Abstract:
Motivated by the fact that in nature almost all phenomena behave
randomly in some scales and deterministically in some other scales, we
build up a framework suitable to tackle both deterministic and stochastic homogenization
problems simultaneously, and also separately. Our approach,
the stochastic ∑-convergence, can be seen either as a multiscale stochastic approach
since deterministic homogenization theory can be seen as a special case
of stochastic homogenization theory (see Theorem 3), or as a conjunction of
the stochastic and deterministic approaches, both taken globally, but also each
separately. One of the main applications of our results is the homogenization
of a model of rotating fluids.
