bluuebunny/crossref_metadata_2025 huggingface dataset:
Gravitational lenses and plastic simulators
Authors: Adler Ronald J. , Barber William C. , Redar Mark E.
Published: March 2005

The deflection of light by a gravitational field is an important prediction of general relativity. It is thus an interesting problem to illustrate the deflection by simulating the appearance of astronomical objects as seen through a gravitational field. To do this we have constructed plastic lenses to simulate the gravitational deflection of light for three cases: a point mass, a sphere of constant density, and an isothermal gas sphere. In this paper we discuss the calculation of the deflection for any distribution of mass, the shape of general simulation lenses, and the construction of plastic simulation lenses. To illustrate the results we present photos of a grid, a dark spot, and a field of stars and galaxies seen through the lenses. The photos clearly display the distortion of images, Einstein rings and arcs, and brightness intensification.
Lorentz contraction: A real change of shape
Authors: Sorensen Raymond A.
Published: March 2005

A simple model of a solid is created by use of a few charged point particles interacting only with electromagnetic forces. Such a model cannot fix the size of the solid since the particles will be in unstable equilibrium, but the shape will be determined by the requirement of equilibrium. It is then easy to show that when this solid is in motion, it must Lorentz contract in the direction of the motion (as compared with the transverse dimensions) in order for the charges to remain in equilibrium.
Chaotic behavior of the Zeeman Catastrophe Machine
Authors: Litherland Trevis J. , Siahmakoun Azad
Published: March 2005

In this paper, a computer simulation will first demonstrate the catastrophe-theoretic features and rich dynamical behavior of the Zeeman Catastrophe Machine. Furthermore, the salient features of the simulated behavior will be demonstrated with the aid of a shaft encoder interfaced to a PC. The period-doubling route to chaos will be noted in both the simulation and experiment.
Light cones inside the Schwarzschild radius
Authors: Gautreau Ronald
Published: March 2005

Novikov has developed a reference system built around radially moving geodesic clocks that allows particle and light signal trajectories to be followed across the Schwarzschild radius Rs. We utilize Novikov’s reference system to demonstrate that in any light cone inside Rs, there exists a naturally occurring limiting timelike geodesic that divides the light cone into two parts. The limiting geodesic corresponds to a ‘‘last’’ particle that falls from, or rises to, Rs. It is seen in all coordinate systems that allow trajectories to be followed inside Rs. We show how the limiting geodesic appears in Kruskal–Szekeres coordinates and in a geodesic clock analog to Eddington–Finkelstein coordinates. Limitations on the range of validity of the Novikov reference system are also described.
Asymptotic form of the penetration probability of the quantum harmonic oscillator into the classically forbidden region
Authors: Atems D. E. , Wadehra J. M.
Published: March 2005

The penetration probability of the quantum harmonic oscillator into the classically forbidden region is examined in the limit of large quantum numbers using analytical methods. An expression is derived for the asymptotic form of the penetration probability, and is shown to be in good agreement with an earlier result obtained by numerical methods. The asymptotic form of the probability density in the region between the classical turning points is also presented and found to have a simple physical interpretation.
Quantum hydrodynamics and virial theorems
Authors: Price Peter J.
Published: March 2005

This paper elucidates how many-particle quantum hydrodynamic equations underlie the virial formula, including its surface pressure term. It shows the relation of the field variables to the particle Wigner function, proposes a many-particle ‘‘liquid’’ model to approximate these variables, and discusses its application to electrons in semiconductor nanostructures.
Thermoacoustic heat pumps with maximum power transfer
Authors: Ahlborn Boye , Camire Jean
Published: March 2005

Ideal thermoacoustic heat pumps deliver a maximum heat flux if they operate at 1/3 of the Carnot efficiency COD Car=Tc/(Th−Tc). The best position for the stack is about λ/8 from the closed end.
Retardation and relativity: The case of a moving line charge
Authors: Jefimenko Oleg D.
Published: March 2005

The electric and magnetic fields of a line charge of finite length uniformly moving along its axis are derived by using retarded field integrals and also by using transformation equations of the special relativity theory. Both derivations yield the same field equations, although the derivation methods are drastically different. In particular, whereas transformation equations generally associated with Lorentz length contraction are crucial for the relativistic derivation, Lorentz contraction is not used in the retarded field derivation. On the other hand, although the retarded field derivation is based on the idea that retardation in the propagation of electromagnetic effects is a fundamental electromagnetic phenomenon, the relativistic derivation does not take retardation into account. An examination of the two solutions indicates that the field equations obtained classically and relativistically are identical because retardation is implicit in relativistic transformations.
Analysis of asymmetric confined quantum systems by the direct variational method
Authors: Marín J. L. , Rosas R. , Uribe A.
Published: March 2005

