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Bounds on the effective conductivity of two-dimensional composites made of n ≧ 3 isotropic phases in prescribed volume fraction: the weighted translation method

Published online by Cambridge University Press:  14 November 2011

V. Nesi
V. Nesi
Affiliation:
Dipartimento di Matematica Pura ed Applicata, Universita' degli Studi de L'Aquila, 67010 L'Aquila, Italy
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Abstract

We establish lower and upper bounds which are valid for the overall conductivity of twodimensional composites. They are based on a method which modifies the so-called translation method in a way which makes it effectively much more flexible. When specialised to composites of n > 2 isotropic phases, the new bounds are often strictly better than all the previously known ones. From the mathematical point of view, the improvement is due mainly to a new regularity result in p.d.e.s [2]. From the physical point of view the latter can be interpreted as a result bounding in a suitable sense the fluctuations of the ‘electric field’.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 6 , 1995 , pp. 1219 - 1239
Copyright
Copyright © Royal Society of Edinburgh 1995

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