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Aug 2004

Volume 72, Issue 8, pp. 983-1135

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Resource Letter FNP-1: Frontiers of nuclear physics

G. F. Bertsch

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 983 | Cited 2 times

Online Publication Date: Jul 2004

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This Resource Letter provides a bibliography of the current research activities in nuclear physics and also a guide for finding useful nuclear data. The major areas included are nuclear structure and reactions, symmetry tests, nuclear astrophysics, nuclear theory, high-density matter, and nuclear instrumentation. © 2004 American Association of Physics Teachers.
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01.50.-i Educational aids
01.30.Tt Bibliographies
01.30.Rr Surveys and tutorial papers; resource letters
24.10.-i Nuclear reaction models and methods
11.30.-j Symmetry and conservation laws

Unfamiliar trajectories for a relativistic particle in a Kepler or Coulomb potential

Timothy H. Boyer

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 992 | Cited 8 times

Online Publication Date: Jul 2004

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Relativistic particles in the Kepler and Coulomb potentials may have trajectories that are qualitatively different from the trajectories found in nonrelativistic mechanics. Spiral scattering trajectories were pointed out by C. G. Darwin in 1913 in connection with the relativistic Rutherford scattering of classical charged particles. Relativistic trajectories are of current interest in connection with Cole and Zou’s computer simulation of the hydrogen ground state in classical physics. © 2004 American Association of Physics Teachers.
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01.50.-i Educational aids
03.30.+p Special relativity

Solutions of relativistic Newton’s equations for nonconstant fields

R. E. Wooten and J. H. Macek

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 998 | Cited 1 time

Online Publication Date: Jul 2004

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Newton’s second law can be readily solved for many forces, but few situations can be solved for the relativistic form of Newton’s second law. The only problems directly solvable are those involving charged particles in constant electromagnetic fields. If the external field represents a light pulse, Dirac’s relativistic equation can be solved, as done by Volkov in 1935. Classical solutions based on Volkov’s work employ the Hamilton–Jacobi equations. We discuss the solution of this problem using Newton’s equations, thereby making the solution more accessible. © 2004 American Association of Physics Teachers.
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01.40.Di Course design and evaluation
03.65.Pm Relativistic wave equations

A computational approach to teaching conservative chaos

Todd Timberlake

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1002 | Cited 3 times

Online Publication Date: Jul 2004

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A computational approach to teaching conservative chaos that is suitable for undergraduates in an upper-level classical mechanics course is discussed. Some ways that computation can be used to facilitate the teaching of several important topics in conservative chaos are described. © 2004 American Association of Physics Teachers.
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05.45.Gg Control of chaos, applications of chaos
01.50.Lc Laboratory computer use

An experiment in nonlinear beam theory

A. Valiente

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1008 | Cited 1 time

Online Publication Date: Jul 2004

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An undergraduate level experiment involving the nonlinear mechanics of deformable bodies is described. The phenomenon of interest is the large elastic sideways deflection of a column under compressive loading. The experimental arrangement and the measurement’s simple equipment are usually found in undergraduate laboratories. The analysis is more involved because the use of nonelementary functions is required. To circumvent this difficulty, the analysis can be done with a spreadsheet or a data analysis program that has been preprogrammed to compute the required integrals. © 2004 American Association of Physics Teachers.
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01.50.Pa Laboratory experiments and apparatus
01.50.Lc Laboratory computer use
46.70.De Beams, plates, and shells
46.25.-y Static elasticity

Lenz vector operations on spherical hydrogen atom eigenfunctions

C. E. Burkhardt and J. J. Leventhal

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1013 | Cited 4 times

Online Publication Date: Jul 2004

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We show that operators capable of converting certain spherical hydrogen atom eigenfunctions into others by raising the angular momentum quantum number l can be constructed from components of the quantum mechanical Lenz vector operator. The derivation is performed using formalism no more sophisticated than that used to derive the properties of the angular momentum ladder operators in undergraduate quantum mechanics courses. The properties of these Lenz vector operators illustrate the accidental degeneracy of the hydrogen atom because they change the quantum number l without affecting n. © 2004 American Association of Physics Teachers.
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01.40.Di Course design and evaluation
03.65.Ca Formalism
02.10.Ud Linear algebra

Quantum interference in a driven washboard potential

Quentin Thommen, Jean Claude Garreau, and Véronique Zehnlé

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1017 | Cited 3 times

Online Publication Date: Jul 2004

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The dynamics of a quantum particle in a one-dimensional, tilted (“washboard”) and time-dependent lattice is studied. The approach uses quantum mechanics at the undergraduate level and leads to analytical results that show a rich variety of dynamical behavior and illustrate the fundamental role of interference in quantum systems. © 2004 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.Ta Foundations of quantum mechanics; measurement theory

