A stochastic continuum dynamical system based on a dimensional reduction procedure (Q1269833)

An important aspect of modelling phenomena related to bodies with microstructure is to take into account the stochastic properties that are inherent in such problems. The paper extends the concept of a three-scale modelling of behaviour of materials, considers the evolution of probability densities that arise in the application of such a procedure, and determines the relations between the probability densities on different levels of description. The Hamiltonian dynamical system with stochastic initial conditions is used to describe the behaviour of groups of atoms constituting the body. The dimensional reduction of such a system proves to be advantageous. It is shown that the internal state variables are useful in the creation of stochastic operators on more averaged levels. The paper also compares the features of the present model with statistical mechanics.