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Cognitive biases can move opinion dynamics from consensus to signatures of transient chaos
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| Pengarang | : | Emily Dong; Sarah Marzen |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 92 (No. 10) |
| Halaman | : | 801-808 |
| Abstrak | : | Interest in how democracies form consensus has increased recently, with statistical physics and economics approaches both suggesting that there is convergence to a fixed point in belief networks, but with fluctuations in opinions when there are “stubborn” voters. We modify a model of opinion dynamics in which agents are fully Bayesian to account for two cognitive biases: confirmation bias and in-group bias. Confirmation bias occurs when the received information is considered to be more likely to align with the receiver's beliefs. In-group bias occurs when the receiver further considers the information to be more likely when the receiver's beliefs and the sender's beliefs are aligned. We find that when there are no cognitive biases, a network of agents always converges to complete consensus. With confirmation bias alone, polarization can occur. With both biases present, consensus and polarization are possible, but when agents attempt to counteract confirmation bias, there can be signatures of transient chaos and ongoing opinion fluctuations. Based on this simple model, we conjecture that complex opinion fluctuations might be a generic feature of opinion dynamics when agents are Bayesian with biases. |
Numerical simulation projects in micromagnetics with Jupyter
| Pengarang | : | Martin Lonsky; Martin Lang; Samuel Holt; Swapneel Amit Pathak; Robin Klause; Tzu-Hsiang Lo; Marijan Beg; Axel Hoffmann; Hans Fangohr |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 92 (No. 10) |
| Halaman | : | 794-800 |
| Abstrak | : | We report a case study where an existing materials science course was modified to include numerical simulation projects on the micromagnetic behavior of materials. The Ubermag micromagnetic simulation software package is used in order to solve problems computationally. The simulation software is controlled through the Python code in Jupyter notebooks. Our experience is that the self-paced problem-solving nature of the project work can facilitate a better in-depth exploration of the course contents. We discuss which aspects of the Ubermag and the project Jupyter ecosystem have been beneficial for the students' learning experience and which could be transferred to similar teaching activities in other subject areas. |
Demonstrating two-particle interference with a one-dimensional delta potential well
| Pengarang | : | Zhi Jiao Deng; Xin Zhang; Yong Shen; Wei Tao Liu; Ping Xing Chen |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 92 (No. 10) |
| Halaman | : | 786-793 |
| Abstrak | : | In quantum mechanics, the exchange symmetry of wave functions for identical particles has observable effects, including the widely studied Hong–Ou–Mandel (HOM) effect. A theoretical description using second quantization is elegant but abstract. In contrast, this paper describes a simple model of two-particle interference using a one-dimensional delta potential well as a beam splitter. The conditions for the HOM effect are derived from the perspective of wave packet evolution. Furthermore, the interference processes of bosons, fermions, and distinguishable particles are demonstrated and compared in detail. The method presented here is concrete, easy to visualize, and can help students to better understand the effects arising from the exchange symmetry of wave functions. The main results can be animated for classroom teaching or developed into an undergraduate seminar topic. |
Gravitational waves without general relativity redux
| Pengarang | : | Robert C. Hilborn |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 92 (No. 10) |
| Halaman | : | 780-785 |
| Abstrak | : | An electromagnetic-like model of gravitational radiation reproduces many features of the gravitational waves emitted by orbiting binary systems and observed by the LIGO-Virgo collaboration. However, that model predicts a total gravitational wave power emission which is smaller than that predicted by general relativity. In this paper, we improve the electromagnetic-like model by considering the energy-momentum tensor of the binary source and revisiting a numerical factor in the expressions that link the gravitational mass/energy currents to the vector potential. The enhanced model's results for the total gravitational wave power emitted by a binary source before coalescence are in complete agreement with general relativistic predictions. This approach makes gravitational wave physics accessible to a broad audience without requiring any knowledge of general relativity. |
A simplified relativity experiment
| Pengarang | : | David P. Jackson; Fedya Grishanov; Noah Lape; Emma Lothrop |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 92 (No. 10) |
| Halaman | : | 775-779 |
| Abstrak | : | We describe a simplified experiment that can be used to verify the relativistic energy-momentum relationship for beta particles emitted from a 204Tl source. The experiment makes use of an exempt radioactive source and is therefore ideal for institutions that do not maintain a Nuclear Regulatory Commission (or state) license. The relativistic beta particles are injected into a uniform magnetic field and the maximum radius of the trajectories is determined. Comparing this radius to the relativistic and non-relativistic predictions demonstrates that only the relativistic equations are consistent with the data. The simplicity of the experiment and analysis makes this project ideal for inclusion in a sophomore-level modern physics course. |
