Search query: Applications Of Percolation Theory

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abstract: Connectivity as the Essential Physics of Disordered Systems Elements of Percolation Theory Characterization of Porous Media Earthquakes, and Fracture and Fault in Patterns in Heterogeneous Rock Single Phase Flow in Reservoir Rock Hydrodynamic Dispersion and Groundwater Flow in Rock Two Phase Flow in Porous Media Transport, Reaction, and Deposition in Evolving Porous Media Fractal Diffusion and Reaction Kinetics Vibrations and Density of States of Disordered Materials Structural, Mechanical, and Rheological Properties of Branched Polymers and Gels Morphological and Transport Properties of Composite Media Hopping Conductivity of Semiconductors Percolation in Biological Systems.
author_names: Mtabazi G Sahini

Muhammad Sahimi
title: Applications of percolation theory
year: 1994

abstract: Critical path analysis and percolation theory are known to predict accurately dc and low frequency ac electrical conductivity in strongly heterogeneous solids, and have some applications in statistics. Much of this work is dedicated to review the current state of these theories. Application to heterogeneous porous media has been slower, though the concept of percolation was invented in that context. The definition of the critical path is that path which traverses an infinitely large system, with no breaks, which has the lowest possible value of the largest resistance on the path. This resistance is called the rate limiting, or critical, element, Rc. Mathematical schemes are known for calculating Rc in many cases, but this application is not the focus here. The condition under which critical path analysis and percolation theory are superior to other theories is when heterogeneities are so strong, that transport is largely controlled by a few rate limiting transitions, and the entire potential field governing the transport is influenced by these individual processes. This is the limit of heterogeneous, deterministic transport, characterized by reproducibility (repeatability) This work goes on to show the issues in which progress with this theoretical approach has been slow (in particular, the relationship between a critical rate, or conductance, and the characteristic conductivity) and what progress is being made towards solving them. It describes applications to saturated and unsaturated flows, some of which are new. The state of knowledge regarding application of cluster statistics of percolation theory to find spatial variability and correlations in the hydraulic conductivity is summarized. Relationships between electrical and hydraulic conductivities are explored. Here, as for the relationship between saturated and unsaturated flows, the approach described includes new applications of existing concepts. The specific case of power law distributions of pore sizes, a kind of 'random' fractal soil is discussed (critical path analysis would not be preferred for calculating the hydraulic conductivity of a regular fractal) " 2001 Elsevier Science Ltd. All rights reserved.
author_names: Allen G Hunt
title: Applications of percolation theory to porous media with distributed local conductances
year: 2001

abstract: There is increasing interest in the use of the percolation paradigm to analyse and predict the progress of disease spreading in spatially structured populations of animals and plants. The wider utility of the approach has been limited, however, by several restrictive assumptions, foremost of which is a strict requirement for simple nearest neighbour transmission, in which the disease history of an individual is influenced only by that of its neighbours. In a recent paper, the percolation paradigm has been generalized to incorporate synergistic interactions in host infectivity and susceptibility, and the impact of these interactions on the invasive dynamics of an epidemic has been demonstrated. In the current paper, we elicit evidence that such synergistic interactions may underlie transmission dynamics in real world systems by first formulating a model for the spread of a ubiquitous parasitic and saprotrophic fungus through replicated populations of nutrient sites and subsequently fitting and testing the model using data from experimental microcosms. Using Bayesian computational methods for model fitting, we demonstrate that synergistic interactions are necessary to explain the dynamics observed in the replicate experiments. The broader implications of this work in identifying disease control strategies that deflect epidemics from invasive to non invasive regimes are discussed.
author_names: Jonathan J Ludlam

Gavin J Gibson

Wilfred Otten

Christopher A Gilligan
title: Applications of percolation theory to fungal spread with synergy
venue: Journal of The Royal Society Interface
year: 2011

author_names: Gary A Talbot
title: Applications of Percolation Theory
year: 1995

abstract: The review is a brief description of the state of problems in percolation theory and their numerous applications, which are analyzed on base of interesting papers published in the last 15 20 years. At the submitted papers are studied both the cluster system of the physical body and its impact on the object in general, and adequate mathematical tools for description of critical phenomena too. Of special interest are the data, first, the point of phase transition of certain of percolation system is not really a point, but it is a critical interval, and second, in vicinity of percolation threshold observed many different infinite clusters instead of one infinite cluster that appears in traditional consideration.
author_names: Alexander Herega
title: Some Applications of the Percolation Theory. Brief Review of the Century Beginning
year: 2015

abstract: During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous transitions, the percolation transitions occurring in complex systems are often of different types such as discontinuous, hybrid, and infinite order phase transitions. Thus, percolation has received considerable attention in network science community. Here we present a very brief review of percolation theory recently developed, which includes those types of phase transitions, critical phenomena, and finite size scaling theory. Moreover, we discuss potential applications of theoretical results and several open questions including universal behaviors.
author_names: Deokjae Lee

Byungnam Kahng

Y S Cho

Kwang-Il Goh

D -S Lee
title: Recent Advances of Percolation Theory in Complex Networks
year: 2018

abstract: In the experimental work presented here, fire spread was studied through various laboratory and full scale models containing different types of combustible and noncombustible materials. We have exa.
author_names: J Nahmias

Herve Tephany

Jose A M S Duarte

Sophie Letaconnoux
title: Fire spreading experiments on heterogeneous fuel beds. Applications of percolation theory
year: 2000

abstract: The application of percolation theory concepts to modelling of a single particle char gasification has been summarized. Emphasis has been placed on the interpretation and evaluation of transport and fragmentation properties of the changing pore structure during gasification. The qualitative behavior of the model in both the kinetically and the diffusionally controlled regimes clearly reflect the strong influence of structural properties on gasification. Furthermore, the good agreement between these model predictions and reported experimental observations are encouraging for further use of percolation theory in modelling changing coal structures. 25 references, 7 figures, 2 tables.
author_names: Sebastian C Reyes

Klavs F Jensen
title: Applications of percolation theory to the analysis of coal gasification
year: 1985

abstract: Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied to describe a large variety of natural, technological and social systems. Percolation models serve as important universality classes in critical phenomena characterized by a set of critical exponents which correspond to a rich fractal and scaling structure of their geometric features. In this review we will first outline the basic features of the ordinary model and take a glimpse at a number of selective variations and modifications of the original model. Directed percolation process will be also discussed as a prototype of systems displaying a nonequilibrium phase transition. After a short review on SLE, we will provide an overview on existence of the scaling limit and conformal invariance of the critical percolation. We will also establish a connection with the magnetic models. Recent applications of the percolation theory in natural and artificial landscapes are also reviewed.
author_names: Abbas Ali Saberi
title: Recent advances in percolation theory and its applications
year: 2015

author_names: Tamaz L Chelidze
title: Applications of percolation theory: By M. Sahimi. Taylor Francis, London, 1994, hardcover, 258 pp. PS40.00. (ISBN 0 7484 0075 3)
year: 1995