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 e of conducting phases surrounded by dielectric shells of thickness epsilon eta included in a conductive matrix. Such a hierarchy will be obtained from the Maxwell equations by means of a concentration process eta-->0, followed by a homogenization limit with respect to epsilon. These models are then compared with regard to their physical meaning and mathematical issues.
Amar, M., Andreucci, D., Bisegna, P., Gianni, R. (2006). On a hierarchy of models for electrical conduction in biological tissues. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 29(7), 767-787 [10.1002/mma.709].
On a hierarchy of models for electrical conduction in biological tissues
BISEGNA, PAOLO;
2006-01-01
Abstract
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 e of conducting phases surrounded by dielectric shells of thickness epsilon eta included in a conductive matrix. Such a hierarchy will be obtained from the Maxwell equations by means of a concentration process eta-->0, followed by a homogenization limit with respect to epsilon. These models are then compared with regard to their physical meaning and mathematical issues.| File | Dimensione | Formato | |
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