March 6th, 2020

лошадь, диаграмма, Фейнман

Ньютон и мой любимый алгоритм Верле

Newton's discrete dynamics:

In 1687 Isaac Newton published PHILOSOPHIÆ\ NATURALIS PRINCIPIA MATHEMATICA, where the classical analytic dynamics was formulated. But Newton also formulated a discrete dynamics, which is the central difference algorithm, known as the Verlet algorithm. In fact Newton used the central difference to derive his second law. The central difference algorithm is used in computer simulations,where almost all Molecular Dynamics simulations are performed with the Verlet algorithm or other reformulations of the central difference algorithm. Here we show, that the discrete dynamics obtained by Newtons algorithm for Kepler's equation has the same solutions as the analytic dynamics. The discrete positions of a celestial body are located on an ellipse, which is the exact solution for a shadow Hamiltonian nearby the Hamiltonian for the analytic solution.
Comments: 14 pages, 4 figures
лошадь, диаграмма, Фейнман

Как наматывать ВТСП-магниты

Не вчитывался, но, похоже, техническое использование высокотемпературных сверхпроводников вполне себе прогрессирует:

Non-Planar Coil Winding Angle Optimization for Compatibility with Non-Insulated High-Temperature Superconducting Magnets:
лошадь, диаграмма, Фейнман

Что-то популярное о теории относительности

Вроде и Беркли, а все равно у них масса зависит от скорости...

Simple Relativity Approach to Special Relativity:

The development of both special and general relativity is accomplished in a series of 6 papers using a simple approach. The purpose is to explain the how and why of relativity to a broad public, and to be useful for students of physics by providing alternate ways to develop and view relativistic phenomena. In this first paper, the rules for special relativity are developed to explain velocity-related time dilation and length contraction, and the interchangeable nature of mass and energy. In subsequent papers, conservation of energy is applied to show how gravity affects time speed, fall velocities, and length measurements, the effect known as the Shapiro Time Delay, the precession of satellites and planets, gravitational lensing, the appearance of Lorentz contraction and a simple resolution of the Ehrenfest paradox.
Comments: 9 pages, 5 figures

И/ до кучи, еще что-то как бы популярное, но хоть ссылками ценно:

The Platonic solids and fundamental tests of quantum mechanics:

The Platonic solids is the name traditionally given to the five regular convex polyhedra, namely the tetradron, the octahedron, the cube, the icosahedron and the dodecahedron. Perhaps strongly boosted by the towering historical influence of their namesake, these beautiful solids have, in well over two millenia, transcended traditional boundaries and entered the stage in a range of disciplines. Examples include natural philosophy and mathematics from classical antiquity, scientific modeling during the days of the european scientific revolution and visual arts ranging from the renaissance to modernity. Motivated by mathematical beauty and a rich history, we consider the Platonic solids in the context of modern quantum mechanics. Specifically, we construct Bell inequalities whose maximal violations are achieved with measurements pointing to the vertices of the Platonic solids. These Platonic Bell inequalities are constructed only by inspecting the visible symmetries of the Platonic solids. We also construct Bell inequalities for more general polyhedra and find a Bell inequality that is more robust to noise than the celebrated Clauser-Horne-Shimony-Holt Bell inequality. Finally, we elaborate on the tension between mathematical beauty, which was our initial motivation, and experimental friendliness, which is necessary in all empirical sciences.