Form macroscale models via an ensemble of microscale phase-shifts

Prof. A.J. Roberts (University of Adelaide)

Thursday 15th May 14:00-15:00
Maths 311B

Abstract

Many physical scenarios involve detailed microscale physics
in large-scale macroscale domains. For example, modern
`smart' materials have complex microscale structure, often
with unknown macroscale closure. For such multiscale
systems, we research the relation between the descriptions
at the different space and time scales. Here let's explore
the closures required to translate microscale knowledge to a
system-level macroscopic description. Endemic practice is
to identify processes in `Representative Volume Elements'
(RVEs), typically leading to macroscale continuum PDEs.
The example of Brownian Bugs shows that such RVE arguments
are unsound. Instead, RVEs should be reinterpreted via
ensemble averages. Similarly, homogenised models of
heterogeneous microscale structures invariably invoke RVEs.
Simple heterogeneous problems illustrate that we should
instead homogenise via the ensemble of all phase-shifts of
the heterogeneity. Such a framework also empowers efficient
and accurate computational homogenisation.

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