水野将司教授(Dept. Math., College of Sci. Tech., Nihon University)

演講時間：112年3月21日下午2點
演講地點：A813教室

講題：Fokker-Planck model of grain boundary motion

摘要：In this talk, first, we consider the mathematical model of
grain boundary motion via stochastic differential equations. The
proposed model involves an anisotropic grain boundary energy that
depends on the lattice misorientation and considers the mobility of
the triple junctions. The joint distribution function of the state
variable, that is, the misorientations and the triple junctions, obeys
some Fokker-Planck equation. Under the fluctuation-dissipation
assumption, we will derive the relationship between Brownian motions
and the mobility of the state variables.

Next, we consider the long-time behavior of a solution to the
Fokker-Planck equation. Precisely, we prove the exponential stability of
the equilibrium state. The main idea to prove the stability is to use
the space of "weighted" square-integrable functions and the Poincare
inequality. Then we propose a new formula for the triple junction and
the misorientation.

This talk is based on the joint work with Yekaterina Epshteyn and Chun
Liu.