VARIATIONAL TREATMENT OF AN ABSORPTION PROBLEM IN RANDOM HETEROGENEOUS MEDIA


MARKOV K., KOLEV M.

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, cilt.32, sa.12, ss.1859-1875, 1994 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 32 Konu: 12
  • Basım Tarihi: 1994
  • Doi Numarası: 10.1016/0020-7225(94)90083-3
  • Dergi Adı: INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
  • Sayfa Sayıları: ss.1859-1875

Özet

The paper is devoted to the steady-state problem of absorption of a diffusing species in a random heterogenous medium. The variational principles of classic type, using ensemble averaging, are first discussed and then used for derivation of variational estimates on the effective absorption coefficient (sink strength) of the medium. The estimates are three-point, i.e. they employ statistical information, contained in the l-point correlation functions for the medium up to l = 3, and could be viewed as counterparts of the well-known Beran's bounds in the scalar conductivity problem. Moreover, the bounds are third-order in the weakly-inhomogeneous case. Explicit results are obtained for Miller's cellular media which indicate that the bounds remain useful even when the absorption capabilities of the constituents differ 100 times.