Random resistor network with an exponentially wide distribution of bond conductances.
Random resistor network with an exponentially wide distribution of bond conductances.
复制标题
键电导呈指数分布的随机电阻网络。
DOI：
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发表时间：
1989
期刊：
影响因子：
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通讯作者：
Halperin
中科院分区：
文献类型：
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作者：
Ty;Halperin
We use a percolation analysis to study the conductivity of a random resistor network with bond conductances ${g}_{i}={g}_{0}mathrm{exp}(ensuremath{lambda}{x}_{i})$, where ${x}_{i}$ is a random variable. In the limit $ensuremath{lambda}ensuremath{
ightarrow}ensuremath{infty}$, we may write the network conductivity as $ensuremath{sigma}=C{a}^{2ensuremath{-}d}{g}_{c}{ensuremath{lambda}}^{ensuremath{-}y}$ where $a$ is the lattice constant, $y$ a critical exponent, $C$ a constant, and ${g}_{c}$ the percolation conductance. We derive rigorous bounds to $ensuremath{sigma}$ and we present evidence that supports the hypothesis that $y=0$ for all two-dimensional lattices. Numerical results for a $d=3$ simple-cubic lattice are presented.
We use a percolation analysis to study the conductivity of a random resistor network with bond conductances ${g}_{i}={g}_{0}mathrm{exp}(ensuremath{lambda}{x}_{i})$, where ${x}_{i}$ is a random variable. In the limit $ensuremath{lambda}ensuremath{
ightarrow}ensuremath{infty}$, we may write the network conductivity as $ensuremath{sigma}=C{a}^{2ensuremath{-}d}{g}_{c}{ensuremath{lambda}}^{ensuremath{-}y}$ where $a$ is the lattice constant, $y$ a critical exponent, $C$ a constant, and ${g}_{c}$ the percolation conductance. We derive rigorous bounds to $ensuremath{sigma}$ and we present evidence that supports the hypothesis that $y=0$ for all two-dimensional lattices. Numerical results for a $d=3$ simple-cubic lattice are presented.