The variational method is used to calculate the ground state energy of the hydrogen atom confined within hard spherical and cylindrical surfaces, for an atomic nucleus which is off the center of symmetry of the confining boundary. It is shown that the wave function for the free hydrogen atom in spherical coordinates (referred to the center of symmetry of the confining geometry) can be used without further assumptions to construct the trial wave function systematically. The latter is assumed to be the product of the free wave function and a simple cutoff function that satisfies the appropriate boundary conditions. We compute the ground state energy for these systems and the results are in good agreement with more sophisticated calculations, thus proving the reliability of the proposed strategy.
Dynamical evolution of a fermionic anharmonic oscillator
Authors: Barrozo M. C. D. , Thomaz M. T. , de Toledo Piza A. F. R.
Published: March 2005

We use reduced density matrix methods of general applicability in many-body physics to study one-particle properties of a simple, soluble quantum system, the fermionic anharmonic oscillator. The time evolution of a general initial state of this system is worked out and analyzed in detail from this point of view. We use a canonical transformation of the Bogoliubov type to enhance the power of the one-particle reduced description and show that the reduced density matrix corresponds in general to a statistical mixture even if the state of the entire many-body system is described in terms of a state vector (pure state).
Mechanical resonance displaying changes in phase to large audiences
Authors: Dorner R. , Kowalski L. , Stein M.
Published: March 2005

This article describes lecture demonstration apparatus for displaying free and forced oscillations of a mechanical system to a large class. The setup described won first prize at the AAPT apparatus competition in August 1994. A Plexiglas blade clamped at one end is magnetically driven by a low-frequency generator–amplifier. The frequencies are so low (between 0.2 and 1.2 Hz) that visual observations of displacements are possible. The driving voltage, associated with the force applied, is visualized with a row of 20 light-emitting diodes, a laser pointer projecting displacements, and a photosensor providing sound cues for phase references. Dependence of amplitude and phase on frequency can be seen, heard, and recorded by a large group of students. The apparatus is simple enough to be replicated and used at all levels of physics teaching. Technical details on the LED display unit, and some theoretical considerations, are described in two appendices.
The physics of perfect rockets
Authors: Gowdy Robert H.
Published: March 2005

The most efficient way to operate a rocket is to increase its exhaust velocity as it accelerates. When this increase is done properly, the final kinetic energy of the rocket is maximized. It is shown that the resulting ‘‘perfect rocket’’ is far simpler to analyze than the traditional constant-thrust rocket and provides an excellent application of the material taught in all first semester noncalculus physics courses.
A mechanical resonance apparatus for undergraduate laboratories
Authors: Jones Christopher C.
Published: March 2005

A heavy duty hacksaw blade and a 1000 turn pick-up coil form the basis of a mechanical oscillator for a laboratory exercise in mechanical resonance designed for either the elementary course or in association with an upper level mechanics course. Damped harmonic motion, amplitude, and phase resonance curves, and the transient motion of the system can be studied. Since the resonant frequencies are in the 10 to 20 Hz range, a digital multimeter can be used to record accurate amplitude resonance curves with minimal tedium.
Duality transformations and the Liénard–Wiechert fields of a dual-charged particle
Authors: Heras José A.
Published: March 2005

In this paper we demonstrate how a duality transformation allows us to derive the Liénard–Wiechert fields of a particle possessing both electric and magnetic charge (i.e., the so-called dual-charged particle) in terms of the well-known Liénard–Wiechert fields of the electric charge. By making use of this result, we derive also the Larmor formula for a nonrelativistic, accelerated dual-charged particle.
Potentials and bound states
Authors: Buell Walter F. , Shadwick B. A.
Published: March 2005

We discuss several quantum mechanical potential problems, focusing on those which highlight commonly held misconceptions about the existence of bound states. We present a proof, based on the variational principle, that certain one dimensional potentials always support at least one bound state, regardless of the potential’s strength. We examine arguments concerning the existence of bound states based on the uncertainty principle and demonstrate, by explicit calculations, that such arguments must be viewed with skepticism.
Laboratory experiment for the ratio of specific heats of air
Authors: Mottmann J.
Published: March 2005

A simple introductory setup is described that takes a gas through a complete thermodynamic cycle; air is the working substance. The ratio of specific heats for air is easily measured.
On the problem of making science attractive for women and minorities: An annotated bibliography
Authors: Yarrison-Rice Jan M.
Published: March 2005

How can educators assess and address the lack of interest exhibited by underrepresented youth in science? What strategies can be employed to recruit and retain these young people? Along with a bibliography, the author provides the reader with a brief summary of 20 notable works in the field of recruitment and retention of underrepresented students in math and science. Although highlighted retention and intervention programs reported herein are targeted at young women in particular, many of the suggested strategies are applicable to all students regardless of race, gender, or socio-economic background. It provides scientists who have an interest in science education with basic literature addressing this topic.
The interstellar traveler
Authors: Lagoute C. , Davoust E.
Published: March 2005

