{'fraction_non_alphanumeric': 0.015927189988623434, 'fraction_numerical': 0.0, 'mean_word_length': 5.285714285714286, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Conductivity and diffusion near the percolation threshold

We consider the scaling properties of the conductivity for non-zero frequencies. We analyse the relevance of various models to descriptions of actual experimental situations. We discuss more particularly the equivalence between conduction and diffusion. In this case, we find a regime where the conductivity is proportional to the size L of the sample, corresponding to an anomalous skin effect. This L dependence leads to a frequency-dependent conductivity different from the result of Gefen, Aharony and Alexander. We finally introduce a model consisting of a two-dimensional random resistor system lying on a three-dimensional substrate made of capacitors. This might be relevant to describe a system of conducting particles deposited on a thin insulating substrate such as considered recently by Laibowitz and Gefen.