the departure. In the usual space–time, the person must at some point change direction to return to their starting point, and the event of the return is unambiguously timelike separated from the event of the departure. If space is circular rather than linear, however, a superluminal traveler can return home without changing direction, and the issue of whether the return is unambiguously later or earlier than the departure needs to be reconsidered. The device of avoiding a direction change by considering a circular space has been considered by other authors in the context of the twin paradox. In this article I will discuss the twin paradox and superluminal travel on a cylindrical space–time with particular attention to the role of coordinate patchings and their physical interpretation.