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Feb 2013

Volume 81, Issue 2, pp. 85-159

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Why do bubbles in Guinness sink?

E. S. Benilov, C. P. Cummins, and W. T. Lee

American Journal of Physics -- February 2013 -- Volume 81, Issue 2, pp. 88

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Stout beers show the counter-intuitive phenomena of sinking bubbles, while the beer is settling. Previous research suggests that this phenomenon is due to the small size of the bubbles in these beers and the presence of a circulatory current, directed downwards near the side of the wall and upwards in the interior of the glass. The mechanism by which such a circulation is established and the conditions under which it will occur has not been clarified. In this paper, we use simulations and experiments to demonstrate that the flow in a glass of stout beer depends on the shape of the glass. If it narrows downwards (as the traditional stout glass, the pint, does), the flow is directed downwards near the wall and upwards in the interior and sinking bubbles will be observed. If the container widens downwards, the flow is opposite to that described above and only rising bubbles will be seen.
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47.00.00 Fluid dynamics

Re-examining the value of old quantization and the Bohr atom approach

Todd S. Garon, Nelia Mann, and Ellen M. McManis

American Journal of Physics -- February 2013 -- Volume 81, Issue 2, pp. 92

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We use old quantization to predict features of the energy spectrum for bound states in spherically symmetric potentials. We review the application of this method to simple quantum mechanical systems with known analytic results and show that old quantization, while not generally capable of predicting the exact quantum-mechanical spectrum, does consistently give useful information. We then apply the method to a logarithmic potential and compare the results with a numerically calculated spectrum. Finally, we use these techniques to predict the number of bound states in the Yukawa potential and again compare the results with those obtained numerically. In all cases old quantization provides good predictive power for the main features of the true quantum-mechanical problem, and thus can serve as a “back-of-the-envelope” technique for providing rough, qualitative information about the system.
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03.65.-w Quantum mechanics

Vector acoustic intensity around a tuning fork

Daniel A. Russell, Justin Junell, and Daniel O. Ludwigsen

American Journal of Physics -- February 2013 -- Volume 81, Issue 2, pp. 99

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The acoustic intensity vector field around a tuning fork is investigated. Theory for a longitudinal quadrupole source predicts a well-defined transition between near-field and far-field, with significant circulation of sound energy in the near-field. Vector components of the time-averaged intensity were measured using a two-microphone intensity probe and found to agree well with predictions from theory. The vector intensity map is interpreted, and shown to provide useful information about the near-field of an acoustic source.
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43.00.00 Acoustics

Wave transmission through periodic, quasiperiodic, and random one-dimensional finite lattices

Braulio Gutiérrez-Medina

American Journal of Physics -- February 2013 -- Volume 81, Issue 2, pp. 104

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The quantum mechanical transmission probability is calculated for one-dimensional finite lattices with three types of potentials: periodic, quasiperiodic, and random. When the number of lattice sites included in the computation is systematically increased, distinct features in the transmission probability vs. energy diagrams are observed for each case. The periodic lattice gives rise to allowed and forbidden transmission regions that correspond to the energy band structure of the infinitely periodic potential. In contrast, the transmission probability diagrams for both quasiperiodic and random lattices show the absence of well-defined band structures and the appearance of wave localization effects. Using the average transmissivity concept, we show the emergence of exponential (Anderson) and power-law bounded localization for the random and quasiperiodic lattices, respectively.
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03.65.-w Quantum mechanics
71.00.00 Electronic structure of bulk materials

252Cf fission-neutron spectrum using a simplified time-of-flight setup: An advanced teaching laboratory experiment

F. D. Becchetti, M. Febbraro, R. Torres-Isea, M. Ojaruega, and L. Baum

American Journal of Physics -- February 2013 -- Volume 81, Issue 2, pp. 112

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The removal of PuBe and AmBe neutron sources from many university teaching laboratories (due to heightened security issues) has often left a void in teaching various aspects of neutron physics. We have recently replaced such sources with sealed 252Cf oil-well logging sources (nominal 10–100 μCi), and developed several experiments using them as neutron sources. This includes a fission-neutron time-of-flight experiment using plastic scintillators, which utilizes the prompt γ rays emitted in 252Cf spontaneous fission as a fast timing start signal. The experiment can be performed with conventional nuclear instrumentation and a 1-D multi-channel pulse-height analyzer, available in most advanced teaching laboratories. Alternatively, a more sophisticated experiment using liquid scintillators and n/γ pulse-shape discrimination can be performed. Several other experiments using these neutron sources are also feasible. The experiments can introduce students to the problem of detecting the dark matter thought to dominate the universe and to the techniques used to detect contraband fissionable nuclear materials.
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01.50.Pa Laboratory experiments and apparatus
20.00.00 NUCLEAR PHYSICS

Obtaining Maxwell's equations heuristically

Gerhard Diener, Jürgen Weissbarth, Frank Grossmann, and Rüdiger Schmidt

American Journal of Physics -- February 2013 -- Volume 81, Issue 2, pp. 120

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Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure of the microscopic Maxwell equations for the electromagnetic fields can be deduced heuristically by using the transformation properties of the fields under space inversion and time reversal. Using the experimental facts of charge conservation and that electromagnetic waves propagate with the speed of light, together with Galilean invariance of the Lorentz force, allows us to finalize Maxwell's equations and to introduce arbitrary electrodynamics units naturally.
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41.00.00 Electromagnetism; electron and ion optics

A thermoacoustic oscillator powered by vaporized water and ethanol

Daisuke Noda and Yuki Ueda

American Journal of Physics -- February 2013 -- Volume 81, Issue 2, pp. 124 | Cited 1 time

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We measure the temperature difference required to drive a thermoacoustic oscillator containing air, water vapor, and liquid water as the working fluids. The oscillator is composed of a large tube containing an array of narrow tubes connected at one end to a tank of liquid water. When the water is heated, the temperature difference across the tube array increases until thermoacoustic oscillations occur. The temperature difference at the onset of oscillation is measured to be 56 °C, significantly smaller (by ∼ 200 °C) than the temperature measured when the tank is filled with dry air instead of water. The temperature difference can be further reduced to 47 °C by using ethanol instead of water.
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43.00.00 Acoustics

Reinventing the wheel: The chaotic sandwheel

Anthony Tongen, Roger J. Thelwell, and David Becerra-Alonso

American Journal of Physics -- February 2013 -- Volume 81, Issue 2, pp. 127

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The Malkus chaotic waterwheel, a tool to mechanically demonstrate Lorenzian dynamics, motivates the study of a chaotic sandwheel. We model the sandwheel in parallel with the waterwheel when possible, noting where methods may be extended and where no further analysis seems feasible. Numerical simulations are used to compare and contrast the behavior of the sandwheel with the waterwheel. Simulations confirm that the sandwheel retains many of the elements of chaotic Lorenzian dynamics. However, bifurcation diagrams show dramatic differences in where the order-chaos-order transitions occur.
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05.45.-a Nonlinear dynamics and chaos
45.00.00 Classical mechanics of discrete systems
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