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Liouville integrability may not be what you think
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| Pengarang | : | F. Leyvraz |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 4) |
| Halaman | : | 320-327 |
| Abstrak | : | One path to solving for the motion of a mechanical system involves finding a sufficient number of conserved quantities. The Liouville–Arnol'd theorem states that this motion has a simple structure that can be described using action–angle variables. This is often taken to mean that the motion can be described in simple terms and that the system can be “solved exactly” in the intuitive sense that we can fully describe the orbits. In this paper, we consider this last claim, which is not a consequence of the theorem itself, and show a counterexample: we display a system satisfying the hypotheses, and thus the conclusions, of the Liouville–Arnol'd theorem, but the orbits of which can be arbitrarily complex. It is shown that the difficulty in the analysis of our examples is intrinsic and not due to any lack of ingenuity in expressing the solution. Rather, the orbits are complex in nature and derive this feature from an underlying chaotic dynamic. |
Unveiling the interdisciplinary character of negative pressure
| Pengarang | : | Francisco F. Barbosa; Lucas Squillante; Roberto E. Lagos-Monaco; Mariano de Souza; Luciano Ricco; Antonio C. Seridonio |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 4) |
| Halaman | : | 314-319 |
| Abstrak | : | We explore the concept of negative pressure and its relevance in a variety of physical contexts: the expansion of the universe, mixture theory, cavitation, and the capillary effect in plants. Using thermodynamic arguments, we discuss the intricate connection between negative pressure and negative thermal expansion. We highlight the fact that metastable states and competing phases are often associated with the emergence of negative pressure. We also propose a new link between the effective Grüneisen parameter and nucleation theory. |
A derivation of precessional effects in the Foucault pendulum using complex numbers
| Pengarang | : | Morgan Facchin |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 4) |
| Halaman | : | 308-313 |
| Abstrak | : | It is found that the exact equations governing the motion of the Foucault pendulum take a simpler form when describing the pendulum's position as a complex number evolving in the complex plane. In this description, three notable effects (the intrinsic precession, the Foucault precession, and the Crane effect) appear as natural solutions without prior assumptions on their precessional nature. The pedagogical value of the problem is discussed, emphasizing its connections to time-reversal symmetry and the use of complex numbers in two-dimensional problems. |
Interplay between Airy and Coriolis precessions in a real Foucault pendulum
| Pengarang | : | N. N. Salva; H. R. Salva |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 4) |
| Halaman | : | 297-307 |
| Abstrak | : | We study the precession of a Foucault pendulum using a new approach. We characterize the support anisotropy by the difference between the maximum and minimum periods of the pendulum along the principal axes of the support. Then, we compute the total precession rate, taking into account both the Airy precession of a spherical pendulum and the Coriolis precession due to the Earth's rotation. To study the resulting motion, we developed a calculation loop, period after period, that describes the movement of the oscillatory trajectory of the bob. To test our model, we mounted a test pendulum of 480.3 cm length and measured its periods and precession. The rate of precession is sensitive to the dimensions of the pendulum, the anisotropy of the support, and the initial conditions. We find that for certain amplitudes, the precession can stop entirely while the pendulum continues to oscillate. It is also possible to obtain continuous precession at lower oscillation amplitudes. We give an upper bound for this critical oscillation amplitude. We close with a discussion of the implications of our findings for the design of Foucault pendulums used in demonstrations and lab experiments. |
An undergraduate lab experiment on matched filtering as used in gravitational wave detection
| Pengarang | : | Michael Daam; Antje Bergmann; Carsten Rockstuhl; Ronny Nawrodt |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 3) |
| Halaman | : | 272-280 |
| Abstrak | : | The detection of gravitational waves using matched filtering algorithms is just one example of the critical role that computational data analysis plays in contemporary physics. We present an undergraduate laboratory experiment where students apply matched filtering methods to detect weak signals in their noisy measurement data. The experiment is based on a Michelson interferometer and requires little additional equipment. To make the experiment accessible to students without programming skills, we developed an open-source graphical user interface for the matched filter search, which is also presented in this article. Finally, we demonstrate the ability to detect weak signals obtained with the experimental setup described here. |