Heisenbergs 1939 reactor theory, Serbers 1943 Los Alamos Primer, and Heisenbergs 1945 Farm Hall critical mass calculation
| Pengarang | : | Joseph L. McCauley |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 92 (No. 10) |
| Halaman | : | 765-774 |
| Abstrak | : | There is disagreement over how much Werner Heisenberg knew about reactors and the bomb 1939–1945. A critical paper, declassified and returned to the Germans in 1971, has been inadequately understood in the controversy. Heisenberg calculated the critical radius for a spherical reactor with a tamper but the same formula applies whether spherical reactor or spherical bomb because his result is independent of the reactor's neutron source at criticality (a bomb has no external neutron source). He didn't emphasize the source-independence of the critical radius but instead misinterpreted it. Under captivity at Farm Hall in England in 1945 with eight other leading German nuclear researchers and Max v. Laue, Heisenberg recalled his 1939 theory from memory and made the same critical radius calculation for a bomb with a tamper that Serber had made in 1943 at Los Alamos. Heisenberg's 1945 formula for a bomb is identical to his 1939 critical radius formula derived for a reactor. His 1945 predictions for the numerical values of the critical radius are close to Serber's, except that Heisenberg only knew the fast fission cross section within two bounds, 0.5 and 2.5 barn. Serber's fast fission cross section was in the middle at 1.5 barn. This places Heisenberg's 1939 and 1945 theory and calculations, finally, in the correct historic context. |
Heat engines with finite reservoirs
| Pengarang | : | Randall D. Knight |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 92 (No. 10) |
| Halaman | : | 759-764 |
| Abstrak | : | Typical textbook analyses of heat engines assume that the temperatures of thermal reservoirs do not change; that is, the reservoirs have infinite heat capacity. Several authors have investigated the performance of reversible heat engines for which reservoirs have finite heat capacities and thus the reservoir temperatures do change with time. We find that previous studies have been too restrictive in that they assumed that the reservoir temperature change per cycle is infinitesimal and that the engine ceases operation when the hot reservoir cools to match the temperature of the cold reservoir. We model a Carnot-like engine and show that (1) the problem can be solved exactly with no requirement for infinitesimal temperature changes and (2) there is nothing special about the instant when the temperatures converge, with the device transitioning smoothly from a heat engine to a refrigerator. We find explicit expressions for the limiting reservoir temperature and the total efficiency. |
Elongation of a ferrofluid droplet near a permanent magnet: A tidal or magnetic energy effect
| Pengarang | : | Zoe Boekelheide |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 92 (No. 10) |
| Halaman | : | 752-758 |
| Abstrak | : | Ferrofluid droplets falling toward a permanent magnet elongate as they approach the magnet. This phenomenon has been proposed as a way to visualize how tidal (nonuniform) forces can cause stretching/elongation of objects, such as the bulging of Earth's oceans under the nonuniform force of the Moon's gravity. In this manuscript, we analyze a ferrofluid in the nonuniform magnetic field of a permanent magnet and compare a simple model for the tidal stretching mechanism with the magnetic energy mechanism, which is known to stretch a ferrofluid droplet even in a uniform magnetic field. Far from the magnet, both mechanisms display power-law behavior as a function of the distance to the magnet z; for the tidal mechanism, the droplet's elongation is proportional to 1/?8?, while that due to the magnetic energy mechanism is proportional to 1/?6?. Thus, the elongation of a droplet falling toward a permanent magnet is initially dominated by the magnetic energy effect. The tidal effect overtakes the magnetic energy effect as the droplet approaches the magnet, and at a critical distance, a tidal disruption event occurs. This system can be studied in the laboratory and could be used as an exploratory laboratory for student-designed experimentation. |
What is a degree of freedom Configuration spaces and their topology
| Pengarang | : | Juan Margalef-Bentabol; D. Leigh Herman; Ivan Booth |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 92 (No. 10) |
| Halaman | : | 743-751 |
| Abstrak | : | Understanding degrees of freedom in classical mechanics is fundamental to characterizing physical systems. Counting them is usually easy, especially if we can assign them a clear meaning. However, the precise definition of a degree of freedom is not usually presented in first-year physics courses since it requires mathematical knowledge only learned in more advanced courses. In this paper, we use a pedagogical approach motivated by simple but non-trivial mechanical examples to define degrees of freedom and configuration spaces. We highlight the role that topology plays in understanding these ideas. |
The physics of everesting on a bicycle
| Pengarang | : | Martin Bier |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 92 (No. 10) |
| Halaman | : | 737-742 |
| Abstrak | : | Among cycling enthusiasts the word “everest” has also become a verb over the last few years. “To everest” means going up and down the same hill or mountain until the elevation of Mount Everest (8848 m) has been accumulated in the course of the repeated ascents. It has been suggested that considerable advantage can be obtained by having a strong tailwind on the climbs. We make a quantitative assessment and show that the effect of a tailwind is small. Using control coefficients, we furthermore assess how factors such as weight reduction, increased power output, and improved aerodynamics can enhance the performance. |