RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
Video Library
Archive
Most viewed videos

Search
RSS
New in collection





You may need the following programs to see the files






Sixth International Conference on Differential and Functional Differential Equations DFDE-2011
August 16, 2011 12:55, Moscow
 


Homogenization of spin energies

A. L. Piatnitskiab

a Lebedev Physical Institute, Moscow, Russia
b Narvik University College, Narvik, Norway
Video records:
Flash Video 1,750.9 Mb
Flash Video 288.0 Mb

Number of views:
This page:144
Video files:99

A. L. Piatnitski


Видео не загружается в Ваш браузер:
  1. Установите Adobe Flash Player    

  2. Проверьте с Вашим администратором, что из Вашей сети разрешены исходящие соединения на порт 8080
  3. Сообщите администратору портала о данной ошибке

Abstract: The talk will focus on homogenization and $\Gamma$-convergence of surface and line energies defined on lattice (spin) systems in $\mathbf Z^d$ through bond interactions. We will dwell on nearest neighbours interaction systems and consider both periodic and random statistically homogeneous ergodic cases.
Given a smooth bounded domain $G\subset\mathbf R^n$ and a small parameter $\varepsilon>0$, we denote $\varepsilon\mathbf Z^d\cup G$ by $G_\varepsilon$ and, for a function $u$ defined on $G_\varepsilon$, consider the energy
$$ E_\varepsilon(u)=\sum_{i,j\in G_\varepsilon}\varepsilon^{d-1}c_{ij}(u_i-u_j)^2, \qquad c_{ij}\ge 0, \quad c_{ij}=0 if |i-j|\ne\varepsilon. $$
Our goal is to study the limit behaviour of $E_\varepsilon$ as $\varepsilon\to 0$.

Language: English

SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru
 
Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020