We investigate the physics of an interstellar journey on board a spaceship with a constant acceleration, in the framework of special relativity. It is in principle possible to cross the Galaxy within a human lifetime. The aspect of the sky seen from the spaceship is severely distorted by relativistic aberration; most of the visible sky shrinks to a small region of strongly enhanced luminance in the direction of motion, leaving the rest of the celestial sphere almost entirely dark. The invisible universe becomes perceptible by the traveler, as the infrared and radio radiations are Doppler-shifted to visible frequencies in the direction of motion. Navigational problems posed by these relativistic effects are examined.
Periodic orbits of the integrable swinging Atwood’s machine
Authors: Nunes Ana , Casasayas Josefina , Tufillaro Nicholas
Published: March 2005

We identify all the periodic orbits of the integrable swinging Atwood’s machine by calculating the rotation number of each orbit on its invariant tori in phase space, and also providing explicit formulas for the initial conditions needed to generate each orbit.
Time-dependent perturbation and exact results for the periodically driven quantum harmonic oscillator
Authors: Akridge Russell
Published: March 2005

Transition amplitudes and probabilities for the harmonic oscillator with a forcing function proportional to cos(ωt) beginning at time zero are calculated to lowest nonvanishing order using time-dependent perturbation theory. The results are compared with the exact amplitudes and probabilities. When the exact amplitude is expanded in a Taylor series in powers of the coupling constant, the individual terms turn out to be the perturbation amplitudes, showing that the complete series of perturbation amplitudes converges to the exact amplitude.
The Ricci tensor of a diagonal metric
Authors: Boyling J. B.
Published: March 2005

Formulas in suffix notation are obtained for the general diagonal component and the general off-diagonal component of the Ricci tensor of a pseudo-Riemannian manifold of arbitrary dimension with diagonal metric. Two applications to general relativity are briefly considered.
The magnetic Kronig–Penney model
Authors: Ibrahim I. S. , Peeters F. M.
Published: March 2005

The properties of electrons moving in two dimensions in a one-dimensional periodic magnetic field is investigated. The magnetic field is modeled by an alternating sequence of equally spaced Dirac delta spikes along the x axis. This model is the magnetic analog of the classic Kronig–Penney problem.
Virial theorem in quantum statistical mechanics for a charged particle in an electromagnetic field
Authors: Kobe Donald H.
Published: March 2005

The virial theorem is derived in quantum statistical mechanics for a time-dependent Hamiltonian that describes a charged particle in a time-dependent electromagnetic field. The time derivative of the expectation value of the Clausius operator satisfies an equation which is the same form as the classical equation for the Clausius function (r⋅mv). By taking a time average, the virial theorem of quantum mechanics for time-dependent states is obtained. By taking a statistical average and a time average, the virial theorem of quantum statistical mechanics is obtained.
The Millikan oil-drop experiment: Making it worthwhile
Authors: Jones Ray C.
Published: March 2005

Improvements to the Millikan oil drop experiment as it is performed in teaching laboratories are described. Enhancement of the optics in the oil-drop apparatus greatly improves the visibility of the drops. Accurate timing of their motion becomes possible since they are now bright and sharply focused. With improved timing, the parameters such as microscope calibration and plate separation can become the principal sources of experimental error. Methods are described to accurately determine these experimental parameters. The workload for the experimenter is greatly reduced by using a computer to: act as a smart stopwatch, calculate the drop charge in real time, perform the statistics, and make records of the experiment. The convenience and speed offered by the computer, coupled with improved optics, relieves the eyestrain, fatigue, and frustration usually associated with this experiment. Nye’s watch oil was used in this study. A return to Millikan’s original iteration method for the correction to Stokes’ law lowers the calculated charge for small drops by about 2%. With these improvements the calculated charges are sufficiently accurate that guesswork as to the multiplicity of their charge is essentially eliminated. A student typically obtains the value of the electronic charge accurate to about 1% with 1 h of experimentation. Student and instructor satisfaction are much improved.
Teaching physics on line
Authors: Smith Richard C. , Taylor Edwin F.
Published: March 2005

Since 1986 we have offered courses on special relativity and general relativity in a variety of formats over computer networks nationwide to a mix of high school students, high school teachers, college students, and college professors. Using ideas from many sources, we have evolved a highly structured format that keep students working every day and talking extensively with one another over the conference system. Obligatory student ‘‘Reading Memos’’ bring a flood of comments and complaints essential to evaluation of student progress and revision of the text. We consider possible reasons why these courses from the United States have not worked with participants in Europe, and speculate about possible consequences of future technological developments.
Electronic paramagnetism in biomolecular structure and function
Authors: Brill A. S. , Fiamingo F. G. , Gerstman B. S.
Published: March 2005

Intrinsic paramagnetic states are ubiquitous in biological systems, and extrinsic paramagnetic probes are often introduced in studies of biomolecular structure. The measurements of electron paramagnetic resonance and magnetic susceptibility are commonly employed in investigations of biomolecular paramagnetism. How the data obtained from these measurements are used to arrive at electronic structure, and how the electronic structure and its changes relate to biologically functional processes, are the subjects of this review. Emphasis is placed upon the role of magnetic measurements in quantifying the special properties which proteins confer upon iron and copper ions.
A simple mechanical model for the diatomic molecule exhibiting a magnetic monopole in nuclear dynamics
Authors: Foat Jason , Lam Kai S.
Published: March 2005

