February 2022 AJP coverFebruary 2022 Issue,

Volume 90, No. 2


Making digital aquatint with the Ising model featured

Aquatint is a printmaking technique that gives visual texture to prints. This patterning is shown to be similar to patterns that emerge from the Ising model of magnetism. We provide a concrete Python-based example that generates semi-realistic textures and can be used to manipulate existing images. Our experience in classrooms of first year seminar undergraduate students shows that this activity helps artistically inclined students to develop an interest in physics and computer science. It may also be suitable for a joint art and science project for high-school seniors.



In this issue: February 2022 by Joseph Amato, John Essick, Harvey Gould, Claire A. Marrache-Kikuchi, Beth Parks, B. Cameron Reed and Jan Tobochnik. DOI:10.1119/5.0083055


Making digital aquatint with the Ising model by Yannick Meurice. DOI: 10.1119/10.0006525
Calling all art-lovers! The mathematical machinery of the Ising model, familiar as a theoretical description of ferromagnetism, is employed to add interesting “texture” to an existing work of art, such as a painting or photograph, mimicking the chemically-based “aquatint” technique developed by Francisco Goya (The Disasters of War), Pablo Picasso, and others. Best of all, the materials described herein have been successfully used by the author in first year seminar classes, spurring interest in physics and computer science among artistically-inclined students.

Band formation and defects in a finite periodic quantum potential by Todd K. Timberlake and Neilson Woodfield. DOI: 10.1119/10.0006391
Periodic quantum systems, such as regularly spaced atoms in a solid, are characterized by energy spectra with well-defined bands of energy levels separated by gaps. The formation of band structures is usually analyzed with Bloch's theorem, but this can be abstract for beginning students. This paper examines the energy states of a one-dimensional system comprising Dirac delta-function wells embedded in an infinite square well. The spacing and strength of the Dirac wells can be varied to show how bands and gaps respond and to simulate the presence of defects in an otherwise periodic structure. In the following companion paper by Carr et al., a similar topic is dealt with in a very different way: an experimental demonstration of defects and band formation using a classical analog system with coupled harmonic oscillators. Both papers are appropriate for intermediate and upper-level students.

A classical analog for defects in quantum band formation by Paolo Francisco, Tadan Cobb, Shawn A. Hilbert and Scott Carr. DOI: 10.1119/10.0009053
The collective mechanical behavior of a linear system of masses and springs can mimic that of a one-dimensional crystal. In particular, the resonance frequencies of the mechanical system are analogous to the crystal's electronic energies, and there is a frequency gap akin to a bandgap in a semiconductor. In this paper, the authors examine the effect of changing the mass or the spring constant in one of the mechanical oscillators and thus simulate the introduction of a defect in the crystal. The defect's resonance frequency can be theoretically calculated and compared with experiment. This work shows how a macroscopic mechanical system can serve as proxy for a microscopic quantum system. It could be used in an undergraduate advanced mechanics class, building a connection with condensed matter physics.

Investigating and improving student understanding of the basics for a system of identical particles by Christof Keebaugh, Emily Marshman and Chandralekha Singh. DOI: 10.1119/10.0006910
Systems of identical particles are notoriously difficult for students to understand. This paper describes student difficulties and presents a series of reflective exercises, a QuILT, that guide students to a greatly increased understanding, both at the undergraduate and graduate level.

Illustrations of loosely bound and resonant states in atomic nuclei by A. C. Dassie, F. Gerdau, F. J. Gonzalez, M. Moyano and R. M. Id Betan. DOI: 10.1119/10.0007045
The use of S-matrices is essential in analyzing nuclear physics experiments, but their meanings can be opaque. This paper seeks to help physicists develop a better understanding of these matrices by applying them to classical and quantum mechanical scattering problems.

Velocity reciprocity and the relativity principle by Patrick Moylan. DOI: 10.1119/10.0009219
Velocity reciprocity is the property that pairs of inertial reference frames will measure each other to have equal and opposite relative velocities. While this is true for the Galilean and Lorentz transformations, it need not be true in general. This paper analyses the group-theoretic foundations of relativity theory to explore what additional assumptions must be made for velocity reciprocity to hold, and also explores the misconception that velocity reciprocity follows from the relativity of motion principle. In particular, the underappreciated importance of Henri Poincaré's demand that the principle of relativity be accorded universal validity is emphasized. Appropriate for students of modern physics and mathematics familiar with the rudiments of group theory.

Subtle features in projectile motion with quadratic drag found through Taylor series expansions by Antonio Corvo. DOI: 10.1119/10.0009227
The problem of projectile motion with air drag is notoriously difficult to approximate. The author presents an insightful trick: Expand the horizonal velocity in powers of inverse velocity. The result provides useful theoretical comparisons for data collected in the teaching lab and also a lesson in applications of the Taylor expansion.


Exploring complex pattern formation with convolutional neural networks by Christian Scholz and Sandy Scholz. DOI: 10.1119/5.0065458
Machine learning is becoming more and more important in the analysis of data in many fields including physics. In this paper, the authors provide a pedagogical introduction to how a convolutional neural network can be used to classify the complex patterns created by simulations of a coupled reaction-diffusion system.


Theoretical and experimental examination of simple coaxial photonic crystals for undergraduate teaching by Xubo Guo, Yingying Liu, Ying Chang, Meihong Zhu and Liuwan Zhang. DOI: 10.1119/5.0059320
A coaxial photonic crystal, composed of a single type of coaxial cable, is used to study fundamental properties of photonic crystals. Using only a function generator and oscilloscope, photonic crystal effects, including photonic bandgap, highly superluminal group velocity, and the influence of defects, are investigated. Experimental results are compared to a theory based on transfer matrices. The work described here offers an affordable addition to the undergraduate instructional laboratory.


Beyond Global Warming: How Numerical Models Revealed the Secrets of Climate Change by Syukuro Manabe and Anthony J. Broccoli. DOI: 10.1119/5.0084647

About AJP

General Information, Resources for Authors, Reviewers, and Readers


Additional Resources