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Jun 2013

Volume 81, Issue 6, pp. 405-479

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Photonic Rutherford scattering: A classical and quantum mechanical analogy in ray and wave optics

Markus Selmke and Frank Cichos

American Journal of Physics -- June 2013 -- Volume 81, Issue 6, pp. 405

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Using Fermat's least-optical-path principle, the family of ray trajectories through a special (but common) type of a gradient refractive index lens n(r) = n0+ΔnR/r is solved analytically. The solution gives a ray equation r(ϕ) that is closely related to Rutherford scattering trajectories; we therefore refer to this refraction process as “photonic Rutherford scattering.” It is shown that not only do the classical limits correspond but also the wave-mechanical pictures coincide—the time-independent Schrödingier equation and the Helmholtz equation permit the same mapping between the scattering of massive particles and optical scalar waves. Scattering of narrow beams of light finally recovers the classical trajectories. The analysis suggests that photothermal single-particle microscopy measures photonic Rutherford scattering in specific limits and allows for an individual single-scatterer probing. A macroscopic experiment is demonstrated to directly measure the scattering angle to impact parameter relation, which is otherwise accessible only indirectly in Rutherford-scattering experiments.
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42.00.00 Optics

Modern cosmology: Interactive computer simulations that use recent observational surveys

Jacob Moldenhauer, Larry Engelhardt, Keenan M. Stone, and Ezekiel Shuler

American Journal of Physics -- June 2013 -- Volume 81, Issue 6, pp. 414

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We present a collection of new, open-source computational tools for numerically modeling recent large-scale observational data sets using modern cosmology theory. These tools allow both students and researchers to constrain the parameter values in competitive cosmological models, thereby discovering both the accelerated expansion of the universe and its composition (e.g., dark matter and dark energy). These programs have several features to help the non-cosmologist build an understanding of cosmological models and their relation to observational data, including a built-in collection of several real observational data sets. The current list of built-in observations includes several recent supernovae Type-Ia surveys, baryon acoustic oscillations, the cosmic microwave background radiation, gamma-ray bursts, and measurements of the Hubble parameter. In this article, we discuss specific results for testing cosmological models using these observational data.
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07.05.Tp Computer modeling and simulation
98.00.00 Stellar systems; interstellar medium; galactic and extragalactic objects and systems; the Universe

The mechanical career of Councillor Orffyreus, confidence man

Alejandro Jenkins

American Journal of Physics -- June 2013 -- Volume 81, Issue 6, pp. 421

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In the early 18th century, J. E. E. Bessler, known as Orffyreus, constructed several wheels that he claimed could keep turning forever, powered only by gravity. He never revealed the details of his invention, but he conducted demonstrations (with the machine's inner workings covered) that persuaded competent observers that he might have discovered the secret of perpetual motion. Among Bessler's defenders were Gottfried Leibniz, Johann Bernoulli, Professor Willem 's Gravesande of Leiden University (who wrote to Isaac Newton on the subject), and Prince Karl, ruler of the German state of Hesse-Kassel. We review Bessler's work, placing it within the context of the intellectual debates of the time about mechanical conservation laws and the (im)possibility of perpetual motion. We also mention Bessler's long career as a confidence man, the details of which were discussed in popular 19th-century German publications but have remained unfamiliar to authors in other languages.
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01.65.+g History of science
45.20.dg Mechanical energy, work, and power

Optimal pacing for running 400- and 800-m track races

James Reardon

American Journal of Physics -- June 2013 -- Volume 81, Issue 6, pp. 428

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We present a toy model of anaerobic glycolysis that utilizes appropriate physiological and mathematical consideration while remaining useful to the athlete. The toy model produces an optimal pacing strategy for 400-m and 800-m races that is analytically calculated via the Euler-Lagrange equation. The calculation of the optimum v(t) is presented in detail, with an emphasis on intuitive arguments in order to serve as a bridge between the basic techniques presented in undergraduate physics textbooks and the more advanced techniques of control theory. Observed pacing strategies in 400-m and 800-m world-record races are found to be well-fit by the toy model, which allows us to draw a new physiological interpretation for the advantages of common weight-training practices.
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02.30.Xx Calculus of variations
87.00.00 Biological and medical physics

Photon charge experiment

A. Hankins, C. Rackson, and W. J. Kim

American Journal of Physics -- June 2013 -- Volume 81, Issue 6, pp. 436

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The deflection of a laser beam traveling through a modulated electric field is measured using phase-sensitive detection to place an upper bound on the photon charge. An upper limit of 10−14e is obtained. Our approach provides a simple experimental scheme for angle measurements and is suitable as a laboratory exercise for both advanced undergraduate and beginning graduate students in physical science.
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01.50.Pa Laboratory experiments and apparatus
14.00.00 Properties of specific particles

