Internal Stress Analysis of Homogenized Joints-Homogenized Crack Propagation in Rock (2nd Report)-

Local and Homogenized Equations

Homogenization theory is concerned with finding the appropriate homogenized (or averaged, or macroscopic) governing partial differential equations describing physical processes occurring in heterogeneous materials when the length scale of the heterogeneities tends to zero. In such instances it is desired that the effects of the microstructure reside wholly in the macroscopic or effective proper...

Homogenized Down-up Algebras

This paper studies two homogenizations of the down-up algebras introduced in [1]. We show that in all cases the homogenizing variable is not a zero-divisor, and that when the parameter β is non-zero, the homogenized down-up algebra is a Noetherian domain and a maximal order, and also Artin-Schelter regular, Auslander regular, and Cohen-Macaulay. We show that all homogenized down-up algebras hav...

A Homogenized Cutting Plane Method

An Investigation of Stress Wave Propagation Through Rock Joints and Rock Masses

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Spectral Measure and Approximation of Homogenized Coefficients

Abstract. This article deals with the numerical approximation of effective coefficients in stochastic homogenization of discrete linear elliptic equations. The originality of this work is the use of a well-known abstract spectral representation formula to design and analyze effective and computable approximations of the homogenized coefficients. In particular, we show that information on the ed...