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Jul 2013

Volume 81, Issue 7, pp. 485-559

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Improving the quantification of Brownian motion

Marco A. Catipovic, Paul M. Tyler, Josef G. Trapani, and Ashley R. Carter

American Journal of Physics -- July 2013 -- Volume 81, Issue 7, pp. 485

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Brownian motion experiments have become a staple of the undergraduate advanced laboratory, yet quantification of these experiments is difficult, typically producing errors of 10%–15% or more. Here, we discuss the individual sources of error in the experiment: sampling error, uncertainty in the diffusion coefficient, tracking error, vibration, and microscope drift. We model each source of error using theoretical and computational methods and compare the model to our experimental data. Finally, we describe various ways to reduce each source of error to less than 1%, improving the quantification of Brownian motion.
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01.50.Pa Laboratory experiments and apparatus
05.40.Jc Brownian motion

On back-reaction in special relativity

William M. Nelson

American Journal of Physics -- July 2013 -- Volume 81, Issue 7, pp. 492

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Back-reaction of fields plays an important role in the generation of particle masses and the mass-energy equivalence of special relativity, but the most natural demonstrations using classical models result in apparent errors such as the notorious “4/3” problem. Here, we discuss the resolution of these discrepancies within the underlying atomic description of matter, with the aim of encouraging classroom discussion of back-reaction and its connection to relativistic effects.
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03.30.+p Special relativity
41.00.00 Electromagnetism; electron and ion optics

Tensors: A guide for undergraduate students

Franco Battaglia and Thomas F. George

American Journal of Physics -- July 2013 -- Volume 81, Issue 7, pp. 498

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A guide on tensors is proposed for undergraduate students in physics or engineering that ties directly to vector calculus in orthonormal coordinate systems. We show that once orthonormality is relaxed, a dual basis, together with the contravariant and covariant components, naturally emerges. Manipulating these components requires some skill that can be acquired more easily and quickly once a new notation is adopted. This notation distinguishes multi-component quantities in different coordinate systems by a differentiating sign on the index labelling the component rather than on the label of the quantity itself. This tiny stratagem, together with simple rules openly stated at the beginning of this guide, allows an almost automatic, easy-to-pursue procedure for what is otherwise a cumbersome algebra. By the end of the paper, the reader will be skillful enough to tackle many applications involving tensors of any rank in any coordinate system, without index-manipulation obstacles standing in the way.
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02.00.00 Mathematical methods in physics

Stefan–Boltzmann law for the tungsten filament of a light bulb: Revisiting the experiment

Marcello Carlà

American Journal of Physics -- July 2013 -- Volume 81, Issue 7, pp. 512

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A classical laboratory experiment to verify the Stefan-Boltzmann radiation law with the tungsten filaments of commercial incandescent lamps has been fully revisited, collecting a fairly large amount of data with a computer-controlled four-channel power supply. In many cases, the total power dissipated by the lamp is well described by a sum of two power-law terms, with one exponent very close to 4, as predicted by the radiation law, and the other very close to 1, as for simple heat conduction. This result was true even for filament surfaces with a shiny metallic appearance, whose emissivity should vary with temperature.
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05.00.00 Statistical physics, thermodynamics, and nonlinear dynamical systems

Rotating frame analysis of rigid body dynamics in space phasor variables

Shayak Bhattacharjee

American Journal of Physics -- July 2013 -- Volume 81, Issue 7, pp. 518

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We propose a new method of attacking problems in rigid body rotation, focusing on the heavy symmetric top. The technique is a direct extension of the method traditionally applied to the free symmetric top. We write Euler's equations in a frame which is attached to the top and thus shares its entire angular velocity. The structure of the resulting equations is such that it is advantageous to cast and solve them in terms of complex variables (space phasors). Through this formalism, we obtain a direct link between the initial conditions at the time of launch and the subsequent behavior of the top. The insertion of a damping term allows us to further explain the behavior of a top where the pivot is non-ideal and has friction. Finally, we make some suggestions regarding experimental verification of our results.
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45.20.dc Rotational dynamics

On the universality of free fall, the equivalence principle, and the gravitational redshift

