Space-filling constraint on transport in random aggregates
Space-filling constraint on transport in random aggregates
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DOI：
10.1103/physrevb.30.4093
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发表时间：
1984-10
影响因子：
3.7
通讯作者：
T. Witten;Y. Kantor
中科院分区：
文献类型：
--
作者：
T. Witten;Y. Kantor
输运性质，如电导率的标度不变的结构，如随机聚集体是由一个光谱维数指数d。我们调查的行为的分支结构，没有环路，使用几何约束的载流骨干。结构适合d维空间的要求对d维施加了新的约束。主链的分支之间的距离Δ必须是沿着沿着测量的跨度N的数量级。在温和的标度假设下，该距离Δ控制电导。我们用分形维数D和将N与几何尺寸L（N <$L δ）联系起来的标度幂δ来表示d：δ= D（2 d − 1）。这意味着对于D< 2的这种支化结构，d < 4 3。
Transport properties such as conductivity on scale-invariant structures such as random aggregates are governed by a spectral dimension exponent d ̃. We investigate the behavior of d ̃ for branched structures without loops using geometric constraints on their current-carrying backbone. The requirement that the structure fit into d-dimensional space imposes a new constraint on d ̃. The distance Δ between branches of the backbone must be of the order of the span N measured along the backbone. Under mild scaling assumptions this distance Δ controls the conductance. We express d ̃ in terms of the fractal dimension D and the scaling power δ relating N to the geometric size L (N∼ L δ): δ= D (2 d ̃− 1). This implies that d ̃< 4 3 for such branched structures with D< 2.