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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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