On multi-scale percolation behaviour of the effective conductivity for the lattice model with interacting particles
| Autor: | R. Piasecki, D. Frączek, W. Olchawa, R. Wiśniowski |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Statistics and Probability
Physics Percolation critical exponents Condensed matter physics Statistical Mechanics (cond-mat.stat-mech) business.industry FOS: Physical sciences Percolation threshold Conductivity Condensed Matter Physics 01 natural sciences Directed percolation 010305 fluids & plasmas Lattice (order) 0103 physical sciences Microemulsion Fixed length 010306 general physics business Thermal energy Condensed Matter - Statistical Mechanics |
| DOI: | 10.48550/arxiv.1506.05156 |
| Popis: | Recently, the effective medium approach using 2x2 basic cluster of model lattice sites to predict the conductivity of interacting droplets has been presented by Hattori et al. To make a step aside from pure applications, we have studied earlier a multi-scale percolation, employing any kxk basic cluster for non-interacting particles. Here, with interactions included, we examine in what way they alter the percolation threshold for any cluster case. We found that at a fixed length scale k the interaction reduces the range of shifts of the percolation threshold. To determine the critical concentrations, the simplified model is used. It diminishes the number of local conductivities into two main ones. In the presence of a dominance of the repulsive interaction over the thermal energy, the exact percolation thresholds at scales k=2 and 3 can be obtained from analytical formulas. Furthermore, by a simple reasoning, we obtain the limiting threshold formula for odd k. When k>>1, the odd-even difference becomes negligible. Hence, the 0.75 is the highest possible value of the threshold. 13 pages with 6 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|