Geometry and asymptotics in homogenization

  • S. M. Kozlov
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 5)


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 [1] and some further investigations.


Effective Parameter Inhomogeneous Medium Percolation Theory Morse Function Hexagonal Packing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    S.M. Kozlov, Geometric aspects of homogenization Russian Math. Surveys 40 (1989), 79–120.Google Scholar
  2. [2]
    S.M. Kozlov, The averaging of random structures Docl Akad. Nauk. SSSR, 241(1978), 1016–1019, Matem. Sbornik, 1979, 199–212.Google Scholar
  3. [3]
    V.L. Berdicevskii, Variational principle in spatial medium M. “Nauka”, 1983 (In Russian).Google Scholar
  4. [4]
    J.M. Newman, Marine Hydrodynamic MIT Press, 1977.Google Scholar
  5. [5]
    C.A. Rogers, Packing and Covering Cambridge Univ. Press, 1964.MATHGoogle Scholar
  6. [6]
    R.V. Galiulin, Crystallographic geometry M. 1985 (In Russian).Google Scholar
  7. [7]
    J.B. Keller, A theorem on the conductivity of a composite medium J. Math. Phys. 5, 548–549.Google Scholar
  8. [8]
    S.M. Kozlov, Duality of one type of variational problems Functional Anal. Appl. 17 (1983), 171–175.CrossRefGoogle Scholar
  9. [9]
    L.V. Berlyand, S.M. Kozlov, Asymptotic of effective moduli for elastic chess composite, (in publication).Google Scholar
  10. [10]
    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
  11. [11]
    DJ. Bergman, Elastic moduli near percolation in two dimensional random network of rigid and nonrigid bounds Physical Review B, 33, 1986, 2013–2016.CrossRefGoogle Scholar
  12. [12]
    S.M. Kozlov, Homogenization for disordered systems Thesis, Moscow, 1988.Google Scholar
  13. [13]
    H. Kesten, Percolation theory for mathematicians Birkhäuser Boston Inc., 1982.MATHGoogle Scholar
  14. [14]
    S.M. Kozlov, Asymptotics of the Laplace-Dirichlet integrals Funct. Anal. Appl. 40, 1990.Google Scholar
  15. [15]
    S.M. Kozlov, Reducability and averaging of quasiperiodic operators Transactions of Moscow Mathematical Society 46,1983.Google Scholar
  16. [16]
    S.M. Kozlov, Random walks and averaging in inhomogeneous media Russian Math. Survey 40, 1985, 61–120.MATHGoogle Scholar
  17. [17]
    S.M. Kozlov, Effective diffusion for Focker-Flank equation Matem. Zametki 45, 1989, 19–31.Google Scholar

Copyright information

© Birkhäuser Boston 1991

Authors and Affiliations

  • S. M. Kozlov
    • 1
  1. 1.Moscow Institute of Civil EngineeringMoscowUSSR

Personalised recommendations