A differential formulation of diffraction theory for the undergraduate optics course

Timothy M. Pritchett and A. David Trubatch

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1026 | Cited 2 times

Online Publication Date: Jul 2004

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The integral formulation of the Huygens–Fresnel principle embodied by the Fresnel–Kirchhoff and Rayleigh–Sommerfeld diffraction formulas constitutes standard treatment of scalar diffraction theory. It is not generally appreciated that the same results can be obtained by using standard methods to solve the relevant partial differential equations: the exact Rayleigh–Sommerfeld integral is equivalent to the scalar Helmholtz equation, and the Rayleigh–Sommerfeld integral in the Fresnel approximation is equivalent to the paraxial wave equation. In view of students’ familiarity with the latter partial differential equation, some pedagogical advantages may be realized if diffraction theory is also formulated in terms of partial differential equations as a supplement to the usual integral formulation.
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01.50.-i Educational aids
42.25.Fx Diffraction and scattering
02.30.Jr Partial differential equations

Quality factors and conductances in Helmholtz resonators

Michael J. Moloney

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1035 | Cited 2 times

Online Publication Date: Jul 2004

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Three glass bottles were investigated as Helmholtz resonators. The acoustical conductance C of each neck region was determined experimentally and compared to the calculated values, even though no conductance could be calculated for the flaring region of each bottle. The quality factor Q also was measured for 15 frequencies. The theoretical Q values were computed using the experimental C values and were found to be slightly higher than the measured Q values, probably due to the inability to calculate small wall losses in the flaring region beyond the neck. © 2004 American Association of Physics Teachers.
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43.10.Sv Education in acoustics, tutorial papers of interest to acoustics educators
01.50.My Demonstration experiments and apparatus
43.25.Gf Standing waves; resonance

Relativistic orbits with computer algebra

Frank Y.-H. Wang

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1040 | Cited 3 times

Online Publication Date: Jul 2004

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We use computer algebra to derive the equations of motion from the Lagrangian, solve the equations of motion numerically, and plot the numerical solutions, to discover the difference between trajectories of a particle under gravity based on Newtonian theory and general relativity with the Schwarzschild and the Kerr metric. © 2004 American Association of Physics Teachers.
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01.50.ht Instructional computer use
04.20.Fy Canonical formalism, Lagrangians, and variational principles
02.70.Wz Symbolic computation (computer algebra)
02.60.Lj Ordinary and partial differential equations; boundary value problems
02.30.Hq Ordinary differential equations

Visual appearance of a Morris–Thorne-wormhole

Thomas Müller

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1045 | Cited 7 times

Online Publication Date: Jul 2004

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Following the paper of Morris and Thorne on wormholes as a tool for teaching general relativity, we present the visual appearance of this simple spacetime using an embedding diagram and a raytracing program. Even if such a wormhole is not physically reasonable, we take the risk and take a short trip to an unreasonable parallel universe. © 2004 American Association of Physics Teachers.
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01.50.-i Educational aids
04.20.Gz Spacetime topology, causal structure, spinor structure
98.80.Jk Mathematical and relativistic aspects of cosmology

Analytical solution for photonic band-gap crystals using Drude conductivity

Brian Schulkin, Laszlo Sztancsik, and John F. Federici

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1051 | Cited 5 times

Online Publication Date: Jul 2004

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An analytical solution for the photonic band-gap of semiconductor structures in the terahertz (THz) frequency range is discussed. In analogy with the Kronig–Penney model for electronic band-gaps in periodic potentials, Maxwell’s equations for the propagation of light in the photonic crystal are transformed into an equivalent form of Schrödinger’s equation. In the THz frequency range, the refractive index of the semiconductor is well represented by a frequency-dependent Drude model. We thus find a Kronig–Penney type solution for the photonic band-gap crystal. © 2004 American Association of Physics Teachers.
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01.50.-i Educational aids
78.20.Ci Optical constants (including refractive index, complex dielectric constant, absorption, reflection and transmission coefficients, emissivity)
42.70.Qs Photonic bandgap materials
71.15.Ap Basis sets (LCAO, plane-wave, APW, etc.) and related methodology (scattering methods, ASA, linearized methods, etc.)

