## Mathematics Faculty Articles

#### Title

Curvilinear Polyadic Moments of the Boltzmann Equation. I. Polyadic Hierarchy for An N-Species, Dilute, "Point" Plasma

#### Document Type

Article

#### Publication Date

5-1-1970

#### Publication Title

Annals of Physics

#### ISSN

0003-4916

#### Volume

58

#### Issue/No.

1

#### First Page

157

#### Last Page

175

#### Abstract

The Maxwell transport equation is rederived, using a *general curvilinear polyadic moment***S(r, v**, *t*) of the Boltzmann equation. When this moment is specified in turn to be the velocity polyads S = *m*, *m*v, *m*vv,···, *m*vv ··· v, the coupled hierarchy of velocity moments for an *N* species, dilute, point plasma is thereby obtained. For suitable choices of **S** and proper polyadic contractions, all of the dilute, point-plasma transport equations can be derived. Explicit results include: (1) The polyadic transport equation, with arbitrary acceleration **a**, for the *l*-th *order poly-pressure**Γ**l* = *ϱ*〈*ννν*···*ν*〉 (*l* terms). (2) The *first seven moment* transport equations, for both arbitrary acceleration a and electromagnetic acceleration q(E + v × B), governing the flow of mass density ϱ, continuum velocity **V**, energy density *e*, heat flux vector **q**, pressure tensor **P**, heat flux tensor **Q**, and moment of momentum r × *m*V.

Included, also, is a brief outline of future papers in this series and an appendix summarizing the *curvilinear polyadic calculus* used throughout the series.

#### NSUWorks Citation

Hawkins, Lawrence Carl, "Curvilinear Polyadic Moments of the Boltzmann Equation. I. Polyadic Hierarchy for An N-Species, Dilute, "Point" Plasma" (1970). *Mathematics Faculty Articles*. 49.

https://nsuworks.nova.edu/math_facarticles/49

#### DOI

10.1016/0003-4916(70)90242-3