A very simple model of a diatomic molecule—a rigid dumbbell-flywheel system—is used to illustrate the close relationship between molecular dynamics and gauge fields. It is shown that, under the adiabatic approximation and certain assumptions, even a simple classical analysis yields a Lorentz force in nuclear dynamics due to a magnetic monopole gauge field. This classical treatment, however, fails to explain the origin of the ‘‘magnetic’’ force. An exact quantum mechanical treatment based on relinquishing the Born–Oppenheimer approximation reveals unambiguously both the origin and the nature of the monopole gauge potential, justifies the adiabatic approximation, and yields an expression for the energy eigenvalues. We believe this simple and exactly solvable model is not only suitable as a pedagogical tool for molecular dynamics, but also ideal for communicating some aspects of the physics behind gauge field theories to advanced undergraduates.
Pressure melting and ice skating
Authors: Colbeck S. C.
Published: March 2005

Pressure melting cannot be responsible for the low friction of ice. The pressure needed to reach the melting temperature is above the compressive failure stress and, if it did occur, high squeeze losses would result in very thin films. Pure liquid water cannot coexist with ice much below −20 °C at any pressure and friction does not increase suddenly in that range. If frictional heating and pressure melting contribute equally, the length of the wetted contact could not exceed 15 μm at a speed of 5 m/s, which seems much too short. If pressure melting is the dominant process, the water films are less than 0.08 μm thick because of the high pressures.
A ‘‘black box’’ moment of inertia apparatus
Authors: Amato Joseph C. , Williams Roger E. , Helm Hugh
Published: March 2005

We describe an apparatus with which the shape, size, and composition of a concealed body are determined by measuring the body’s moments of inertia about its three principal axes. The apparatus is constructed using inexpensive, easily obtained materials and components. Just as in professional research, students must rely solely on their data to guide them to the correct answer. Response to the experiment has been very favorable.
Exact solution to the field equations in the case of an ideal, infinite solenoid
Authors: Templin Jacques D.
Published: March 2005

The calculation of the induced electromotive force in a circular coil placed around the outside of an infinitely long, ideal solenoid is found in many textbooks. This calculation has led to some confusion since we appear to have a changing magnetic field producing an electric field in a region where there is no magnetic field. An exact solution of Maxwell’s equations is given when the source is a steady alternating current. The results of the two methods are compared. In addition, this solution makes it possible to give an exact calculation of the radiation reaction and compare it with the radiated power.
Evaluation of the eigenvalues of multiple quantum-well potentials
Authors: Deck R. T. , Li Xiangshan
Published: March 2005

We present a method for determining the bound and quasibound state eigenvalues of an arbitrary multiple quantum-well potential based on the poles of the reflection coefficient at the first boundary of the potential. The method has the advantage of computational simplicity and can be used to approximate the eigenvalues of a coordinate-dependent potential. As examples, the method is used to determine the bound and tunneling state eigenvalues of a three-boundary potential and the bound state eigenvalues of a five quantum-well potential. The method is compared with other methods of analysis of quantum-well potentials.
Sudden expansion or squeezing of a harmonic oscillator
Authors: Aslangul Claude
Published: March 2005

I consider the dynamics of a harmonic oscillator when its (circular) frequency ω is suddenly changed by a given factor λ. This exactly solvable time-dependent system can be analyzed by using the basic tools of quantum mechanics and provides a simple illustration of their mutual relations and usefulness.
Statistical interpretation of 10−24 moles and less
Authors: Das Bedamati , Gupta-Bhaya Pinaki
Published: March 2005

A few examples of systems in thermodynamic equilibrium are cited in the classic text of Lewis and Randall [Thermodynamics (McGraw-Hill, New York, 1960)] which are problematic in that classical thermodynamics predicts the presence of a very small fraction of a single atom in a given form, e.g., tungsten vapor present in equilibrium with solid at 100 °C (p≂10−105 atmosphere). Lewis and Randall state, however, that the vapor pressure of a normal system, e.g., water at room temperature and that of tungsten at 100 °C, can be used ‘‘with the same sense of security.’’ They do not elaborate further. The problem is analyzed from first principles and it is pointed out that the apparent incongruity in having a fractional atom is removed in the density matrix description of the equilibrium state. A description of the equilibrium state that avoids the concept of a ‘‘fractional atom’’ has to identify the equilibrium property as a time average. The shortcoming of such a description is pointed out.
Flow profile study using miniature laser-Doppler velocimetry
Authors: Booij W. E. , de Jongh A. , de Mul F. F. M.
Published: March 2005

