The stochastic approach in analysis-the structures with vacancies and impurities

Abstract

The stochastic approach to the problem of deformed bulk structures is a unique possibility for obtaining a so-so real picture of physical processes in these structures. The chain of identical atoms with random distances between neighbours as well as the chain with random masses at equal distances is analysed. These analyses were generalized to complex chains, which are spatially and mass deformed. The approximations used were incommensurability; one and more rough, continual approximation. The probabilities are of exponential type. It means that the error in estimation on the basis of stochastical method can go to 100% maximally. © 2007 Springer Science+Business Media, LLC.