Exact relations between critical exponents for elastic stiffness and electrical conductivity of percolating networks
✍ Scribed by David J. Bergman
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 191 KB
- Volume
- 338
- Category
- Article
- ISSN
- 0921-4526
No coin nor oath required. For personal study only.
✦ Synopsis
Arguments are presented to demonstrate that exact equality relations exist between the critical exponents which characterize the macroscopic conductivity s e and the macroscopic elastic stiffness moduli C e of percolating systems in two or three dimensions. Using the notation s e pDp t ; C e pDp T for the critical behavior of a randomly diluted system slightly above the percolation threshold p c (Dp p À p c > 0), and s e pjDpj Às ; C e pjDpj ÀS for the critical behavior of a random mixture of normal and perfectly conducting or normal and perfectly rigid constituents slightly below that threshold (Dp p À p c o0), I show that T ¼ t þ 2n and S ¼ s; where n is the percolation correlation length critical exponent xpjDpj Àn (Dp_0).