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Percolation and epidemics

Sergey N. Dorogovtsev

in Lectures on Complex Networks

Published in print:
2010
Published Online:
May 2010
ISBN:
9780199548927
eISBN:
9780191720574
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199548927.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter considers the organization of connected components in uncorrelated networks, in particular, the structure and size of a giant connected component. These properties are closely related to ... More


Fractured Porous Media

Pierre M. Adler, Jean-François Thovert, and Valeri V. Mourzenko

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199666515
eISBN:
9780191748639
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199666515.001.0001
Subject:
Physics, Condensed Matter Physics / Materials

This book aims to estimate the macroscopic properties of fractures, fracture networks and fractured porous media from easily measurable quantities. Attention is focused on geological media where ... More


Optimization

Sergey N. Dorogovtsev

in Lectures on Complex Networks

Published in print:
2010
Published Online:
May 2010
ISBN:
9780199548927
eISBN:
9780191720574
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199548927.003.0014
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter demonstrates how a universal requirement for optimality leads to the complex structural organization of a network. It discusses a long-lasting criticism of the preferential concept and ... More


Percolation and network resilience

Mark Newman

in Networks

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805090
eISBN:
9780191843235
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805090.003.0015
Subject:
Physics, Theoretical, Computational, and Statistical Physics

A discussion of the site percolation process on networks and its application as a model of network resilience. The chapter starts with a description of the percolation process, in which nodes are ... More


ELECTRON MOBILITY IN DENSE HE GAS

A.F. Borghesani

in Ions and electrons in liquid helium

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199213603
eISBN:
9780191707421
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213603.003.0027
Subject:
Physics, Condensed Matter Physics / Materials

Experiments on the mobility of electrons in dense helium gas elucidated how localized electron states develop when the gas density gas is increased. Up to 77 K, the density dependence of the mobility ... More


First Steps in Random Walks: From Tools to Applications

J. Klafter and I. M. Sokolov

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199234868
eISBN:
9780191775024
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199234868.001.0001
Subject:
Physics, Soft Matter / Biological Physics

The name “random walk” for a problem of a displacement of a point in a sequence of independent random steps was coined by Karl Pearson in 1905 in a question posed to readers of “Nature”. The same ... More


HOPPING CONDUCTIVITY

V.F. Gantmakher

in Electrons and Disorder in Solids

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198567561
eISBN:
9780191718267
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567561.003.0004
Subject:
Physics, Condensed Matter Physics / Materials

This chapter is dedicated to electron transitions between localized states. After a description of the states with the help of localization radius and the general expression for the transition ... More


Percolation and network resilience: A discussion of one of the simplest of processes taking place on networks, percolation, and its use as a model of network resilience

M. E. J. Newman

in Networks: An Introduction

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199206650
eISBN:
9780191594175
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199206650.003.0016
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter examines one of the simplest network processes, which is percolation. This leads to an elegant theory concerning the robustness of networked systems to the failure of their components. ... More


Random systems

Hidetoshi Nishimori and Gerardo Ortiz

in Elements of Phase Transitions and Critical Phenomena

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577224
eISBN:
9780191722943
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577224.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Real materials always contain randomness or disorder that cannot be expressed by idealized simple model systems. The present chapter studies the effects of randomness on phase transitions and ... More


Classical Percolation, Generalized Percolation and Cascades

Ginestra Bianconi

in Multilayer Networks: Structure and Function

Published in print:
2018
Published Online:
July 2018
ISBN:
9780198753919
eISBN:
9780191815676
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198753919.003.0012
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter characterizes the robustness of multiplex and multilayer networks using classical percolation, directed percolation and antagonistic percolation. Classical percolation determines whether ... More


Epidemics on networks

Mark Newman

in Networks

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805090
eISBN:
9780191843235
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805090.003.0016
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the spread of diseases over contact networks between individuals and the methods used to model this process. The chapter begins with an introduction to the classic models of ... More


The geometry of fracture networks

Pierre M. Adler, Jean-François Thovert, and Valeri V. Mourzenko

in Fractured Porous Media

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199666515
eISBN:
9780191748639
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199666515.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

This chapter deals with the geometry of random networks. The fractures are generally considered as plane objects such as polygons. The most important question relative to these networks is whether ... More


Elementary Theory of the Interaction of Electromagnetic Fields with Dielectric Materials

Yuri Feldman, Paul Ben Ishai, Alexander Puzenko, and Valerică Raicu

in Dielectric Relaxation in Biological Systems: Physical Principles, Methods, and Applications

Published in print:
2015
Published Online:
August 2015
ISBN:
9780199686513
eISBN:
9780191766398
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199686513.003.0002
Subject:
Physics, Soft Matter / Biological Physics

This chapter presents a brief introduction to the modern theory of dielectrics. The different polarization mechanisms in static and time-dependent fields are discussed and the complex dielectric ... More


Random walks on percolation structures

J. Klafter and I.M. Sokolov

in First Steps in Random Walks: From Tools to Applications

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199234868
eISBN:
9780191775024
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199234868.003.0010
Subject:
Physics, Soft Matter / Biological Physics

In this chapter another, experimentally widespread, situation is considered. The random walk takes place not on a homogeneous lattice, where each site in principle accessible to the walker, but on a ... More


Manganites

Vladimir Z. Kresin, Hans Morawitz, and Stuart A. Wolf

in Superconducting State: Mechanisms and Properties

Published in print:
2013
Published Online:
January 2014
ISBN:
9780199652556
eISBN:
9780191767784
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199652556.003.0012
Subject:
Physics, Condensed Matter Physics / Materials

There is a large similarity between two families of the mixed-valence compounds, cuprates and manganites. Manganites display the colossal magnetoresistance phenomenon (CMR). A transition to the ... More


Basic agent models

František Slanina

in Essentials of Econophysics Modelling

Published in print:
2013
Published Online:
January 2014
ISBN:
9780199299683
eISBN:
9780191747038
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199299683.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In this chapter it is shown how economic phenomena emerge from the behaviour of individual agents. The first paradigmatic model is based on the concept of self-organised criticality. The second, ... More


Percolation and universality

Joseph F. Boudreau and Eric S. Swanson

in Applied Computational Physics

Published in print:
2017
Published Online:
February 2018
ISBN:
9780198708636
eISBN:
9780191858598
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198708636.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Percolation deals with global properties of random configurations of local objects. While simple to implement in models, understanding percolation requires skill in pattern recognition and analysis. ... More


Random graphs

Mark Newman

in Networks

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805090
eISBN:
9780191843235
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805090.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

An introduction to the mathematics of the Poisson random graph, the simplest model of a random network. The chapter starts with a definition of the model, followed by derivations of basic properties ... More


Network Dynamics

David D. Nolte

in Introduction to Modern Dynamics: Chaos, Networks, Space, and Time

Published in print:
2019
Published Online:
November 2019
ISBN:
9780198844624
eISBN:
9780191880216
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198844624.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

A language of nodes and links, degree and moments, and adjacency matrix and distance matrix, among others, is defined and used to capture the wide range of different types and properties of network ... More


The Dynamics on Single Networks

Ginestra Bianconi

in Multilayer Networks: Structure and Function

Published in print:
2018
Published Online:
July 2018
ISBN:
9780198753919
eISBN:
9780191815676
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198753919.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter provides the relevant background on the network dynamics of complex networks formed by just one layer (single networks). Emergent properties of network dynamics are characterized using ... More


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