Higher Order Macro Coefficients in Periodic Homogenization

Higher Order Correlation coefficients

Exponential Homogenization of Linear Second Order Elliptic PDEs with Periodic Coefficients

A problem of homogenization of a divergence-type second order uniformly elliptic operator is considered with arbitrary bounded rapidly oscillating periodic coefficients, either with periodic “outer” boundary conditions or in the whole space. It is proved that if the right-hand side is Gevrey regular (in particular, analytic), then by optimally truncating the full two-scale asymptotic expansion ...

Error estimates for periodic homogenization with non-smooth coefficients

In this paper we present new results regarding the H1 0 -norm error estimate for the classical problem in homogenization using suitable boundary layer correctors. Compared with all the existing results on the subject, which assume either smooth enough coefficients or smooth data, we use the periodic unfolding method and propose a new asymptotic series to approximate the solution uε with an erro...

Auxiliary Sdes for Homogenization of Quasilinear Pdes with Periodic Coefficients

We study the homogenization property of systems of quasi-linear PDEs of parabolic type with periodic coefficients, highly oscillating drift and highly oscillating nonlinear term. To this end, we propose a probabilistic approach based on the theory of forward–backward stochastic differential equations and introduce the new concept of " auxiliary SDEs. " 1. Introduction and assumptions.

Higher-order virial coefficients of water models.

We use the Mayer sampling method, with both direct and overlap sampling, to calculate and compare classical virial coefficients up to B6 for various water models (SPC, SPC/E, MSPC/E, TIP3P, and TIP4P). The precision of the computed values ranges from 0.1% for B2 to an average of 25% for B6. When expressed in a form scaled by the critical properties, the values of the coefficients for SPC water ...