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Coherent diffraction imaging in the undergraduate laboratory
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| Pengarang | : | J. Nicholas Porter; David J. Anderson; Julio Escobedo; David D. Allred; Nathan D. Powers; Richard L. Sandberg |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 5) |
| Halaman | : | 415-421 |
| Abstrak | : | We present an undergraduate optics instructional laboratory designed to teach skills relevant to a broad range of modern scientific and technical careers. In this laboratory project, students image a custom aperture using coherent diffraction imaging, while learning principles and skills related to digital image processing and computational imaging, including multidimensional Fourier analysis, iterative phase retrieval, noise reduction, finite dynamic range, and sampling considerations. After briefly reviewing these imaging principles, we describe the required experimental materials and setup for this project. Our experimental apparatus is both inexpensive and portable, and a software application we developed for interactive data analysis is freely available. |
An undergraduate laboratory experiment on nucleation and growth via polarizing optical microscopy of semicrystalline polymers
| Pengarang | : | F. Scurti; L. Reynolds |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 5) |
| Halaman | : | 406-414 |
| Abstrak | : | Here, we describe a set of experiments that enables undergraduate students to perform and understand nucleation and growth utilizing the concept of birefringence. Semicrystalline polymers, e.g., polyethylene oxide, exhibit a Maltese cross extinction pattern when they are imaged under polarizing optical microscopy with crossed polars (i.e., two polarizers whose axes are oriented at right angle to each other). This behavior is due to the birefringence of the polymer's spherulite, which is its building block, analogous to the grains of a metal. In this instructional laboratory experiment, samples of polyethylene oxide were crystallized at three different transformation temperatures of 295, 273, and 77 K. Taking advantage of the birefringence of spherulites, the dependence of the microstructure with undercooling is shown. In particular, smaller spherulite sizes were obtained with larger undercoolings. It is also shown that the temperature dependence of the resulting polymer microstructure is in agreement with the analytical model for a nucleation and growth process. Finally, a live transformation of solidification of polyethylene oxide from the melt was recorded under crossed polars at room temperature via video microscopy. The time-dependent data that describe the advancement of the phase transformation are in excellent agreement with the Avrami model. |
A first encounter with exceptional points in a quantum model
| Pengarang | : | C. A. Downing; V. A. Saroka |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 5) |
| Halaman | : | 396-405 |
| Abstrak | : | An exceptional point is a special point in parameter space at which two (or more) eigenvalues and eigenvectors coincide. The discovery of exceptional points within mechanical and optical systems has uncovered peculiar effects in their vicinity. Here, we consider perhaps the simplest quantum model that exhibits an exceptional point and allows for an analytical treatment. In particular, we reexamine a two-level atom driven by a laser and suffering from losses. The same exceptional point arises in several non-Hermitian matrices, which determine various aspects of the dynamics of the system. There are consequences for some important observables, for example, the spectrum evolves from being a Lorentzian-like singlet to a Mollow triplet upon passing through the exceptional point. Our analysis supports the perspective that viewing certain quantum systems through the lens of exceptional points offers some desirable explanatory advantages. |
Temperature as joules per bit
| Pengarang | : | Charles Alexandre Bédard; Sophie Berthelette; Xavier Coiteux-Roy; Stefan Wolf |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 5) |
| Halaman | : | 390-395 |
| Abstrak | : | In statistical mechanics, entropy is defined as a fundamental quantity. However, its unit, J/K?, involves that of temperature, which is only subsequently defined—and defined in terms of entropy. This circularity arises with the introduction of Boltzmann's constant into the very expression of entropy. The J/K carried by the constant prevents entropy from finding a unit of its own while simultaneously obfuscating its informational nature. Following the precepts of information theory, we argue that entropy is well measured in bits and coincides with information capacity at thermodynamic equilibrium. Consequently, not only is the temperature of a system in equilibrium expressed in J/bit?, but it acquires a clear meaning: It is the cost in energy to increase its information capacity by 1 bit. Viewing temperature as joules per bit uncovers the strong duality exhibited by Gibbs long ago between available capacity and free energy. It also simplifies Landauer's cost and clarifies that it is a cost of displacement, not of erasure. Replacing the kelvin with the bit as an SI unit would remove Boltzmann's constant from the seven defining constants. |
Outcomes of teaching physics using action-adventure scenarios with minimal direct instruction
| Pengarang | : | Samya Zain; Valerie A. Allison |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 5) |
| Halaman | : | 382-389 |
