Collisional invariants

In this case no detailed collision kinetics are involved. The collision parameters rnm and the parameters in the Maxwellian post-collision velocity distribution f m are derived from experimentally determined gas viscosity or diffusivity, and the collisional invariants, respectively. Usually this term is negligible in present experiments, but exceptions exist [16]. In particular for ITER, and the high collisionality there, these terms are expected to become more relevant. However, due to the BGK-approximations made, their implementation into the models does not require further discussion here. 

The relations derived thus far have been obtained from conservation of total energy and conservation of linear momentum. In general, however, the total angular momentum is also a collisional invariant, and additional microscopic information can be obtained from this particular conservation law. Before collision, the initial angular momentum of the system is a vector... 

It is convenient to introduce the notion of collisional invariants (or summational invariants) (e.g., [55], p. 460 [90], p. 150). The validity of (2.211) is commonly justified by the following arguments Due to the symmetry properties of the collision term expression, interchanging variables gives the following equalities ... 

We note that n p is a collisional invariant and therefore remains unchanged by the collision process. In terms of the lattice variables. 

These reactions are invariably fast, whenever they are exoergic, with rate coefficients, k, close to the collisional limiting values, ko 10 ernes [197]. Water has a proton affinity of 7.22 eV (166.5 kcal/mol), and common organic mole-... 

In general, the polarizability is a tensor whose invariants, trace and anisotropy, give rise to polarized and fully depolarized light scattering, respectively. Collision-induced light scattering is caused by the excess polarizability of a collisional pair (or a larger complex of atoms or molecules) that arises from the intermolecular interactions. In Section I.l, we are concerned with the definition, measurement, and computation of interaction-induced polarizabilities and their invariants. 

Let us examine the pair interactions in detail. The polarizability of an atom pair differs from the sum of the atomic polarizabilities because of the anisotropy of a collisional pair. Accordingly, the diatomic polarizability is defined as the polarizability of the interacting pair minus the sum of the polarizabilities of the two isolated atoms. The diatomic polarizability is a tensor. The invariants of the tensor, namely, the isotropic (trace) and anisotropic polzirizabilities, a R) and /3(/ ), respectively, are defined by... 

If we choose as the summational invariants m, mC and mC, we obtain the Cauchy set of conservation equations named the continuity (2.217), the equation of motion (2.223), and the equation of energy (2.230). The only difference in the final result is that the pressure tensor, p, and the heat flux vector, q, are made up of two parts (i.e., a kinetic and a collisional contribution) ... 

In addition to restoring Galilean invariance, this grid-shift procedure accelerates momentum transfer between cells and leads to a collisional contribution to the transport coefficients. If the mean free path A is larger than a/2, the violation of Galilean invariance without grid shift is negligible, and it is not necessary to use this procedure. 

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