A STOCHASTIC APPROACH TO COARSENING OF CELLULAR NETWORKS

作者：Cohen Albert^*

来源：Multiscale Modeling and Simulation, 2010, 8(2): 463-480.

DOI：10.1137/090752985

• grain growth
• nonlinear transport
• martingales
• weak convergence of Markov processes

We prove existence for a system of master equations modeling grain growth proposed in [K. Barmak et al., Remarks on a multiscale approach to grain growth in polycrystals, in Variational Problems in Materials Science, Birkhauser, Basel, 2006, pp. 1-11]. The method used to prove existence for these nonlinear, integro-PDEs employs tools from both functional analysis and probability. The stochastic interpretation for the evolution of the mesoscopic properties of this large scale metastable system we provide here is general enough to apply to other cellular networks. This approach leads to an internally consistent theory and opens a new discussion on asymptotics for the distribution of grains in a two-dimensional network, which is the subject of future work.

• 出版日期2010