We present a physics experiment, in which laser-Doppler velocimetry is used to make first-year university physics students realize that the idealized solutions offered by standard text books seldom are applicable without corrections, which often are numerical. This is demonstrated by carefully measuring and calculating the flow profile in a rectangular pipe.
Demonstration of Amperian currents
Authors: Dearden E. W.
Published: March 2005

The availability of thin rectangular ceramic permanent magnets, uniformly hard magnetized parallel to the small dimension, now makes it easy to present a compelling visual demonstration of the Amperian view of magnetization to large classes, and to estimate the magnetic properties by simple fundamental measurement.
Electrostatic energy of a system of charges and dielectrics
Authors: Das Bedamati , Ghosh Avik , Gupta-Bhaya Pinaki
Published: March 2005

The expression for the energy of a system of charges and linear dielectrics is divided into terms arising from the coulomb energy of subsystems of free and bound charges, from their interaction, and from the energy stored in the dielectric in the process of creating the bound charges.
Electromagnetic forces on dissipative dielectric media
Authors: Giner V. , Sancho M. , Martínez G.
Published: March 2005

The standard treatment of electric and magnetic forces on material bodies, based on energy conservation through the calculation of the work done in the course of a displacement of the object, fails when media are dissipative. We emphasize that the study of these systems requires consideration of the general momentum balance that leads to obtaining the forces by integration of the Maxwell stress tensor across the body surface. We study the influence of losses in some examples, including the cases of a liquid between charged parallel plates and a dielectric sphere in a nonuniform field. An analysis of the physical origin of the differences with the corresponding loss free cases, based on the study of the electric forces on true and polarization charges, is made.
Self-directed learning: A heretical experiment in teaching physics
Authors: Silverman M. P.
Published: March 2005

An account is given of the instruction of university-level introductory physics courses according to an educational framework in which (1) curiosity-driven inquiry is recognized as an essential activity of both science and science teaching; (2) the principal role of the instructor is to provide students the incentive to learn science through their pursuit of personally meaningful questions; (3) the commission of errors is regarded as a natural concomitant to learning and is not penalized; (4) emphasis is placed on laboratory investigations that foster minimally restrictive free exploration rather than prescriptive adherence to formal procedure; (5) research skills are developed through out-of-class projects that involve literature search, experiment, and the modeling of real-world physical phenomena: (6) the precise and articulate use of language is regarded as seminal to communication in science (as it is in the humanities) and is promoted through activities that help develop written and oral language skills; (7) the evaluation of student performance is based on a portfolio of accomplished work rather than on the outcome of formal testing.
Making the invisible visible: A teaching/learning environment that builds on a new view of the physics learner
Authors: Goldberg Fred , Bendall Sharon
Published: March 2005

We briefly describe a new view of the science learner that has emerged from recent research and then discuss how we have built on this view to design a physics course for prospective elementary teachers. The main goals are to help students develop robust conceptual models in various physics domains and to help them become more aware of, and more responsible for, their own learning. The integrated set of course activities to help promote these goals includes the use of highly interactive multimedia computer programs and the writing and collaborative peer evaluations of comprehensive explanations of novel phenomena. Evidence is provided to suggest that the total course environment has helped accomplish our goals.
Vibrational properties of a loaded string
Authors: Parmley Samantha , Zobrist Tom , Clough Terry , Perez-Miller Anthony , Makela Mark , Yu Roger
Published: March 2005

In this paper we discuss our study of a string–mass chain and its anology to quantum mechanical systems. Theoretical predictions are made based upon the numerical solution to the wave equation. These predictions are tested experimentally using both normal mode analysis and pulse analysis. The frequency band structures for periodic and disordered string mass chains are studied as well as their corresponding eigenfunctions. The theoretical and experimental results are in accord. This experiment, suitable for advanced physics majors, demonstrates many important features of quantum mechanics: eigenvalues, superposition principle, band structure, gap modes, and Anderson localization.
The approximation to the exponential decay law
Authors: Jakobovits H. , Rothschild Yehuda , Levitan J.
Published: March 2005

The exponential decay law is a consequence of the choice of the ‘‘Breit–Wigner’’ energy distribution when the integration over the energy is extended from −∞ to +∞. We explain why the Breit–Wigner function is the natural choice and study by the method of steepest descent and by direct integration how an integration over the physically relevant positive energy spectrum affects the decay law.
Modernizing introductory physics
Authors: Holbrow C. H. , Amato J. C. , Galvez E. J. , Lloyd J. N.
Published: March 2005

Since 1985 the Colgate University Department of Physics and Astronomy has been reshaping the first term of introductory calculus-level physics to answer the question: ‘‘Why do we believe in atoms and the properties ascribed to them?’’ This paper describes the new course, its 400-page text, its ten laboratories, its six computer exercises, and how these work together successfully to serve several purposes: For those students who do not continue on with any more physics, it is a good introduction to physics; for the many students whose quantitative skills need enhancing, it provides a better chance to improve those skills than traditional introductory physics; by its emphasis on wave-particle duality and mass-energy equivalence, the course introduces students to important quantum and relativistic ideas that are fundamental to most of what contemporary physicists actually do. We also extract from our reform efforts some lessons useful to anyone undertaking to change introductory physics.
D-dimensional moments of inertia
Authors: Bender Carl M. , Mead Lawrence R.
Published: March 2005