Educational Shack–Hartmann wavefront sensor
| Pengarang | : | Khosrow Hassani; Veyana Khajehhassanirabori |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 3) |
| Halaman | : | 264-271 |
| Abstrak | : | The Shack–Hartmann wavefront sensor (SHWFS) is a standard detector used in the measurement of a light wave's wavefront shape. However, its relatively high price restricts its use as an educational tool in instructional optics laboratories. In this work, we show how a low-cost educational SHWFS can be assembled using spare parts and also provide the computational codes necessary to analyze the obtained data. We demonstrate the utility of our sensor by measuring the collimation of a beam, comparing the shape of sample spherical and cylindrical wavefronts, and demonstrating some effects of lens aberrations. We also discuss the spatial resolution and measurement uncertainties of this sensor. The experimental results are in excellent agreement with theoretical calculations. The outcomes of this work can enhance the efficiency of instructional optics laboratories and enrich the knowledge of students regarding important concepts in classical optics. |
Graphical approach to Bells inequalities
| Pengarang | : | Krzysztof Rebilas |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 3) |
| Halaman | : | 260-263 |
| Abstrak | : | Following an approach proposed by Eberhard, a graphical representation of entangled particles is used to provide insight into the meaning and direct experimental consequences of local realism. The most famous Bell-type theorems, like the original inequality developed by Bell, as well as the ones presented by Clauser, Horne, Shimony, and Holt, Clauser and Horn, Eberhard, d'Espagnat, and Maccone, are then derived by means of the graphical method. The universality and efficiency of the presented method in achieving different Bell's inequalities follow from making local realism explicitly a starting point in our general reasoning. The pedagogical and illustrative nature of the approach makes it easy to see directly how all the miscellaneous inequalities are actually rooted in the local realist view on microscopic particles. |
Note on a classical case of self-organization: The Persian Immortals
| Pengarang | : | Santos Bravo Yuste |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 3) |
| Halaman | : | 258-259 |
| Abstrak | : | In an article in this journal, Kanellopoulos, Razis, and van der Weele provided a key formula that describes the evolution of the cumulative distribution of the Persian Immortals' fighting abilities during a battle where fallen soldiers, who are more likely to be weaker than average, are replaced by reserve soldiers with average strength. They also calculated the limit distribution, which shows the final strength advantage of the fighting army over the reserve unit. However, their arguments to derive the mentioned key formula may be difficult to follow for some readers who are not familiar with how the cumulative distribution function of a set changes when some of its elements are replaced. Here, we present a simpler yet more general method to derive this formula. This makes Kanellopoulos, Razis, and van der Weele's compelling exercise more appropriate for an introductory undergraduate course. |
Color-coding strategies for multiple representations
| Pengarang | : | Brianna S. Dillon Thomas |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 3) |
| Halaman | : | 256-257 |
| Abstrak | : | This paper shows that color-coding strategies can be used to support multiple representations of physics concepts in instructional materials. They are straightforward to implement and can be adapted to instruction at a variety of levels. |
Toward a more coherent and profession-related physics teacher education: Linking subject-specific and physics education content in the study entry phase
| Pengarang | : | Antonia Bauer; Jonas Gleichmann; Philipp Bitzenbauer |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 93 (No. 3) |
| Halaman | : | 250-255 |
| Abstrak | : | The introductory phase of the physics teacher education program at the Friedrich–Alexander University Erlangen–Nuremberg (FAU), Germany, was redesigned to improve the coherence of the program and reduce the high dropout rates in the introductory phase of the physics teacher education program by making the courses more relevant and appealing to the students' future professional roles. The new organization combines subject-specific lectures on experimental physics with a simultaneous presentation of the corresponding perspectives of physics education through a new course called “Focus Class: physics education and school-related topics.” This new course is directly linked to the subject-specific content of the lecture and focuses on the conceptual hurdles that school students may encounter when confronted with the subject matter being taught in lectures and emphasizes active learning strategies. In this paper, we describe the course design and report on student experiences from an evaluation of the course. |