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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Homogenization of a front propagation model in dynamic environments
动态环境 前端传播模型 均质化 一阶哈密尔顿-雅可比方程
2023/4/18
In this talk I will review the developments of homogenization theory for a front propagation model. It is described by a first order Hamilton-Jacobi equation with a Hamiltonian that grows linearly wit...
Homogenization of reconstructed crystal surfaces:Fick’s law of diffusion
Homogenization reconstructed crystal surfaces Fick’s law of diffusion
2015/10/16
Fick’s law for the diffusion of adsorbed atoms adatoms on crystal surfaces below roughening is generalized to account for surface reconstruction. In this case, material parameters vary spatially at ...
Homogenization of composite vicinal surfaces: Evolution laws in 1+1 dimensions
Crystal surface Burton–Cabrera–Frank (BCF) model Line defects Diffusion Macroscopic limit Multiscale expansion
2015/10/16
We apply classical homogenization to derive macroscopic relaxation laws for crystal surfaces with distinct inhomogeneities at the microscale. The proposed method relies on a formal multiscale expansio...
Homogenization of a nonlinear transport equation
Boltzmann Equation Semiconductor Homogenization
2015/10/15
In this paper, we investigate the homogenization of a nonlinearkinetic equation modeling electron transport in semiconductors. We compute effective scattering coefficients for medium with periodic inh...
Random Homogenization of Fractional Obstacle Problems
Random Homogenization Fractional Obstacle Problems
2015/10/15
We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem in perforated domains.
We study the homogenization of an obstacle problem in a perforated domain, when the holes are periodically distributed and have random shape and size. The main assumption concerns the capacity of the ...
Homogenization of a Hele-Shaw problem in periodic and random media
Free boundary problem Hele-Shaw equation Obstacle problem Viscosity solution Homogenization
2015/10/15
We investigate the homogenization limit of a free boundary problem with space-dependent free boundaryvelocities. The problem under consideration has a well-known obstacle problem transformation, forma...
Homogenization of one-phase Stefan-type problems in periodic and random media
one-phase Stefan-type periodic random
2015/10/15
We investigate the homogenization of Stefan-type problems with oscillating diffusion coefficients. Both cases of periodic and random (stationary ergodic) medium are considered. The proof relies on the...
A FAST ALGORITHM FOR REITERATED HOMOGENIZATION
Reiterated homogenization upscaling effective coefficients homogenization map fast algorithms adaptive sampling
2015/7/14
This paper considers the numerical evaluation of effective coefficients for multiscale homogenization problems and proposes a highly efficient algorithm for a certain class of reiterated homogenizatio...
We consider an elliptic eigenvalue problem with a fast cellular flow of amplitude A, in a twodimensional domain with L2 cells. For fixed A, and L → ∞, the problem homogenizes, and has been well studie...
Homogenization driven by a fractional Brownian motion:the shear layer case
Homogenization driven fractional Brownian motion shear layer case
2015/7/14
We consider a passive scalar in a periodic shear flow perturbed by an additive fractional noise with the Hurst exponent H ∈ (0, 1). We establish a diffusive homogenization limit for the tracer when th...
Analysis of the Heterogeneous Multiscale Method for Parabolic Homogenization Problems
Analysis the Heterogeneous Multiscale Method Parabolic Homogenization
2012/8/7
The heterogeneous multiscale method (HMM) is applied to various parabolic problems
with multiscale coefficients. These problems can be either linear or nonlinear. Optimal
estimates are proved for th...
Homogenization and asymptotics for small transaction costs
transaction costs, homogenization, viscosity solutions, asymptotic expansions
2012/2/29
We consider the classical Merton problem of lifetime consumption-portfolio optimization problem with small proportional transaction costs. The first order term in the asymptotic expansion is explicitl...
Homogenization and continuum percolation
Homogenization random media continuum percolation
2011/9/22
Abstract: We propose continuum percolation theory to study homogenization problems of elliptic equations.Our aim is to improve and extend similar results that have been obtained for periodic domains u...