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SUMMARY:Equilibria configurations for epitaxial crystal growth with adatom
 s - Riccardo Cristoferi\, Heriot-Watt University
DTSTART:20190228T150000Z
DTEND:20190228T160000Z
UID:TALK115774@talks.cam.ac.uk
CONTACT:Matthew Thorpe
DESCRIPTION:Surface diffusion is one of the most important mechanisms driv
 ing crystal growth. When bulk diffusion is much faster than the surface on
 e\, the evolution of the profile of the crystal is described by the so cal
 led Einstein-Nernst relation. According to this law\, the normal velocity 
 of the profile is related to the chemical potential. This evolution equati
 on has a variational flavour\, as it can be obtained as a gradient flow of
  a suitable energy.\n\nAlbeit usually neglected\, adatoms (atoms freely di
 ffusing on the surface of the crystal) seem to play a fundamental role in 
 the description of the behaviour of a solid-vapor interfaces. Some years a
 go Fried and Gurtin introduced a system of evolution equations to describe
  such a situation\, where adatoms are treated as a separate variable of th
 e problem. Also such system of evolution equations can be seen as the grad
 ient flow of an energy.\n\nIn this talk a first step in the programme of s
 tudying the above mentioned evolution equations and the associated energy 
 is presented. In particular\, the following topics for the static problem 
 are addressed: regular critical points\, existence and uniqueness of minim
 isers and relaxation of the energy functional in a suitable topology\, as 
 well as a phase-field approximation.\n\nThe talk is based on a work in col
 laboration with Marco Caroccia (Scuola Normale Superiore-Università di Fi
 renze)\, and Laurent Dietrich (Lycée Fabert).
LOCATION:MR 14
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