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Transport at electrodes

Kyösti Kontturi, Lasse Murtomäki, and José A. Manzanares

in Ionic Transport Processes: in Electrochemistry and Membrane Science

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199533817
eISBN:
9780191714825
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199533817.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

This chapter is concerned with transport in the vicinity of electrodes, and hence on the coupling between Faradaic electrode processes and mass transport. It covers transport in stationary and ... More


ELECTRONIC TRANSPORT THROUGH QUASI-ONE-DIMENSIONAL DISORDERED SYSTEMS

Pier A. Mello and Narendra Kumar

in Quantum Transport in Mesoscopic Systems: Complexity and Statistical Fluctuations. A Maximum Entropy Viewpoint

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198525820
eISBN:
9780191712234
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525820.003.0007
Subject:
Physics, Condensed Matter Physics / Materials

This chapter treats the problem of finding the probability distribution of quantities related to quantum transport through a strictly one-dimensional (i.e., 1-channel) and through an N-channel ... More


Geographic Range Expansion of Exotic Birds

Tim M. Blackburn, Julie L. Lockwood, and Phillip Cassey

in Avian Invasions: The Ecology and Evolution of Exotic Birds

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199232543
eISBN:
9780191715983
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232543.003.0006
Subject:
Biology, Ornithology, Biodiversity / Conservation Biology

Once an exotic species has successfully established a self-sustaining population, it may spread beyond its initial point of introduction and establish meaningful interactions with species native to ... More


Mobility of Frenkel Excitons

Vladimir M. Agranovich

in Excitations in Organic Solids

Published in print:
2008
Published Online:
January 2009
ISBN:
9780199234417
eISBN:
9780191715426
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199234417.003.0014
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter discusses the different regimes of mobility of Frenkel excitons. The diffusion equation and diffusion-related quantities (diffusion coefficient/length, diffusion constant, exciton mean ... More


Markov processes in continuous time and space

Eric Renshaw

in Stochastic Population Processes: Analysis, Approximations, Simulations

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199575312
eISBN:
9780191728778
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199575312.003.0006
Subject:
Mathematics, Applied Mathematics, Mathematical Biology

Having dealt with processes in discrete space, and discrete and continuous time, this chapter investigates Markov processes in continuous space and time. It follows a natural progression through the ... More


The thermal diffusion equation

Stephen J. Blundell and Katherine M. Blundell

in Concepts in Thermal Physics

Published in print:
2009
Published Online:
January 2010
ISBN:
9780199562091
eISBN:
9780191718236
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199562091.003.0010
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter looks at solving problems involving the thermal conductivity of matter using a technique developed by mathematicians in the late 18th and early 19th centuries. The key equation describes ... More


Master equations and simulation algorithms for the discrete‐stochastic approach

Daniel T. Gillespie and Effrosyni Seitaridou

in Simple Brownian Diffusion: An Introduction to the Standard Theoretical Models

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199664504
eISBN:
9780191748516
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199664504.003.0006
Subject:
Physics, Soft Matter / Biological Physics

The discrete-stochastic model of diffusion introduced in the preceding chapter implies that the system state evolves in time as what is known as a jump Markov process. The time evolution of such a ... More


Kinetics in Spatially Extended Systems

Karsten Kruse and Johan Elf

in System Modeling in Cellular Biology: From Concepts to Nuts and Bolts

Published in print:
2006
Published Online:
August 2013
ISBN:
9780262195485
eISBN:
9780262257060
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262195485.003.0009
Subject:
Mathematics, Mathematical Biology

This chapter presents theoretical approaches for describing the dynamics of biological systems. The first part discusses continuum descriptions in terms of partial differential equations. Such a ... More


Solution of discrete convection–diffusion problems

A. M. Stuart and E. Söli

in Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics

Published in print:
2014
Published Online:
September 2014
ISBN:
9780199678792
eISBN:
9780191780745
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199678792.003.0008
Subject:
Mathematics, Numerical Analysis, Computational Mathematics / Optimization

