Affine Transformation Groups in Study of Water Molecules Transfer in Presence of Low Density Water Vapour

Abstract

Problems of molecular transfer in gas environment are considered with assumption that part of water molecules may change their properties to provide transfer process. This change consists in increase of dimension of vector space, which used to describe transfer process, from 3 to 4. Other cases of extending of dimension of vector space are particular considered. At first, relations between affine group and Markov chain is considered. In, an action of Markov chain matrix as affine matrix is analyzed with result that point with coordinate number equal 1 is fixed point on straight line. A serious problem remains in relating the mathematical formalism developed for physical understanding of the molecule transfer. However, some properties given by mathematical constructions might arise within experimental studies. In particular, water molecules with 4D-description will not interact with ordinary water molecules and therefore have large molecular mean free path.