| Abstrak | : | In this study, we assess the use of action-adventure scenarios in a college physics course designed for both physics majors and non-majors, built on minimal direct instruction. Students worked collaboratively in heterogeneously assigned pairs or triads to solve the assigned tasks. We focused on students' concept development and their engagement and attitudes in the course. We also investigated whether there were measurable different outcomes between majors and non-majors as well as male- and female-identifying students. The majority of students self-reported that they felt they would remember and be able to apply their knowledge beyond the completion of the course and that the course design enhanced their engagement and effort in the labs. We discuss key components of the course design and provide recommendations for adoption. |
N-body linear force law allowing analytic solutions
| Pengarang | : | Joseph West; Sean P. Bartz |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 5) |
| Halaman | : | 376-381 |
| Abstrak | : | We present a pairwise force law in a system of N particles that produces analytic solutions for an arbitrary number of particles, masses, and initial conditions. Each pair of particles interacts via a force that is proportional to the product of their masses and their separation distance, with the force directed radially. We show that, despite the N-body interaction, each particle behaves as if it interacts only with the center of mass of the system. This effective one-body interaction behaves as Hooke's law with a common frequency for all particles, with the familiar analytic solutions for the trajectories. With these analytic solutions, it is possible to efficiently simulate a collection of these particles and incorporate other external forces. As an example, we simulate the particles within an adiabatically expanding container and calculate pressure and temperature in both the attractive and repulsive cases. |
Internal ballistics of the sling
| Pengarang | : | Karjo, Clara Herlina |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 5) |
| Halaman | : | 367-375 |
| Abstrak | : | The venerable sling is a difficult weapon to master—we show that very precise timing is required to hit a target. Internal ballistics are analyzed to support ancient claims of the weapon's range (exceeding 400 m in some cases). Many simplifying approximations are used to model the complicated internal trajectory of the sling bullet; they yield a useful formula for assessing the capabilities of a sling. Our analysis has pedagogical value in demonstrating the efficacy of well-chosen approximations in practical physics calculations. |
Quantum fields from dimensional analysis: Applications in condensed matter systems
| Pengarang | : | Richard Robinett |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 4) |
| Halaman | : | 344-356 |
| Abstrak | : | We extend the use of dimensional analysis beyond the usual problems in the undergraduate curriculum to ones in particle and gravitational physics, to explore the range of its applicability, both across level (from advanced undergraduate to graduate level and research problems), and also across fields of study. We especially focus on the transfer of ideas from field theory to modern condensed matter physics systems, where experimental realizations are possible at much more accessible scales. |
Solving introductory physics problems recursively using iterated maps
| Pengarang | : | L. Q. English; D. P. Jackson; D. Richeson; W. A. Morgan; K. Sigmon; G. Vollmer; E. Dunkel; J. Zavrel; J. Wiseman |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 4) |
| Halaman | : | 336-343 |
| Abstrak | : | In an introductory physics problem, students find the depth of a chasm from the time it takes to hear the sound of a dropped boulder hitting the bottom. The standard solution involves a system of two equations with two unknowns, but it turns out that a recursive method will also give the right answer. We analyze this non-traditional approach using iterated maps and determine the conditions under which it converges to the correct solution. Interestingly, the iterative method fails when the well depth is large enough for the rock to reach the speed of sound. Beyond this depth, convergence does not occur due to a series of period-doubling bifurcations, and we show that the iterated map under consideration is conjugate to the logistic map. Perhaps surprisingly, the inclusion of air resistance leads to the same qualitative results. We also demonstrate that the method outlined here can be used to solve other introductory physics problems. |
Active charge and discharge of a capacitor: Scaling solution and energy optimization
| Pengarang | : | S. Faure; D. Guéry-Odelin; C. A. Plata; A. Prados |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 4) |
| Halaman | : | 328-335 |
| Abstrak | : | We study—both theoretically and experimentally—charging and discharging capacitors that are actively controlled using a voltage source. We show how an appropriate choice of control voltage allows the charging or discharging to take place very slowly (quasistatically). Conversely, we study the price to be paid in terms of Joule heat when we speed up these processes. Finally, we develop optimal processes that minimize energy consumption for a finite charging time. Our study combines fundamental concepts in thermodynamics, classical mechanics, and electrical circuits. This topic lends itself well to an experimental project in the classroom, involving computer control of a voltage source, data acquisition, and processing. |