The sled race

Gerald E. Hite

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1055 | Cited 1 time

Online Publication Date: Jul 2004

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If two sleds with the same initial speed cross a valley, one over a horizontal bridge and the other through the valley, which sled will reach the other side first? If there is no friction and the sled in the valley does not leave the ground, it is easy to see that it will win. To answer the question when friction is present, a valley consisting of circular arcs of equal radii is considered. For this simple, but realistic valley, analytic solutions for the speed of the sleds are used to determine how the outcome of the race depends on friction. © 2004 American Association of Physics Teachers.
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01.40.-d Education
46.55.+d Tribology and mechanical contacts
06.30.Bp Spatial dimensions (e.g., position, lengths, volume, angles, and displacements)

Reappraising Einstein’s 1909 application of fluctuation theory to Planckian radiation

F. E. Irons

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1059 | Cited 2 times

Online Publication Date: Jul 2004

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Einstein’s 1909 application of fluctuation theory to Planckian radiation is challenged by the fact that radiation within a completely reflecting cavity is not in thermal equilibrium and therefore should not qualify as a candidate for analysis by Einstein’s theory. We offer an alternative interpretation wherein Planck’s function, to which Einstein applied his theory, represents the source function in the wall material surrounding a real, partially reflecting cavity. The source function experiences thermal fluctuations and radiation within the cavity (which originates in the wall material and has an intensity equal to the source function) fluctuates in concert. That is, blackbody radiation within a real cavity exhibits the thermal fluctuations predicted by Einstein, but the fluctuations have their origin in the wall material and are not intrinsic to radiation. © 2004 American Association of Physics Teachers.
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01.40.G- Curricula and evaluation
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
44.40.+a Thermal radiation
03.65.-w Quantum mechanics

The distribution of composite measurements: How to be certain of the uncertainties in what we measure

M. P. Silverman, W. Strange, and T. C. Lipscombe

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1068 | Cited 6 times

Online Publication Date: Jul 2004

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We derive expressions for the exact probability distribution functions and statistical moments of measurements represented as products and quotients of independent random variables, test these relations by means of the α and β branching decays of 212Bi, and discuss the implications of our theory for the measurement of lipid-panel analytes in the assessment of the risk of coronary heart disease. © 2004 American Association of Physics Teachers.
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23.60.+e α decay
23.40.-s β decay; double β decay; electron and muon capture
01.50.Kw Techniques of testing
02.50.Ng Distribution theory and Monte Carlo studies
02.50.Cw Probability theory
27.80.+w 190 ≤ A ≤ 219

Fermi and Bose pressures in statistical mechanics

Loyal Durand

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1082 | Cited 1 time

Online Publication Date: Jul 2004

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I show how the pressure in Fermi and Bose systems, identified in standard discussions of quantum statistical mechanics by the use of thermodynamic analogies, can be derived directly in terms of the flux of momentum across a surface by using the quantum mechanical stress tensor. In this approach, which is analogous to classical kinetic theory, the pressure is naturally defined locally. The approach leads to a simple interpretation of the pressure in terms of the momentum flow encoded in the wave functions. The stress-tensor and thermodynamic approaches are related by an interesting application of boundary perturbation theory for quantum systems. I investigate the properties of quasi-continuous systems, the relations for Fermi and Bose pressures, shape-dependent effects and anisotropies, and the treatment of particles in external fields, and note several interesting problems for graduate courses in statistical mechanics. © 2004 American Association of Physics Teachers.
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01.50.-i Educational aids
05.30.Jp Boson systems
05.30.Fk Fermion systems and electron gas
05.20.Dd Kinetic theory

Steppingstones in Hamiltonian dynamics

Thomas F. Jordan

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1095

Online Publication Date: Jul 2004

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Easy steps through essential Hamiltonian dynamics are outlined, from necessary definitions of Poisson brackets and canonical transformations, to a quick proof that Hamiltonian evolution is made by canonical transformations, the quickest proof of Liouville’s theorem, and on to the Poincaré-Cartan integral invariants and completely integrable dynamics, making room and providing tools for more recent developments. © 2004 American Association of Physics Teachers.
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01.50.Kw Techniques of testing
45.20.Jj Lagrangian and Hamiltonian mechanics
02.30.Rz Integral equations

Generalized Fierz identities

José F. Nieves and Palash B. Pal

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1100 | Cited 9 times

Online Publication Date: Jul 2004

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Low energy weak interaction calculations with fermions frequently involve a superposition of quartic products of Dirac spinors, in which the order of the spinors is not the same in all the contributing terms. A common trick that is used to bring them to a uniform ordering is the Fierz transformation. We show that the standard Fierz transformation quoted in textbooks is one element of a class of transformations that exist between fermion amplitudes that are written with different, arbitrary reorderings, of the spinors. The explicit form of all such transformation matrices is given, and in addition to the usual Lorentz scalar quartic products, we consider the pseudoscalar ones. Moreover, we include the cases in which some, or all, of the spinors in the original amplitude appear in the transformed amplitudes in their Lorentz-invariant complex conjugate form. Such manipulations and formulas are useful in practical calculations, as we show with some examples. © 2004 American Association of Physics Teachers.
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01.40.-d Education
03.30.+p Special relativity
03.65.Pm Relativistic wave equations
02.10.Ud Linear algebra
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An elliptic property of parabolic trajectories

