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Dec 2003

Volume 71, Issue 12, pp. 1223-1325

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Quantum statistics: Is there an effective fermion repulsion or boson attraction?

W. J. Mullin and G. Blaylock

American Journal of Physics -- December 2003 -- Volume 71, Issue 12, pp. 1223 | Cited 6 times

Online Publication Date: Nov 2003

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Physicists often claim that there is an effective repulsion between fermions, implied by the Pauli principle, and a corresponding effective attraction between bosons. We examine the origins and validity of such exchange force ideas and the areas where they are highly misleading. We propose that explanations of quantum statistics should avoid the idea of an effective force completely, and replace it with more appropriate physical insights, some of which are suggested here. © 2003 American Association of Physics Teachers.
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01.50.-i Educational aids
05.30.Fk Fermion systems and electron gas
05.30.Jp Boson systems

An extension of Thomson’s theorem and its application for determining induced charge densities

C. Donolato

American Journal of Physics -- December 2003 -- Volume 71, Issue 12, pp. 1232 | Cited 2 times

Online Publication Date: Nov 2003

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Thomson’s theorem of electrostatics states that the equilibrium distribution of charge on a system of conductors is that of minimum energy relative to other charge distributions with the same amount of charge on each conductor. By an appropriate modification of the energy functional, the theorem is extended to the case where the potential of some conductors, rather than their charge, is fixed. This extension is of interest in the analysis of electrostatic induction. The basic theorem and its extension are applied to a spherical conductor in the presence of a point charge or placed in a uniform external field. The known expressions for the induced surface charge density in different conditions are obtained from the direct minimization of the new functional on the basis of a simple argument. © 2003 American Association of Physics Teachers.
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01.50.-i Educational aids
41.20.Cv Electrostatics; Poisson and Laplace equations, boundary-value problems

Thermodynamics of black holes in a finite box

P. S. Custódio and J. E. Horvath

American Journal of Physics -- December 2003 -- Volume 71, Issue 12, pp. 1237 | Cited 1 time

Online Publication Date: Nov 2003

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We analyze the thermodynamic behavior of black holes in a finite closed box. The evolution of the black hole mass is analyzed, with and without radiation initially. We deduce a minimal volume above which one black hole can lose all of its mass to the box, a result that agrees with a previous analysis by Page. The equilibrium times and masses are evaluated and their behavior is discussed. We show that N black holes achieve the same equilibrium masses even though the initial masses were different. The total entropy of the system is used to derive the functional dependence of the equilibrium mass on the box volume, the number of black holes, and the temperature of the radiation. A set of problems devised to reinforce the concepts is also presented. © 2003 American Association of Physics Teachers.
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01.50.-i Educational aids
04.70.-s Physics of black holes
97.60.Lf Black holes

A formula for the number of days between the winter solstice and the latest sunrise

Matthias Reinsch

American Journal of Physics -- December 2003 -- Volume 71, Issue 12, pp. 1242

Online Publication Date: Nov 2003

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A simple closed-form expression for the number of days between the winter solstice and the latest sunrise is derived. Formulas for the summer solstice and the sunset are derived as well. These approximate formulas make it easy to see the functional dependence on the latitude of the observer. An approximate expression for the difference in time of day between the latest sunrise and the sunrise on the solstice is also derived. The formulas are not valid in the Arctic, Antarctic or tropics. © 2003 American Association of Physics Teachers.
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01.50.-i Educational aids
95.10.Ce Celestial mechanics (including n-body problems)

Microscopic modeling of multi-lane highway traffic flow

Nathan O. Hodas and Anand Jagota

American Journal of Physics -- December 2003 -- Volume 71, Issue 12, pp. 1247

Online Publication Date: Nov 2003

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We discuss a microscopic model for the study of multi-lane highway traffic flow dynamics. Each car experiences a force resulting from a combination of the desire of the driver to attain a certain velocity, aerodynamic drag, and change of the force due to car–car interactions. The model also includes multi-lane simulation capability and the ability to add and remove obstructions. We implement the model via a Java applet, which is used to simulate traffic jam formation, the effect of bottlenecks on traffic flow, and the existence of light, medium, and heavy traffic flow. The simulations also provide insight into how the properties of individual cars result in macroscopic behavior. Because the investigation of emergent characteristics is so common in physics, the study of traffic in this manner sheds new light on how the micro-to-macro transition works in general. © 2003 American Association of Physics Teachers.
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47.11.-j Computational methods in fluid dynamics
01.50.-i Educational aids

Experiments with the drinking bird

J. Güémez, R. Valiente, C. Fiolhais, and M. Fiolhais

American Journal of Physics -- December 2003 -- Volume 71, Issue 12, pp. 1257 | Cited 4 times

