Geometry and asymptotics in homogenization
We will discuss the methods for asymptotic computation of the effective parameters of a heterogeneous medium. Mostly, the case of strongly inhomogeneous media will be considered. The mathematical description of such media includes also a parameter which is responsible for the difference of the medium properties in distinct points. It will be demonstrated that inserting of this parameter shows clearly how the effective parameter depends on the structural medium geometry. This review relies on the work  and some further investigations.
KeywordsEffective Parameter Inhomogeneous Medium Percolation Theory Morse Function Hexagonal Packing
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- S.M. Kozlov, Geometric aspects of homogenization Russian Math. Surveys 40 (1989), 79–120.Google Scholar
- S.M. Kozlov, The averaging of random structures Docl Akad. Nauk. SSSR, 241(1978), 1016–1019, Matem. Sbornik, 1979, 199–212.Google Scholar
- V.L. Berdicevskii, Variational principle in spatial medium M. “Nauka”, 1983 (In Russian).Google Scholar
- J.M. Newman, Marine Hydrodynamic MIT Press, 1977.Google Scholar
- R.V. Galiulin, Crystallographic geometry M. 1985 (In Russian).Google Scholar
- J.B. Keller, A theorem on the conductivity of a composite medium J. Math. Phys. 5, 548–549.Google Scholar
- L.V. Berlyand, S.M. Kozlov, Asymptotic of effective moduli for elastic chess composite, (in publication).Google Scholar
- R. Blumenfeld, D.J. Bergman, Exact calculation to second order of effective dielectric constant of a strongly nonlinear inhomogeneous composite Physical Review B, 40,1989.Google Scholar
- S.M. Kozlov, Homogenization for disordered systems Thesis, Moscow, 1988.Google Scholar
- S.M. Kozlov, Asymptotics of the Laplace-Dirichlet integrals Funct. Anal. Appl. 40, 1990.Google Scholar
- S.M. Kozlov, Reducability and averaging of quasiperiodic operators Transactions of Moscow Mathematical Society 46,1983.Google Scholar
- S.M. Kozlov, Effective diffusion for Focker-Flank equation Matem. Zametki 45, 1989, 19–31.Google Scholar