Graduate Seminar Analysis

Tuesday, June 23, 2015, 2:00pm

Motion of interfaces in random media: pinning and some applications

Patrick Dondl, Durham University

Abstract: We consider the evolution of an interface, subject to a driven mean curvature flow,
in a random environment. The environment is modeled by a non-linear, random, forcing term
in the evolution equation and describes localized obstacles which are harder to penetrate by
the interface. First we will consider a the problem of pinning a nearly flat interface in such a
random field of obstacles, proving existence of a stationary solution of the evolution equation
by a combination of percolation results and sub- and supersolution techniques. This leads to
the emergence of a hysteresis that does not vanish for slow loading, even though the local
evolution law is viscous (in particular, the velocity of the interface in the model is linear in the
driving force). We will then apply some of these ideas to solutions of Landau-de Gennes' theory
of nematic liquid crystals in the sharp interface limit, considering the evolution of interfaces
with spherical initial conditions.

Interessierte sind herzlich eingeladen.

Zeit: 14:00 Uhr

Ort: Seminarraum 001, Erdgeschoss,  Pontdriesch 14-16 , 52062 Aachen