J. L. Fernández-Chapou, A. L. Salas-Brito, and C. A. Vargas

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1109 | Cited 4 times

Online Publication Date: Jul 2004

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Abstract Unavailable
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01.50.-i Educational aids
45.40.Gj Ballistics (projectiles; rockets)

Erratum: “What good is the thermodynamic limit?” [Am. J. Phys. 72 (1), 25–29 (2004)]

Daniel F. Styer

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1110

Online Publication Date: Jul 2004

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Abstract Unavailable
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01.50.-i Educational aids
05.70.-a Thermodynamics
05.20.-y Classical statistical mechanics
99.10.Cd Errata
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A novel electrospray-based ion mobility spectrometer

Ben Bathgate, Eric C. S. Cheong, and Christopher J. Backhouse

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1111 | Cited 1 time

Online Publication Date: Jul 2004

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We present a design for a low-cost ion mobility spectrometer that can be built using the equipment on hand in many electronics-oriented undergraduate laboratories. The construction of this system is based upon the use of printed circuit boards and does not require the specialized drift and sheath gases, vacuum pumps, heater assemblies, high voltage pulsers, or precision pumps that are characteristic of the systems generally reported in the literature. We demonstrate the system in the separation of ions of methanol and water in air. Despite the low cost of this system it has a performance comparable to more complex systems, with a sensitivity of approximately 100 ppm for the protein cytochrome c. This system is suitable for use as an electronics or signal-processing project, or even a biotechnology demonstration. © 2004 American Association of Physics Teachers.
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07.57.-c Infrared, submillimeter wave, microwave and radiowave instruments and equipment
85.40.Ry Impurity doping, diffusion and ion implantation technology

Realization of an optical profiler: Introduction to scanning probe microscopy

J.-M. Friedt

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1118 | Cited 4 times

Online Publication Date: Jul 2004

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Scanning probe microscopy is a widely used instrumentation method based on scanning a probe over a sample to map the spatial variation of a physical property over its surface. Here we present the steps required for the realization of a generic scanning probe microscope. The selected sensor is a CD reader optical head that monitors the distance to the focusing point of a lens by which an infrared laser is focused on the reflecting surface of the sample. We thus develop an optical profiler and illustrate practical examples by mapping the topography of a coin. The focus of this article is to describe a low cost profiler illustrating all the steps of the development, from the definition of the probe of the physical property to be monitored to the result on an actual sample. © 2004 American Association of Physics Teachers.
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07.79.Fc Near-field scanning optical microscopes
06.30.Bp Spatial dimensions (e.g., position, lengths, volume, angles, and displacements)
42.79.Vb Optical storage systems, optical disks
01.50.Pa Laboratory experiments and apparatus
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Concept substitution: A teaching strategy for helping students disentangle related physics concepts

Diane J. Grayson

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1126 | Cited 5 times

Online Publication Date: Jul 2004

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To be effective, physics teachers need both content knowledge and pedagogical content knowledge, which includes knowledge of student conceptions and effective teaching strategies. Although much information is available on student conceptual and reasoning difficulties in physics, much less information is available on how to remedy such difficulties. In this paper I describe a teaching strategy, concept substitution, which is useful when student difficulties arise from a failure to distinguish distinct but related physics concepts. By using the topic of electric circuits as the context, I show how this strategy enables the teacher to identify and build on students’ correct intuition, while enabling students to distinguish among related concepts. I also illustrate the complexity of the conceptual change process, including the presence of intermediate conceptions while the process is taking place. © 2004 American Association of Physics Teachers.
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01.40.G- Curricula and evaluation
01.40.J- Teacher training
01.40.Fk Research in physics education
01.50.My Demonstration experiments and apparatus
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Special Relativity and Motions Faster than Light

Moses Fayngold, Author and John G. Cramer, Reviewer

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1134

Online Publication Date: Jul 2004

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Abstract Unavailable
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01.30.Vv Book reviews
01.40.Di Course design and evaluation
03.30.+p Special relativity

The Snowflake: Winter’s Secret Beauty

Kenneth Libbrecht, Author, Patricia Rasmussen, Author, and Philippe M. Binder, Reviewer

American Journal of Physics -- August 2004 -- Volume 72, Issue 8, pp. 1134

Online Publication Date: Jul 2004

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Abstract Unavailable
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01.30.Vv Book reviews
92.40.Ea Precipitation
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