JanuaryAJP January 2023 2023 Issue,

Volume 91, No. 1


Experimental realization of an additively manufactured monatomic lattice for studying wave propagation

Increasing interest in wave propagation in phononic systems and metamaterials motivates the development of experimental designs, measurement techniques, and fabrication methods for use in basic research and classroom demonstrations. The simplest phononic system, the monatomic chain, exhibits rich physics such as dispersion and frequency-domain filtering. However, a limited number of experimental studies showcase monatomic chains for macroscale observation of phonons. Herein, we discuss the design, fabrication, and testing of monatomic lattices as enabled by three-dimensional (3D) printing. Using this widely available technology, we provide design guidelines for realization of a monatomic chain composed of 3D printed serpentine springs and press-fitted cylindrical masses. We also present measurement techniques that record propagating waves and algorithms for the experimental determination of dispersion behavior.



In this issue: January 2023 by Mario Belloni, Adam Fritsch, Beth Parks, B. Cameron Reed and Todd Springer. DOI: American Journal of Physics 91, 5 (2023); https://doi.org/10.1119/5.0134015
Computation has become an indispensable tool in all areas of physics. As the role of computation grows, it is important to ask how, when, and to whom we teach computation in the physics curriculum. Building on the first two Computational Physics Resource Letters, this new Resource Letter aims to provide resources to educators who want to incorporate computation into their teaching as part of equitable practices.


Resource Letter CP-3: Computational physics by Timothy J. Atherton. DOI: American Journal of Physics 91, 7 (2023); https://doi.org/10.1119/5.0106476
This Resource Letter provides information and guidance for those looking to incorporate computation into their courses or to refine their own computational practice. We begin with general resources, including policy documents and supportive organizations. We then survey efforts to integrate computation across the curriculum as well as provide information for instructors looking to teach a computational physics course specifically. An overview of education research into computation in physics, including materials from beyond Physics Education Research, is then provided, followed by suggestions for tools, languages, and environments. We conclude with some emerging topics for which only preliminary resources exist but represent important topics for future innovation.


The drift motion of a spinning ball on carpet by Keith Zengel and Chris Tamer. DOI: 10.1119/5.0099316
A ball spinning about a vertical axis while rolling along a deformable carpet experiences a drift force perpendicular to its instantaneous velocity, a consequence of a kinetic frictional force that acts near the forward point of contact between the ball and the carpet. This force is in addition to a force of rolling friction that acts perpendicular to the direction of forward motion, also ahead of the ball's center of mass. This article, which is appropriate for students in advanced dynamics classes, analyzes this motion and tests the theory for a golf ball and a superball rolled on high- and low-pile carpets. Not to be missed is a photo of a cat ready to pounce on a superball.

The mass spectrum of quarkonium using matrix mechanics by Aissa Belhouari. DOI: 10.1119/5.0077434
Quantum mechanics is infamous for having very few exactly-solvable problems; every student needs to see analytic and numerical approximation methods. This paper applies a matrix diagonalization/numerical integration method to solve for the energy eigenvalues and hence the mass spectrum of charmonium, a quark/antiquark analog to hydrogen. The results are in close accord with other theoretical treatments and experimental results for this system. This approach uses the familiar infinite-well wavefunctions as a set of basis states, which should be applicable to other problems. Appropriate for intermediate and upper-level students.

Adaptable research-based materials for teaching quantum mechanics by Steven Pollock, Gina Passante and Homeyra Sadaghiani. DOI: 10.1119/5.0109124
The authors present a large collection of resources for teaching undergraduate quantum mechanics that will be primarily useful in a “spins first” approach. Readers will find descriptions of the materials, which include clicker questions, pre-lecture surveys, and homework and exam questions, along with valuable notes for how they can be used in classes.

Low-cost automated spin coater and thermal annealer for additive prototyping of multilayer Bragg reflectors by Nathan J. Dawson, Yunli Lu, Zoe Lowther, Jacob Abell, Nicholas D. Christianson, Aaron W. Weiser and Gioia Aquino. DOI: 10.1119/5.0088776
Photonic crystals such as Bragg reflectors can be constructed from alternating thin layers of polymers. The process is simple in principle, but it requires automation due to the large number of layers needed. This paper shows how an automated spin coater can be built using inexpensive repurposed materials and gives examples of projects that undergraduates can complete using it.

Experimental realization of an additively manufactured monatomic lattice for studying wave propagation by Nehemiah Mork, Sai A. R. Kuchibhatla, Michael J. Leamy and Matthew D. Fronk. DOI: 10.1119/5.0085124
Undergraduates studying wave propagation through solids often model such waves as phonons traveling through simple lattices. However, calculations of such systems are often difficult for students to directly reproduce in the lab. In this paper, the authors describe a simple 3-D printing approach that enables the construction of a macro-scale monatomic lattice for which the dispersion curve can be experimentally calculated using a 2-D Fourier transform, enabling a hands-on student experience with phononic systems and additive manufacturing.

Unexpected optimal measurement protocols in Bell's inequality violation experiments by Alicia Negre, Renaud Mathevet, Benoit Chalopin and Sébastien Massenot. DOI: 10.1119/5.0102516
The violation of Bell's inequality, which demonstrates the non-locality of quantum mechanical states, can be measured experimentally in student laboratories. When performing this experiment, the authors noticed that the measurement error exhibited an unexpected dependence on the ordering of polarizer rotations. This paper shares their confirmation of the effect via careful experiments and computational simulations. Readers may be inspired to consider other experimental situations that could show similar effects due to correlations between measurements.


Concerning classical forces, energies, and potentials for accelerated point charges by Timothy H. Boyer. DOI: American Journal of Physics 91, 74 (2023); https://doi.org/10.1119/5.0094457
The interplay between electric and magnetic fields is one of the many reasons that students find electrodynamics to be a difficult subject.  As an example, the source of changes in magnetic field energy is often not obvious.  Magnetic forces cannot be directly responsible for energy changes since they do no work.  Instead, such energy changes can be related to electric fields in an intricate way.  In this paper, the subtleties of magnetic field energy changes are explored in various situations using the Darwin Lagrangian, an approximation to the full theory of electrodynamics.  Students and instructors of electromagnetism courses will benefit from an example involving two accelerating point charges, which helps to shed light on the subtle connections between electricity and magnetism.

The law of entropy increase for bodies in mutual thermal contact by Ramandeep S. Johal. DOI: American Journal of Physics 91, 79 (2023); https://doi.org/10.1119/5.0124068
This brief Note shares an elegant way to show students that, when two bodies at unequal temperatures are placed in thermal contact and allowed to reach an equilibrium common temperature, the total entropy increases.


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