Collimated blue light generation in rubidium vapor

Marcus B. Kienlen, Noah T. Holte, Hunter A. Dassonville, Andrew M. C. Dawes, Kurt D. Iversen, Ryan M. McLaughlin, and Shannon K. Mayer

American Journal of Physics -- June 2013 -- Volume 81, Issue 6, pp. 442

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We describe an experiment for generating and characterizing a beam of collimated blue light (CBL) in a rubidium vapor. Two low-power, grating-feedback diode lasers, operating at 780.2 nm (5S1/2→5P3/2) and 776.0 nm (5P3/2→5D5/2), respectively, provide step-wise excitation to the 5D excited state in rubidium. Under the right experimental conditions, cascade decay through the 6P excited state will yield a collimated blue (420-nm) beam of light with high temporal and spatial coherence. We investigate the production of a blue beam under a variety of experimental conditions and characterize the spatial coherence and spectral characteristics. This experiment provides advanced undergraduate students with a unique opportunity to investigate nonlinear optical phenomena in the laboratory and uses equipment that is commonly available in laboratories equipped to investigate diode-laser-based absorption spectroscopy in rubidium.
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01.50.Pa Laboratory experiments and apparatus
03.65.-w Quantum mechanics
42.00.00 Optics

An introduction to the spectrum, symmetries, and dynamics of spin-1/2 Heisenberg chains

Kira Joel, Davida Kollmar, and Lea F. Santos

American Journal of Physics -- June 2013 -- Volume 81, Issue 6, pp. 450

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Quantum spin chains are prototype quantum many-body systems that are employed in the description of various complex physical phenomena. We provide an introduction to this subject by focusing on the time evolution of a Heisenberg spin-1/2 chain and interpreting the results based on the analysis of the eigenvalues, eigenstates, and symmetries of the system. We make available online all computer codes used to obtain our data.
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03.65.-w Quantum mechanics
75.00.00 Magnetic properties and materials
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Student understanding of the application of Newton's second law to rotating rigid bodies

Hunter G. Close, Luanna S. Gomez, and Paula R. L. Heron

American Journal of Physics -- June 2013 -- Volume 81, Issue 6, pp. 458

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We report on an investigation of student understanding of rigid body dynamics in which we asked students in introductory calculus-based physics to compare the translational motions of identical rigid bodies subject to forces that differed only in the point of contact at which they were applied. There was a widespread tendency to claim that forces that cause rotational motion have a diminished effect on translational motion. A series of related problems was developed to examine whether similar errors would be made in other contexts, and interviews were conducted to probe student thinking in greater depth. In this paper, we describe the results of our investigation and also describe a series of different interventions that culminated in the development of a tutorial that improves student ability to apply Newton's second law to rotating rigid bodies.
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01.40.Fk Research in physics education
45.00.00 Classical mechanics of discrete systems
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Erratum: “An undergraduate measurement of radiative broadening in atomic vapor” [Am. J. Phys. 80, 740 (2012)]

A. J. Hachtel, J. D. Kleykamp, D. G. Kane, M. D. Marshall, B. W. Worth, J. T. Barkeloo, J. C. B. Kangara, J. C. Camenisch, M. C. Gillette, and S. Bali

American Journal of Physics -- June 2013 -- Volume 81, Issue 6, pp. 471

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Abstract Unavailable
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99.10.-x Errata and other corrections
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Using a mobile phone acceleration sensor in physics experiments on free and damped harmonic oscillations

Juan Carlos Castro-Palacio, Luisberis Velázquez-Abad, Marcos H. Giménez, and Juan A. Monsoriu

American Journal of Physics -- June 2013 -- Volume 81, Issue 6, pp. 472

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We have used a mobile phone acceleration sensor, and the Accelerometer Monitor application for Android, to collect data in physics experiments on free and damped oscillations. Results for the period, frequency, spring constant, and damping constant agree very well with measurements obtained by other methods. These widely available sensors are likely to find increased use in instructional laboratories.
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01.50.My Demonstration experiments and apparatus
45.00.00 Classical mechanics of discrete systems
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Nuclear Forces: The Making of the Physicist Hans Bethe.

Silvan S. Schweber and Kurt Gottfried, Reviewer

American Journal of Physics -- June 2013 -- Volume 81, Issue 6, pp. 476

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

The Fractalist: Memoir of a Scientific Maverick.

Benoit Mandelbrot and Dann Passoja, Reviewer

American Journal of Physics -- June 2013 -- Volume 81, Issue 6, pp. 477

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

Quasicrystals: A Primer (2nd ed.).

Christian Janot and Walter Steurer, Reviewer

American Journal of Physics -- June 2013 -- Volume 81, Issue 6, pp. 478

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Abstract Unavailable
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01.30.Vv Book reviews
61.00.00 Structure of solids and liquids; crystallography

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American Journal of Physics -- June 2013 -- Volume 81, Issue 6, pp. 479

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