August 28th, 2020

Мой любимый алгоритм Верле для магнитной силы

A Magnetic Velocity Verlet Method: https://arxiv.org/abs/2008.11810
A. Chambliss, J. Franklin
We discuss an extension of the velocity Verlet method that accurately approximates the kinetic-energy-conserving charged particle motion that comes from magnetic forcing. For a uniform magnetic field, the method is shown to conserve both particle kinetic energy and magnetic dipole moment better than midpoint Runge-Kutta. We then use the magnetic velocity Verlet method to generate trapped particle trajectories, both in a cylindrical magnetic mirror machine setup, and for dipolar fields like the earth's magnetic field. Finally, the method is used to compute an example of (single) mirror motion in the presence of a magnetic monopole field, where the trajectory can be described in closed form.
Comments: To appear, American Journal of Physics

Классические тесты ОТО

Classical Tests of General Relativity Part I: Looking to the Past to Understand the Present: https://arxiv.org/abs/2008.11177
Jorge Pinochet (как много в Чили Пиночетов!..)
Einstein's theory of general relativity (GR) provides the best available description of gravity. The recent detection of gravitational waves and the first picture of a black hole have provided spectacular confirmations of GR, as well as arousing substantial interest in topics related to gravitation. However, to understand present and future discoveries, it is convenient to look to the past, to the classical tests of GR, namely, the deflection of light by the Sun, the perihelion precession of Mercury, and the gravitational redshift of light. The objective of this work is to offer a non-technical introduction to the classical tests of GR. In this first part of the work, some basic concepts of relativity are introduced and the principle of equivalence is analysed. The second part of the article examines the classical tests.
Comments: 9 pages, 6 figures. Physics Education 2020

Студенты, питон и уравнения в частных производных

Питон переползает через Урал
(эпиграф для старперов:))

Специально для уважаемого :

Introducing students to research codes: A short course on solving partial differential equations in Python: https://arxiv.org/abs/2008.10931

Pavan Inguva, Vijesh J. Bhute, Thomas N.H. Cheng, Pierre J. Walker
Recent releases of open-source research codes and solvers for numerically solving partial differential equations in Python present a great opportunity for educators to integrate these codes into the classroom in a variety of ways. The ease with which a problem can be implemented and solved using these codes reduce the barrier to entry for users. We demonstrate how one of these codes,FiPy, can be introduced to students through a short course using progression as the guiding philosophy. Four exercises of increasing complexity were developed. Basic concepts from more advanced numerical methods courses are also introduced at appropriate points. To further engage students, we demonstrate how an open research problem can be readily implemented and also incorporate the use of ParaView to post-process their results. Student engagement and learning outcomes were evaluated through a pre and post-course survey and a focus group discussion. Students broadly found the course to be engaging and useful with the ability to easily visualise the solution to PDEs being greatly valued. Due to the introductory nature of the course, due care in terms of set-up and the design of learning activities during the course is essential. This course, if integrated with appropriate level of support, can encourage students to use the provided codes and improve their understanding of concepts used in numerical analysis and PDEs.
Comments: 12 pages, 9 figures. Fixed references

Двигатель Стирлинга и еще кое-что

Stirling engine operating at low temperature difference: https://arxiv.org/abs/2003.07157
Alejandro Romanelli
The paper develops the dynamics and thermodynamics of Stirling engines that run with temperature differences below 100 0C. The working gas pressure is analytically expressed using an alternative thermodynamic cycle. The shaft dynamics is studied using its rotational equation of motion. It is found that the initial volumes of the cold and hot working gas play a non-negligible role in the functioning of the engine.
American Journal of Physics, Vol. 88, Issue 4, 2020-03-20

The Fluidyne engine: https://arxiv.org/abs/1812.11100
Alejandro Romanelli
The Fluidyne is a two-part hot-air engine, which has the peculiarity that both its power piston and displacer are liquids. Both parts operate in tandem with the common working gas (air) transferring energy from the displacer to the piston side, from which work is extracted. We describe analytically the thermodynamics of the Fluidyne engine using the approach previously developed for the Stirling engine. We obtain explicit expressions for the amplitude of the power piston movement and for the working gas temperatures and pressure as functions of the engine parameters. We also study numerically the power and efficiency of the engine in terms of the phase shift between the motions of piston and displacer.