Applied Analysis Seminar - Abstracts
Talk
Friday, 8 November 2019, 10:30-11:30 in HG03.082
Mark Peletier (TU Eindhoven)
Gradient Flows and Large Deviations
Abstract
During the last ten years we have discovered a tight link between gradient
flows on one hand and large deviations on the other. Gradient flows are a
class of dynamical systems: evolution equations driven by the 'fastest
decrease' of an energy or entropy functional. Large deviation theorems
give rigorous asymptotic characterizations of rare events of random variables.
These two unlikely bedfellows turn out to be closely related, in the case of
evolution equations that arise as macroscopic, upscaled limits of stochastic
processes. Such evolution equations arise in many physical processes: diffusion,
heat conduction, fluid flow, elasticity, plasticity, chemical reactions, and
many more. In this talk I will show how these two concepts relate to each other
and to the underlying physics, chemistry, or biology. I also will show how it
leads to a rigorous underpinning of a modelling methodology known as Variational
Modelling, and in this way gives rise to new descriptions of the physical world around us.
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