List of Symbols

inner product

double inner product (contraction over 2 indices)

quadruple inner product (contraction over 4 indices)

n-fold inner product (contraction over n indices)

derivative with respect to position

phase average

greatest integer less than or equal to x.

1

unit tensor, second rank tensor with the Kronecker delta for components ()

first Townsend ionization coefficient

strain rate in Planar Couette systems

6N-dimensional phase space vector

Dirac delta function

=

shear viscosity

bulk viscosity

Heaviside step function

phase space compression factor

mobility

reaction rate

collision frequency

velocity dependent collision frequency

cylindrically symmetric components of

viscous pressure tensor

mass density

,

see page

width parameter of a Gaussian source

non-hydrodynamic relaxation time

potential energy

eigenfunctions of

eigenfunctions of

lth order transport coefficient
(swarms)

reaction rate

drift velocity

diffusion coefficient

inverse of considered as a matrix, .

jth eigenvalue of

components of satisfying cylindrical symmetry

acceleration of swarm particle due to field

boundary, or field inhomogeneity operator

velocity (as in mesoscopic picture)

det

determinant of considered as a matrix =

longitudinal diffusion

transverse diffusion

complementary error function

E

electric field

external thermodynamic force

G

Greens function

H

internal energy of the system =

adiabatic rate of change of internal energy

jth order Hermite polynomial

J

thermodynamic flux

= <J>

collision operator

coordinate of Fourier transform

Boltzmann's constant

K

kinetic energy

L

p-Liouvillean

f-Liouvillean

N

average number density (swarms), number of particles (statistical mechanics)

number density

momentum of the ith particle

P

pressure tensor

co-ordinate of the ith particle

the rth root of

saddle point of

position

Res

residue of f at

S

source function

t

time

time at which the swarm peak arrives at the collector

T

temperature

streaming velocity

drift velocity

non-hydrodynamic part of the density