A. M. Nobili, D. M. Lucchesi, M. T. Crosta, M. Shao, S. G. Turyshev, R. Peron, G. Catastini, A. Anselmi, and G. Zavattini

American Journal of Physics -- July 2013 -- Volume 81, Issue 7, pp. 527

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Through the contributions of Galileo, Newton, and Einstein, we recall the universality of free fall (UFF), the weak equivalence principle (WEP), and the strong equivalence principle (SEP), in order to stress that general relativity requires all test masses to be equally accelerated in a gravitational field; that is, it requires UFF and WEP to hold. The possibility of testing this crucial fact with null, highly sensitive experiments makes these the most powerful tests of the theory. Following Schiff, we derive the gravitational redshift from the WEP and special relativity and show that, as long as clocks are affected by a gravitating body like normal matter, measurement of the redshift is a test of UFF/WEP but cannot compete with direct null tests. A new measurement of the gravitational redshift based on free-falling cold atoms and an absolute gravimeter is not competitive either. Finally, we compare UFF/WEP experiments using macroscopic masses as test bodies in one case and cold atoms in the other. We conclude that there is no difference in the nature of the test and that the merit of any such experiment rests on the accuracy it can achieve and on the physical differences between the elements it can test, macroscopic proof masses being superior in both respects.
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04.00.00 General relativity and gravitation
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Of pendulums, polymers, and robots: Computational mechanics with constraints

Franz J. Vesely

American Journal of Physics -- July 2013 -- Volume 81, Issue 7, pp. 537

Online Publication Date: Jun 2013

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The motion of point masses under the influence of a potential can be computed by simple methods. However, if the trajectories are restricted by mechanical constraints such as strings, rails, crankshafts, and molecular bonds, special numerical techniques must be invoked. The need for efficient computational strategies is particularly pressing for molecular simulations, where large systems of compound molecules are tracked. The best strategy is the use of Cartesian coordinates in combination with constraint forces in the Lagrange formulation. This approach has led to the extremely successful SHAKE and RATTLE algorithms. The same ideas may be profitably applied in very different fields such as robotics, mechanics, and geometry, and the study of chaos in simple systems.
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02.70.-c Computational techniques; simulations
45.00.00 Classical mechanics of discrete systems
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Combining two reform curricula: An example from a course with well-prepared students

Beth A. Lindsey and Amy Y. Liu

American Journal of Physics -- July 2013 -- Volume 81, Issue 7, pp. 545

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Many studies have separately documented the benefits of research-based curricula and pedagogical methods. Here, we report on the effects of adopting a reform curriculum (Matter and Interactions) in conjunction with a pedagogical tool designed and validated in the context of a traditional treatment of mechanics (Tutorials in Introductory Physics). We document the need for targeted interactive engagement materials (such as the tutorials) even in a course with a population of students who are extremely well-prepared in physics. We describe the modifications necessary to successfully incorporate Tutorials in Introductory Physics into a course using Matter and Interactions, and we present data documenting the success of this approach.
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01.40.Fk Research in physics education
01.40.G- Curricula and evaluation
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Why is the Legendre transformation its own inverse?

Harald Skarke

American Journal of Physics -- July 2013 -- Volume 81, Issue 7, pp. 554

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Abstract Unavailable
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02.00.00 Mathematical methods in physics

On deriving the Maxwellian velocity distribution

Allan Walstad

American Journal of Physics -- July 2013 -- Volume 81, Issue 7, pp. 555

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Maxwell's 1860 derivation of the molecular velocity distribution does not constitute a valid approach for pedagogical use.
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01.65.+g History of science
05.20.-y Classical statistical mechanics
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Something Incredibly Wonderful Happens: Frank Oppenheimer and his Astonishing Exploratorium.

K. C. Cole and Alan J. Friedman, Reviewer

American Journal of Physics -- July 2013 -- Volume 81, Issue 7, pp. 558

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Abstract Unavailable
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01.30.Vv Book reviews
01.60.+q Biographies, tributes, personal notes, and obituaries

BOOKS RECEIVED

American Journal of Physics -- July 2013 -- Volume 81, Issue 7, pp. 559

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