arXiv subjects

Ashmeet Singh

Publications and source records attributed to Ashmeet Singh.

21 records · Page 2Linked to original sources

arXiv2014

Physics from Angular Projection of Rectangular Grids

In this paper, we present a mathematical model for the angular projection of a rectangular arrangement of points in a grid. This simple, yet interesting problem, has both a scholarly value and applications for data extraction techniques to study the physics of various systems. Our work can interest undergraduate students to understand subtle points in the angular projection of a grid and describes various quantities of interest in the projection with completeness and sufficient rigour. We show that for certain angular ranges, the projection has non-distinctness, and calculate the details of such angles, and correspondingly, the number of distinct points and the total projected length. We focus on interesting trends obtained for the projected length of the grid elements and present a simple application of the model to determine the geometry of an unknown grid whose spatial extensions are known, using measurement of the grid projection at two angles only. Towards the end, our model is shown to have potential applications in various branches of physical sciences including crystallography, astrophysics and bulk properties of materials.

physics.gen-ph↗

arXiv2014

Relativistic corrections to the central force problem in a generalized potential approach

We present a novel technique to obtain relativistic corrections to the central force problem in the Lagrangian formulation, using a generalized potential energy function. We derive a general expression for a generalized potential energy function for all powers of the velocity, which when made a part of the regular classical Lagrangian can reproduce the correct (relativistic) force equation. We then go on to derive the Hamiltonian and estimate the corrections to the total energy of the system up to the fourth power in $|\vec{v}|/c$. We found that our work is able to provide a more comprehensive understanding of relativistic corrections to the central force results and provides corrections to both the kinetic and potential energy of the system. We employ our methodology to calculate relativistic corrections to the circular orbit under the gravitational force and also the first-order corrections to the ground state energy of the hydrogen atom using a semi-classical approach. Our predictions in both problems give reasonable agreement with the known results. Thus we feel that this work has pedagogical value and can be used by undergraduate students to better understand the central force and the relativistic corrections to it.

physics.class-ph↗

arXiv2013

A simplistic pedagogical formulation of a thermal speed distribution using a relativistic framework

A novel pedagogical technique is presented that can be used in the undergraduate (UG) class to formulate a relativistically extended Kinetic Theory of Gases and thermal speed distribution, while assuming the basic thermal symmetry arguments of the famous Maxwell-Boltzmann distribution as presented at the UG level. The adopted framework can be used by students to understand the physics in a thermally governed system at high temperature and speeds, without having to indulge in high level tensor based mathematics, as has been done by the previous works in the subject. Our approach, a logical extension of that proposed by Maxwell, will first recapitulate what is taught and known in the UG class and then present a methodology inspired from the Maxwell-Boltzmann framework that will help students to understand and derive the physics of relativistic thermal systems. The methodology uses simple tools well known to undergraduates and involves a component of computational techniques that can be used to involve students in this exercise. We have tried to place the current work in a larger perspective in regard to the earlier works done and emphasize on it's simplicity and accessibility to students. Towards the end, interesting implications of the relativistically extended distribution are presented and compared with the Maxwell-Boltzmann results at various temperatures.

physics.gen-ph↗