2014/11/26 by Parul Maheshwari, Maheshwari, Parul, Gautam Mukhopadhyay +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Acoustic Wave Phenomena Research #Advanced Differential Geometry Research #Advanced Mathematical Theories and Applications #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1411.7398
14 pages
arxiv created 2014/11/26 · openalex publication_date 2014/11/26 · arxiv updated 2014/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A description of Orthogonal Tensor Hermite Polynomials in 3-D is presented. These polynomials, as introduced by Grad in 1949 [1], can be used to obtain a series solution to the Boltzmann Transport Equation. The properties that are explored are scaling, translation and rotation. Order 6 Hermite Tensors are studied while obtaining the rotation relations. From the scaling of the independent variables of particle velocities, a criterion on temperature is obtained which implies that the equation can be applied to binary gas mixtures only if the temperature of the hotter constituent is less than four times that of the cooler one. This criterion and other properties of the tensor hermite polynomials obtained in this paper can be used to study gas dynamics in the thermosphere.