We calculate the moments of inertia of D-dimensional spheres and spherical shells, where D is a complex number. We also examine the moments of inertia of fractional-dimensional geometrical objects such as the Cantor set and the Sierpinski carpet and their D-dimensional analogs.
Surface charges on circuit wires and resistors play three roles
Authors: Jackson J. D.
Published: March 2005

The significance of the surface electric charge densities associated with current-carrying circuits is often not appreciated. In general, the conductors of a current-carrying circuit must have nonuniform surface charge densities on them (1) to maintain the potential around the circuit, (2) to provide the electric field in the space outside the conductors, and (3) to assure the confined flow of current. The surface charges and associated electric field can vary greatly, depending on the location and orientation of other parts of the circuit. We illustrate these ideas with a circuit consisting of a resistor and a battery connected by wires and other conductors, in a geometry that permits solution with a Fourier–Bessel series, while giving flexibility in choice of wire and resistor sizes and location of the battery. Plots of the Poynting vector graphically demonstrate energy flow from the battery to the resistive elements. For a resistor with a large resistance, the potentials and surface charge densities around the current-carrying circuit are nearly the same as for the open circuit with the resistor removed. For such resistors, the capacitance of a resistor and its adjacent elements, defined in terms of the surface and interface charges present while current flows, is roughly the same as the capacitance of the adjacent elements of the open circuit alone. The discussion is in terms of time-independent currents and voltages, but applies also to low-frequency ac circuits.
A graphical representation of the Dirac algebra
Authors: Goodmanson David M.
Published: March 2005

The elements of the Dirac algebra are represented by sixteen 4×4 gamma matrices, each pair of which either commute or anticommute. This paper demonstrates a correspondence between the gamma matrices and the complete graph on six points, a correspondence that provides a visual picture of the structure of the Dirac algebra. The graph shows all commutation and anticommutation relations, and can be used to illustrate the structure of subalgebras and equivalence classes and the effect of similarity transformations. Since gamma matrices are the direct products of two Pauli spin matrices, they provide an appropriate way to describe a system of two spin-1/2 particles. Such multiparticle spin states are intimately connected with the theorems of John Bell. The graph is helpful in analyzing an important example of the Bell–Kochen–Specker theorem.
Surface charges and energy flow in a ring rotating in a magnetic field
Authors: Aguirregabiria J. M. , Hernández A. , Rivas M.
Published: March 2005

An ohmic ring that rotates with constant angular velocity in an external uniform magnetic field is considered as a simple model for a current generator. Under the assumption that all quantities vary slowly in time, the lowest-order approximation to the surface charge density is found. The flux of the Poynting vector through the loop surface is also computed. Unlike in the examples that are given in textbooks, this flux is not always incoming: It has the outgoing direction around the loop parts where the electrons are moving against electrostatic forces.
Visual appearance of a rolling bicycle wheel
Authors: de Souza Ricardo E. , Vasconcelos Giovani L.
Published: March 2005

It is shown that the different patterns of blurriness observed on a photograph of a rolling bicycle wheel give a rather complete picture of the velocity field within a rolling disk.
Pulsed waves: Reflections and the speed of sound
Authors: Yarmus Leonard
Published: March 2005

A simple, direct, and inexpensive determination of the speed of sound in air, suitable for an undergraduate laboratory exercise, is presented. The same apparatus is used to demonstrate acoustic pulse reflections from closed and open ended tubes of circular cross section.
Magnetic damping: Analysis of an eddy current brake using an airtrack
Authors: Cadwell Louis H.
Published: March 2005

A simple theory is proposed using Faraday’s law and the Lorentz force to analyze the effect of magnetic damping on an aluminum plate moving on a horizontal air track as it passes between the poles of a horseshoe magnet. The position, velocity, and acceleration of the nonmagnetic conducting plate are measured as a function of time using a motion detector. Using some simplifying assumptions, a theoretical model is obtained in which a single free parameter is used to fit the experimental data. This parameter corresponds to an effective length (LR) in which the eddy current encounters resistance as it moves around a closed path in the conductor. This leads to some interesting, but unexpected, results about the shape and magnitude of induced eddy currents.
Resource letter EPA-1: Electronic polymers and their applications
Authors: Blatchford J. W. , Epstein A. J.
Published: March 2005

This Resource Letter provides a guide to the literature on electronic polymers and their potential applications. Journal articles and books are cited for the following topics: (i) theories of the electronic structure and excited states of conjugated polymers, the role of electron–phonon and electron–electron interactions in determining these states, the mechanisms of charge transport, and the insulator–metal transition; (ii) information on the synthesis, structure, and morphology of representative polymers; (iii) results of transport, optical, and magnetic measurements on both conductive and semiconducting/insulating materials; and (iv) solid state device and other applications for conjugated polymers.
Poles, bound states, and resonances illustrated by the square well potential
Authors: Sprung D. W. L. , Wu Hua , Martorell J.
Published: March 2005