This chapter concerns iterative methods for solution of discrete convection–diffusion equations. It discusses Krylov subspace methods, principally the generalized minimum residual method, together ... More


The Fickian theory of diffusion

Daniel T. Gillespie and Effrosyni Seitaridou

in Simple Brownian Diffusion: An Introduction to the Standard Theoretical Models

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199664504
eISBN:
9780191748516
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199664504.003.0001
Subject:
Physics, Soft Matter / Biological Physics

The classical macroscopic theory of simple Brownian diffusion focuses on two physical entities: the solute molecular density and the solute molecular flux. This chapter reviews the traditional way in ... More


Fractional diffusion and Fokker‐Planck equations for subdiffusion

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/9780199234868.003.0006
Subject:
Physics, Soft Matter / Biological Physics

This chapter continues the discussion of generalized master equations for CTRW and concentrates on the case of power‐law waiting time distributions lacking the mean. In this case the corresponding ... More


Self-Assembly and Beyond

Troy Shinbrot

in Biomedical Fluid Dynamics: Flow and Form

Published in print:
2019
Published Online:
June 2019
ISBN:
9780198812586
eISBN:
9780191850721
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198812586.003.0013
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Effects of combining reaction with diffusion are examined, and the resulting self-assembly of ordered patterns is overviewed. Turing patterns and limit cycle oscillations are shown to result from ... More


Modeling the Energetic Particles of the Inner Magnetosphere

S. Bourdarie, V. K. Jordanova, M. Liemohn, and T. P. O’Brien

in Waves, Particles, and Storms in Geospace: A Complex Interplay

Published in print:
2016
Published Online:
February 2017
ISBN:
9780198705246
eISBN:
9780191774416
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198705246.003.0006
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

To model the energetic charged particle of the inner magnetosphere, several possibilities are available depending on particle properties (trapped or untrapped). The global modeling of particle ... More


Maximum Principles and Uniqueness Theorems

Charles L. Epstein and Rafe1 Mazzeo

in Degenerate Diffusion Operators Arising in Population Biology (AM-185)

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691157122
eISBN:
9781400846108
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691157122.003.0003
Subject:
Mathematics, Probability / Statistics

This chapter proves maximum principles for two parabolic and elliptic equations from which the uniqueness results follow easily. It also considers the main consequences of the maximum principle, both ... More


Heat flow and thermal relaxation

Andrew M. Steane

in Thermodynamics: A complete undergraduate course

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198788560
eISBN:
9780191830426
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198788560.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The solution of heat flow problems involving the thermal diffusion equation is explained. Conduction through a flat wall and into a sphere is described. A worked example using Fourier analysis is ... More


Lattice Boltzmann for reactive flows

Sauro Succi

in The Lattice Boltzmann Equation: For Complex States of Flowing Matter

Published in print:
2018
Published Online:
June 2018
ISBN:
9780199592357
eISBN:
9780191847967
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199592357.003.0026
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

The dynamics of reactive flows lies at the heart of several important applications, such as combustion, heterogeneous catalysis, pollutant conversion, pattern formation in biology and many others. In ... More


Finite Difference Methods

S. G. Rajeev

in Fluid Mechanics: A Geometrical Point of View

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805021
eISBN:
9780191843136
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805021.003.0014
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

This chapter offers a peek at the vast literature on numerical methods for partial differential equations. The focus is on finite difference methods (FDM): approximating differential operators by ... More


Lévy flights

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/9780199234868.003.0007
Subject:
Physics, Soft Matter / Biological Physics

This chapter returns to simple random walks and considers the case when the mean squared displacement in one step diverges. In the case of step length distributions with power‐law tails the ... More


Self-Organization in Multiplex Networks

Nikos E. Kouvaris and Albert Díaz-Guilera

in Multiplex and Multilevel Networks

Published in print:
2018
Published Online:
December 2018
ISBN:
9780198809456
eISBN:
9780191847073
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198809456.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The chapter “Self-Organization in Multiplex Networks” discusses the use of multiplex networks in studying complex systems and synchronization. An important question in the research of complex systems ... More


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