Online Publication Date: Nov 2003

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We present a simple model of the dynamics of the drinking bird and relate its period to the properties of its internal and external liquids. The effect of humidity on the motion is studied and it is shown that there are two evaporation regimes. The results of the model are in agreement with observations. © 2003 American Association of Physics Teachers.
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01.50.-i Educational aids
45.40.-f Dynamics and kinematics of rigid bodies

Experiments with a sunbird

J. Güémez, R. Valiente, C. Fiolhais, and M. Fiolhais

American Journal of Physics -- December 2003 -- Volume 71, Issue 12, pp. 1264 | Cited 2 times

Online Publication Date: Nov 2003

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A theoretical description of the sunbird, a drinking bird without any external liquid, is compared with experiment. The transient times and the periods of oscillation given by a simulation of the dynamics agree with the measured values. © 2003 American Association of Physics Teachers.
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01.50.-i Educational aids
64.70.F- Liquid-vapor transitions
44.40.+a Thermal radiation

The method of least squares used to invert an orbit problem

Ross Bannister

American Journal of Physics -- December 2003 -- Volume 71, Issue 12, pp. 1268 | Cited 2 times

Online Publication Date: Nov 2003

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Six parameters uniquely describe the orbit of a body about the Sun. Given these parameters, it is possible to make predictions of the body’s position by solving its equation of motion. The parameters cannot be directly measured, so they must be inferred indirectly by an inversion method which uses measurements of other quantities in combination with the equation of motion. Inverse techniques are valuable tools in many applications where only noisy, incomplete, and indirect observations are available for estimating parameter values. The methodology of the approach is introduced and the Kepler problem is used as a real-world example. © 2003 American Association of Physics Teachers.
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01.50.-i Educational aids
98.10.+z Stellar dynamics and kinematics

Mr. Tompkins in Java: Interactive Lorentz transformations

Prasenjit Saha

American Journal of Physics -- December 2003 -- Volume 71, Issue 12, pp. 1276

Online Publication Date: Nov 2003

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This paper describes a simple applet for illustrating Lorentz transformations. The user specifies stationary and moving objects and light pulses, and sees animations of two reference frames. Even with minimal graphics (the objects are colored dots and the light flashes are expanding circles), such animations can make the concepts of redshift, length contraction, time dilation, and non-simultaneity more intuitive than traditional spacetime diagrams. © 2003 American Association of Physics Teachers.
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01.50.-i Educational aids
03.30.+p Special relativity

Euler angle geometry, helicity basis vectors, and the Wigner D-function addition theorem

J. David Pendleton

American Journal of Physics -- December 2003 -- Volume 71, Issue 12, pp. 1280 | Cited 1 time

Online Publication Date: Nov 2003

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Euler angles often are used to describe the orientation of a secondary system rotated relative to a primary system by generating two auxiliary systems and the secondary with three rotations. We use basis vectors to show that the auxiliary systems of the y-convention Euler angles (used in quantum mechanics) are the cylindrical and spherical systems associated with the primary Cartesian system. We then apply Euler angle geometry to obtain an improved expression (and understanding) of the Wigner D-function addition theorem and related geometrical issues. We introduce helicity vectors and express vector spherical harmonics as combinations of Wigner D-functions to show that the D-function addition theorem is implicit within expansions of rotated vector spherical harmonics. As example applications of the Wigner D-function, we obtain an addition theorem for vector spherical harmonics and then simplify a dyadic Green function (related to Mie theory) describing inelastic light scattering from a laser-irradiated spherical droplet containing a fluorescing molecule.
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01.50.-i Educational aids
03.65.-w Quantum mechanics
33.50.Dq Fluorescence and phosphorescence spectra

Vector constants of the motion and orbits in the Coulomb/Kepler problem

Gerardo Muñoz

American Journal of Physics -- December 2003 -- Volume 71, Issue 12, pp. 1292 | Cited 4 times

Online Publication Date: Nov 2003

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The equation for the conic sections describing the possible orbits in a potential V∼r−1 is obtained by means of a vector constant of the motion differing from the traditional Laplace–Runge–Lenz vector. © 2003 American Association of Physics Teachers.
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01.50.-i Educational aids
95.10.Ce Celestial mechanics (including n-body problems)
45.50.Pk Celestial mechanics