Poles of the S matrix in the complex momentum plane are known to be related to the bound states, virtual states, and transmission resonances of the potential. We illustrate this by tracing the motion of the poles in the case of a square well in one dimension. The conditions for appearance of prominent resonances are clarified. It is shown that the graphical solution due to Pitkanen provides the virtual or antibound states as well as the bound states. A near-threshold formula for the binding energies is presented that also works for the antibound states.
The physical pendulum on a cylindrical support
Authors: Giltinan David A. , Wagner David L. , Walkiewicz Thomas A.
Published: March 2005

An alternative derivation is presented for the period of a physical pendulum rotating on a cylindrical support. Absolute and relative accelerations are used to obtain the equations of motion for the pendulum.
The hydraulic jump in radially spreading flow: A new model and new experimental data
Authors: Blackford B. L.
Published: March 2005

A new model for the hydraulic jump in radially spreading flow is presented. The equation of motion for a liquid annulus spreading out under the influence of hydrostatic pressure gradient and Frictional drag is developed. The resulting nonlinear differential equation for the liquid depth, h(r), is solved by computer simulation. The jump is assumed to begin when the laminar flow is engulfed by the underlying boundary layer liquid, as suggested recently in the literature. This complicated mixing process is crudely modeled by a drag term which slows the flow and initiates a positive feedback mechanism culminating at a new critical depth, beyond which the depth increases asymptotically to a final value. The model predicts a new relationship between the laminar flow depth just before the jump and the final depth. An experimental apparatus was built to make detailed measurements of the depth h(r), both in the region before the jump and beyond the jump. The theoretical predictions were compared to the experimental data, and gave surprisingly good agreement by suitable adjustment of the two parameters k and C of the model. The parameter k determines the growth rate of the boundary layer thickness, and C determines the drag force. The results suggest that the usual textbook assumption of zero momentum loss across the jump is not appropriate for this type of hydraulic jump. The case of a hydraulic jump in the absence of gravity is considered also and a much different behavior is predicted, which could be tested by experiment in a microgravity environment.
Resonance response of a moderately driven rigid planar pendulum
Authors: Peters Randall D.
Published: March 2005

The steady-state motion of a rigid planar pendulum has been studied as the drive frequency was tuned through ‘‘resonance’’ of the pendulum. Depending on amplitude of the drive, dramatically different responses were observed. The only motions studied in detail were ones involving period-one limit cycles. A range of surprisingly large hysteresis was discovered, in which amplitude jumps occur in only one direction. A highly nonlinear mode, that is not chaotic, was discovered. It is apparently known by bell ringers but not by physicists. Amplitude jumps out of the bell-ringer mode appear to exhibit transient chaos for some cases.
A maritime analogy of the Casimir effect
Authors: Boersma Sipko L.
Published: March 2005

At sea, on a windless day, in a strong swell, free floating ships will roll heavily. It was believed in the days of the clipper ships that under those circumstances two vessels at close distance will attract each other. Do they? The ships are harmonic oscillators in a wave field and as such analogous to two atoms in the sea of vacuum fluctuations. These atoms do attract: the van der Waals force.
Life and death in an expanding cage and at the edge of a receding cliff
Authors: Krapivsky P. L. , Redner S.
Published: March 2005

The survival probabilities of a particle diffusing within an expanding ‘‘cage’’ and near the edge of a receding ‘‘cliff,’’ with death occurring when the diffuser reaches a boundary of the system, are investigated. Especially interesting behavior arises when the position of the boundary recedes from the diffuser as √At. In this case, the recession matches the rms displacement √Dt with which diffusion tends to bring the diffuser to its demise. For both the cage and cliff problems, the survival probability S(t) exhibits a nonuniversal power-law decay in time, S(t)∼t−β, in which the value of β is dependent on the detailed properties of the boundary motion. Heuristic approaches are applied for the cases of ‘‘slow’’ (A/D≪1) and ‘‘fast’’ (A/D≫1) boundary motion which yield approximate expressions for β. An asymptotic analysis of the survival probability for the cage and cliff problems is also performed. The approximate expressions for β are in good agreement with the exact results for nearly the entire range of possible boundary motions.
Use of the computer for research on student thinking in physics
Authors: Grayson Diane J. , McDermott Lillian C.
Published: March 2005

This paper describes the use of the computer-based interview as a research technique for investigating how students think about physics. Two computer programs provide the context: one intended for instruction, the other for research. The one designed for use as an instructional aid displays the motion of a ball rolling along a track that has level and inclined segments. The associated motion graphs are also shown. The other program, which was expressly designed for use in research, is based on the simulated motion of a modified Atwood’s machine. The programs require students to predict the effect of the initial conditions and system parameters on the motion or on a graph of the motion. The motion that would actually occur is then displayed. The investigation focuses on the reasoning used by the students as they try to resolve discrepancies between their predictions and observations.
A nonlinear mechanical oscillator for physics laboratories
Authors: Dorner R. , Kowalski L. , Stein M.
Published: March 2005

