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On a hierarchy of models for electrical conduction in biological tissues
Author(s) -
Amar M.,
Andreucci D.,
Bisegna P.,
Gianni R.
Publication year - 2005
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.709
Subject(s) - homogenization (climate) , mathematics , hierarchy , thermal conduction , electrical conductor , electrical conduction , limit (mathematics) , dielectric , mathematical analysis , calculus (dental) , physics , thermodynamics , quantum mechanics , ecology , medicine , biodiversity , dentistry , economics , market economy , biology
In this paper we derive a hierarchy of models for electrical conduction in a biological tissue, which is represented by a periodic array of period ε of conducting phases surrounded by dielectric shells of thickness εη included in a conductive matrix. Such a hierarchy will be obtained from the Maxwell equations by means of a concentration process η → 0, followed by a homogenization limit with respect to ε . These models are then compared with regard to their physical meaning and mathematical issues. Copyright © 2005 John Wiley & Sons, Ltd.