A study of electric dipole radiation via scattering of polarized laser light

Natthi L. Sharma, Ernest R. Behringer, and Rene C. Crombez

American Journal of Physics -- December 2003 -- Volume 71, Issue 12, pp. 1294

Online Publication Date: Nov 2003

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We have developed an advanced undergraduate experiment to explore electric dipole radiation in the optical frequency domain. A polarized laser beam is used to illuminate an aqueous suspension of skim milk, and the light scattered from the suspension is measured in the plane perpendicular to the laser beam as a function of the angle θ with respect to the polarization direction and as a function of the perpendicular distance R from the laser beam. When the length of the scattering region, d, is much smaller than R, the measurements agree very well with the sin2 θ/R2 dependence of electric dipole radiation. Increasing the scatterer concentration increases the background of multiply scattered light and decreases the degree of polarization of the scattered light with no appreciable change in the observed sin2 θ/R2 dependence. We discuss variations of the experiment for different instructional needs and describe how an understanding of dipole radiation helps students to appreciate a number of optical phenomena. © 2003 American Association of Physics Teachers.
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01.50.Pa Laboratory experiments and apparatus
42.25.Dd Wave propagation in random media
42.60.Jf Beam characteristics: profile, intensity, and power; spatial pattern formation
82.70.Kj Emulsions and suspensions
41.20.-q Applied classical electromagnetism

Einstein–Cartan theory as a theory of defects in space–time

M. L. Ruggiero and A. Tartaglia

American Journal of Physics -- December 2003 -- Volume 71, Issue 12, pp. 1303 | Cited 8 times

Online Publication Date: Nov 2003

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The Einstein–Cartan theory of gravitation and the classical theory of defects in an elastic medium are presented and compared. The former is an extension of general relativity and refers to four-dimensional space–time, while we introduce the latter as a description of the equilibrium state of a three-dimensional continuum. Despite these important differences, an analogy is built on their common geometrical foundations, and it is shown that a space–time with curvature and torsion can be considered as a state of a four-dimensional continuum containing defects. This formal analogy is useful for illustrating the geometrical concept of torsion by applying it to concrete physical problems. Moreover, the presentation of these theories using a common geometrical basis allows a deeper understanding of their foundations. © 2003 American Association of Physics Teachers.
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01.50.-i Educational aids
04.20.Gz Spacetime topology, causal structure, spinor structure

Coaxial cable analogs of multilayer dielectric optical coatings

María del Mar Sánchez-López, Jeffrey A. Davis, and Karlton Crabtree

American Journal of Physics -- December 2003 -- Volume 71, Issue 12, pp. 1314 | Cited 6 times

Online Publication Date: Nov 2003

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We study the properties of periodic coaxial cable structures (coaxial photonic crystals), where the periodicity consists of alternating cables with low and high impedance. We show that the electrical signal that propagates through these structures leads to similar phenomena as the light propagating through the corresponding multilayer dielectric optical coating structures. In this way, Bragg reflectors, optical thin-film filters, and Fabry–Perot resonators are reproduced in the megahertz frequency range. This represents an inexpensive way of experimentally investigating wave propagation in locally periodic media. © 2003 American Association of Physics Teachers.
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01.50.-i Educational aids
42.79.Wc Optical coatings
68.65.Ac Multilayers
78.67.Pt Multilayers; superlattices; photonic structures; metamaterials
42.70.Qs Photonic bandgap materials
77.55.-g Dielectric thin films
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Comment on “Phase transition-like behavior in a low-pass filter,” by H. Krivine and A. Lesne [Am. J. Phys. 71 (1), 31–33 (2003)]

Jack L. Uretsky

American Journal of Physics -- December 2003 -- Volume 71, Issue 12, pp. 1320

Online Publication Date: Nov 2003

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Abstract Unavailable
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01.50.-i Educational aids
05.70.Fh Phase transitions: general studies
64.60.-i General studies of phase transitions

Comment on “A simple special relativistic perturbation scheme for yielding the general relativistic behavior of point particles and photons in the gravitational field of stars,” by Alex Alaniz [Am. J. Phys. 70 (5), 498–501 (2002)]

J. H. Field

American Journal of Physics -- December 2003 -- Volume 71, Issue 12, pp. 1321

Online Publication Date: Nov 2003

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See Also: Erratum

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© 2003 American Association of Physics Teachers.
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01.50.-i Educational aids
95.30.Sf Relativity and gravitation
04.20.-q Classical general relativity

Where is the “Wien peak”?

Mark A. Heald

American Journal of Physics -- December 2003 -- Volume 71, Issue 12, pp. 1322 | Cited 4 times

Online Publication Date: Nov 2003

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Abstract Unavailable
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01.50.-i Educational aids
07.60.Rd Visible and ultraviolet spectrometers
44.40.+a Thermal radiation
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Facts and Mysteries in Elementary Particle Physics

Martinus J. G. Veltman, Author and Martin L. Perl, Reviewer

American Journal of Physics -- December 2003 -- Volume 71, Issue 12, pp. 1324

Online Publication Date: Nov 2003

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Abstract Unavailable
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01.30.Vv Book reviews
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