This article describes a simple nonlinear mechanical oscillator suitable for an undergraduate physics laboratory. The oscillating system is a Plexiglas blade, with nonlinearity introduced by means of contact with stretched rubber bands. Using a variable driving frequency, students can make amplitude and phase lag measurements with sufficient accuracy for quantitative work. It is possible to study classical resonance with the linear system and then, with the modified system, produce nonlinear effects such as hysteresis.
The reversible process: A zero-entropy-production limit
Authors: Thomsen John S. , Bers Helene C.
Published: March 2005

After the concept of entropy has been introduced in the classical approach to thermodynamics, the definition of a reversible process may be refined in a mathematical way. If a given process can be modified by appropriate adjustment of the thermodynamic force involved so that it approaches a limit of zero entropy production, defining a limit process, and if the reverse process can be similarly modified, defining the same limit process in reverse, then we say that the process is reversible in this limit. Two examples are given, one dealing with the heating of a system and the second involving the adiabatic expansion of a viscous ideal gas.
Validity of variational procedures for resonant states
Authors: García-Zenteno A. , Moshinsky M. , Smirnov Yu. F.
Published: March 2005

The behavior of variational procedures for bound states is well understood, when using harmonic oscillator wave functions whose frequency ω is the only parameter. The same procedure, when applied to problems that have resonant states, shows a completely different behavior. By analyzing the s-wave problem for a cavity potential of the form b′δ(r′−a), we show that, as a function of ω, it gives rise to plateaus that correspond to the real part of the resonant energies, assuming values of b′ related to very narrow resonances compared with their separations. If the latter condition holds, the procedure seems generalizable to other types of potentials.
A simple integrated circuit model of propagation along an excitable axon
Authors: Bunton P. H. , Henry W. P. , Wikswo J. P.
Published: March 2005

We present a simple integrated circuit model of an excitable nerve axon based on a rotating switch. The heart of the circuit consists of two integrated circuits—a dual rotating switch and a quad comparator. Both the passive and active response of a segment of axon membrane are modeled. A single segment exhibits passive cable behavior up to a threshold voltage. Once threshold is reached, the segment ‘‘fires,’’ i.e., currents representative of sodium and potassium depolarizing and repolarizing currents flow sequentially. Furthermore, successive segments have been connected to model an extended section of excitable axon. A linear array of light emitting diodes (LEDs) connected to each segment allows the voltage on that segment to be visibly monitored. When mounted as a two-dimensional LED array, this results in a ‘‘spatial oscilloscope’’ which shows the action potential propagating along the axon. The circuit could serve as a teaching tool for both the biophysics of nerve signal propagation and for electronics. It has the virtue of being relatively simple to understand as it is based on a rotating switch.
Using a moving diffraction grating to simulate the function of an acousto-optic modulator
Authors: Corey R. , Schmidt A. , Saulnier P.
Published: March 2005

We present an instructional undergraduate laboratory that introduces the student to an acousto-optic modulator (AOM) in the context of an optical heterodyning experiment. A moving diffraction grating is used to illustrate the internal functioning of an acousto-optic modulator and to make optical heterodyning experiments accessible to any undergraduate laboratory. The concepts and techniques presented can be used from the introductory through advanced level, in that, students gain direct laboratory experience with diffraction, the Doppler shift of light, construction of a Mach–Zehnder interferometer, optical path length measurements using a heterodyne technique, and sophisticated data analysis techniques.
Introduction to the diffusion Monte Carlo method
Authors: Kosztin Ioan , Faber Byron , Schulten Klaus
Published: March 2005

A self-contained and tutorial presentation of the diffusion Monte Carlo method for determining the ground state energy and wave function of quantum systems is provided. First, the theoretical basis of the method is derived and then a numerical algorithm is formulated. The algorithm is applied to determine the ground state of the harmonic oscillator, the Morse oscillator, the hydrogen atom, and the electronic ground state of the H+2 ion and of the H2 molecule. A computer program on which the sample calculations are based is available upon request.
Quantum mechanical time-development operator for the uniformly accelerated particle
Authors: Robinett R. W.
Published: March 2005

We derive a useful expression for the time-development operator for quantum wave functions, exp(−iĤt/ℏ), for the case of a particle subject to a constant force. We apply it, in both position and momentum space, to construct wave packets that exhibit uniform acceleration. We use these results to generate quantum wave packets corresponding to the motion of a charged particle in a uniform electric field in two different gauges, explicitly demonstrating the change in phase of the wave function under a gauge transformation. The more standard description of the time dependence of accelerating wave packets using the formalism of propagators is briefly reviewed in an Appendix for comparison.