A generalized space-time mathematical homogenization theory, which constructs an equivalent continuum description directly from molecular dynamics (MD) equations, is developed. The noteworthy theoretical findings of this work are: (i) the coarse scale continuum equations (PDEs) obtained from the homogenization of MD equations are identical to those obtained from the classical homogenization of ...

We prove the existence of multiscale Young measures associated with almost periodic homogenization. We give applications of this tool in the homogenization of nonlinear partial differential equations with an almost periodic structure, such as scalar conservation laws, nonlinear transport equations, HamiltonJacobi equations and fully nonlinear elliptic equations. Motivated by the application to ...

In this paper, we present a numerical homogenization scheme for indefinite, timeharmonic Maxwell’s equations involving potentially rough (rapidly oscillating) coefficients. The method involves an H(curl)-stable, quasi-local operator, which allows for a correction of coarse finite element functions such that order optimal (w.r.t. the mesh size) error estimates are obtained. To that end, we exten...

Abstract. This paper is a set of lecture notes for a short introductory course on homogenization. It covers the basic tools of periodic homogenization (two-scale asymptotic expansions, the oscillating test function method and two-scale convergence) and briefly describes the main results of the more general theory of G− or H−convergence. Several applications of the method are given: derivation o...

The segregation of Alloy 718 ingots and the technical factors which affect the ingot homogenization practice are studied in this paper. The segregation and melting point of Alloy 7 18 ingots are studied by DTA, electron microprobe and structure analysis. The elimination of Laves phase is studied in detail. After the solution of Iaves phase the segregation elimination of Nb is reviewed further. ...

We are interested in the homogenization of elastic-electric coupling equation, with rapidly oscillating coefficients, in periodically perforated piezoelectric body. We justify the two first terms in the usual asymptotic development of the problem solution. For the main convergence results of this paper, we use the notion of two-scale convergence. A two-scale homogenized system is obtained as th...

The frequency dependence of the effective permittivities of simple dielectric composites is evaluated by different quasidynamic homogenization methods. Three retrieval approaches based on the scattering parameters are proposed for dielectric materials. A compensation method for the conventional Nicolson-Ross-Weir (NRW) retrieval is applied to eliminate the FabryPérot (FP) resonances and their d...

We compared nucleotide sequences of the transcription-initiation region of five mouse ribosomal DNA (rDNA) clones. Two clones were isolated from Japanese wild mice, Mus musculus molossinus, and the other three from BALB/c mice originating in M. m. domesticus. Two BALB/c clones that are derived from the same chromosome are very similar, suggesting the occurrence of intrachromosomal homogenizatio...

A networked environment suffers from unpredictable speedup behavior during distributed processing due to heterogeneous nature of the hardware and software in the remote machines. It is challenging to get better performance from a distributed system by distributing task in an intelligent manner such that the heterogeneous nature of the system do not have any effect on the speedup ratio. This pap...

Abstract. 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 homogenization problems of practical importance. The main idea of the proposed approach is to introduce a novel object called the homogenization map, approximate it through adaptive interpolation, and...