Stochastic homogenization of heat transfer in polycrystals with nonlinear contact conductivities
Stochastic homogenization of heat transfer in polycrystals with nonlinear contact conductivities
复制标题
具有非线性接触电导率的多晶传热的随机均匀化
DOI：
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发表时间：
2012
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通讯作者：
M. Heida
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作者：
M. Heida
在晶界上具有非线性跳跃条件的多晶体中的热传递问题将使用由Zhikov和Pyatnitskii开发的随机双尺度收敛的方法均匀化[V. V. Zhikov和A.L. Pyatnitskii，Homogenization of random singular structures and random measures，Izv. Math.70（1）（2006），pp. 19-67]和最近延长的作者[M. Heida，随机双尺度收敛的一个推广及其应用，渐近性。Anal.（2010）（出版中）]。它将表明，单调Lipschitz跳跃条件可微0，非线性消失的限制。此外，现有的Poincaré不等式将扩展到更一般的几何设置与唯一的限制，当地的C1-接口有限的强度。特别是，现在可以将结果应用于Poisson-Voronoi细分。
The heat transfer problem in a polycrystal with nonlinear jump conditions on the grain boundaries will be homogenized using the method of stochastic two-scale convergence developed by Zhikov and Pyatnitskii [V.V. Zhikov and A.L. Pyatnitskii, Homogenization of random singular structures and random measures, Izv. Math. 70(1) (2006), pp. 19–67] and recently extended by the author [M. Heida, An extension of stochastic two-scale convergence and application, Asympt. Anal. (2010) (in press)]. It will be shown that for monotone Lipschitz jump conditions differentiable in 0, the nonlinearity vanishes in the limit. Additionally, existing Poincaré inequalities will be extended to more general geometric settings with the only restriction of local C 1-interfaces with finite intensity. In particular, the result can now be applied to the Poisson–Voronoi tessellation.