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Introduction to percolation theory
Dietrich Stauffer,Amnon Aharony +1 more
- 01 Jan 1992
7.4K
TL;DR: In this article, a scaling solution for the Bethe lattice is proposed for cluster numbers and a scaling assumption for cluster number scaling assumptions for cluster radius and fractal dimension is proposed.
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Abstract: Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion in disordered media Coming attractions Further reading Cluster Numbers The truth about percolation Exact solution in one dimension Small clusters and animals in d dimensions Exact solution for the Bethe lattice Towards a scaling solution for cluster numbers Scaling assumptions for cluster numbers Numerical tests Cluster numbers away from Pc Further reading Cluster Structure Is the cluster perimeter a real perimeter? Cluster radius and fractal dimension Another view on scaling The infinite cluster at the threshold Further reading Finite-size Scaling and the Renormalization Group Finite-size scaling Small cell renormalization Scaling revisited Large cell and Monte Carlo renormalization Connection to geometry Further reading Conductivity and Related Properties Conductivity of random resistor networks Internal structure of the infinite cluster Multitude of fractal dimensions on the incipient infinite cluster Multifractals Fractal models Renormalization group for internal cluster structure Continuum percolation, Swiss-cheese models and broad distributions Elastic networks Further reading Walks, Dynamics and Quantum Effects Ants in the labyrinth Probability distributions Fractons and superlocalization Hulls and external accessible perimeters Diffusion fronts Invasion percolation Further reading Application to Thermal Phase Transitions Statistical physics and the Ising model Dilute magnets at low temperatures History of droplet descriptions for fluids Droplet definition for the Ising model in zero field The trouble with Kertesz Applications Dilute magnets at finite temperatures Spin glasses Further reading Summary Numerical Techniques
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Citations
Simulating temporal evolution of pressure in two-phase flow in porous media
TL;DR: In this article, the authors simulated the temporal evolution of pressure due to capillary and viscous forces in two-phase drainage in porous media and investigated the effect of trapped clusters on the pressure evolution and on the effective permeability of the system.
80
Hybrid phase transition into an absorbing state: Percolation and avalanches.
TL;DR: It is shown that the hybrid percolation transition exhibits two kinds of critical behaviors: divergence of the fluctuations of the order parameter and power-law size distribution of finite avalanches at a transition point.
79
Thermal-induced percolation in high-density polyethylene/carbon black composites
TL;DR: In this paper, a first order kinetics aggregation model was introduced into the classical percolation theory to account for the dynamic percolations of carbon black in high-density polyethylene melt.
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Efficient and stable plastic dye-sensitized solar cells based on a high light-harvesting ruthenium sensitizer
Kun-Mu Lee,Shi Jhang Wu,Chia Yuan Chen,Chun Guey Wu,Masashi Ikegami,Kozo Miyoshi,Tsutomu Miyasaka,Kuo-Chuan Ho +7 more
TL;DR: In this paper, a high light harvesting ability heteroleptic ruthenium complex dye, SJW-E1, was examined as a sensitizer for the plastic dye-sensitized solar cells (DSSCs) constructed by a low-temperature electrode preparation method using binder-free TiO2 paste and an ITO-PEN substrate.
79
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Leak-rate of seals: effective medium theory and comparison with experiment
B. Lorenz,Bo N. J. Persson +1 more
TL;DR: In this paper, the authors present an effective medium theory of the leak-rate of rubber seals, which is based on a recently developed contact mechanics theory and compare the theory with experimental results for seals consisting of silicon rubber in contact with sandpaper and sand-blasted PMMA surfaces.
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