Applied Maths Seminar: Roberts -- Coordinate transforms underpin multiscale modelling and reduction in deterministic and stochastic systems

A persistent feature of complex systems in engineering and science is the emergence of
macroscopic, coarse grained, coherent behaviour from the interactions of microscopic
agents (molecules, cells) and with their environment.  In current modeling, ranging from
ecology to materials science, the underlying microscopic mechanisms are known, but the
closures to translate microscale knowledge to a system level macroscopic description are
rarely available in closed form.  Kevrekidis proposes new `equation free’ computational
methodologies to circumvent this stumbling block in multiscale modelling.  Nonlinear
coordinate transforms underpin analytic techniques that support these computational
methodologies.  But to do so we must cross multiple space and time scales, in both
deterministic and stochastic systems, and where the microstructure is either smooth or
detailed.  Using examples, I describe progress in using nonlinear coordinate transforms
to illuminate such multiscale modelling issues.