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Quantitative methods in stochastic homogenization

Final Report Summary - QUANTHOM (Quantitative methods in stochastic homogenization)

The QUANTHOM project, for quantitative methods in stochastic homogenization, aims at
developing mathematical tools allowing to make realistic modelling of composite materials, in
particular when they undergo physical deformation (stretching, compression, shearing).
On the one hand, the project focuses on the microscopic description of such materials (both in terms
of statistical properties and physical laws). On the second hand, the aim is to rigorously derive
macroscopic physical laws that are based on the microscopic laws but are oblivious of the
microscopic details. The originality of the project is to carry out this program in a quantitative way,
which is a challenging problem from the mathematical perspective, and of interest to material
sciences. It involves various fields of mathematics: probability theory, statistical physics, partial
differential equations, calculus of variations, numerical analysis, and scientific computing.