# Philippe H. Trinh : The role of exponentially small effects in the physical sciences

Recently, the development of specialized techniques in mathematics known as
exponential asymptotics has led to the successful resolution of
long-standing problems in topics as varied as crystal growth, dislocations,
pattern formation, turbulence, thin film flow, and hydrodynamics. These
developments have emerged from the realization that in many such problems,
exponentially small effects can significantly change the solutions of the
underlying mathematical models.

In this talk, we will introduce the audience to the history, ideas, and
basic techniques of exponential asymptotics, with particular emphasis on
how to recognize when such approaches are necessary. We will discuss the
19th century struggles of the great Cambridge physicist G.G. Stokes to
better understand what is now known as the Stokes Phenomenon. We will then
show how this understanding would provide the key insight into resolving
two famous problems: the problem of modelling dendritic crystal growth, and
the Saffman-Taylor viscous fingering problem.

Our discussion will conclude with a glimpse of the present and future
applications of exponential asymptotics, notably within the context of
hydrodynamics and ship waves, and for the mathematical modelling of rupture
and singularity formation in fluid flows.

**Category**: Nonlinear and Complex Systems**Duration**: 14:47**Date**: March 31, 2015 at 2:45 PM-
**Tags:**seminar, CNCS Seminar

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