## Mathematical Methods for the Magnetohydrodynamics of Liquid Metals

*Jean-Frédéric Gerbeau, Claude Le Bris, and Tony Lelièvre*

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198566656
- eISBN:
- 9780191718014
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566656.001.0001
- Subject:
- Mathematics, Mathematical Physics

This text focuses on mathematical and numerical techniques for the simulation of magnetohydrodynamic phenomena, with an emphasis on the magnetohydrodynamics of liquid metals, on two-fluid flows, and ... More

## Electromagnetic fields

*Mauro Fabrizio and Morro Angelo*

### in Electromagnetism of Continuous Media: Mathematical Modelling and Applications

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198527008
- eISBN:
- 9780191713316
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198527008.003.0001
- Subject:
- Mathematics, Applied Mathematics

This chapter presents the basic notions of electromagnetism, chiefly the balance laws in global and local form. The corresponding Maxwell’s differential equations and boundary conditions are then ... More

## THE MAGNETOHYDRODYNAMICS EQUATIONS

*Jean-Frédéric Gerbeau, Claude Le Bris, and Tony Lelièvre*

### in Mathematical Methods for the Magnetohydrodynamics of Liquid Metals

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198566656
- eISBN:
- 9780191718014
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566656.003.0001
- Subject:
- Mathematics, Mathematical Physics

This chapter presents how MHD equations can be derived from the general conservation equations for fluid mechanics coupled with the Maxwell equations modelling the electromagnetic phenomena. A ... More

## Transport equations

*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/9780199533817.003.0002
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter examines ion transport processes, their description, and the coupling phenomena. It is established that their rate is proportional to the extent of the deviation from the equilibrium, ... More

## The Einstein‐Maxwell Equations, Extremal Kähler Metrics, and Seiberg‐Witten Theory

*Claude LeBrun*

### in The Many Facets of Geometry: A Tribute to Nigel Hitchin

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199534920
- eISBN:
- 9780191716010
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199534920.003.0003
- Subject:
- Mathematics, Geometry / Topology

Nigel Hitchin has played a key role in the exploration of four-dimensional Riemannian geometry, and in particular has made foundational contributions to the theory of self-dual manifolds, ... More

## Review of classical electrodynamics

*Alan Corney*

### in Atomic and Laser Spectroscopy

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199211456
- eISBN:
- 9780191705915
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199211456.003.0002
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter introduces material relevant to the interaction of atoms and radiation. Maxwell's equations and the electromagnetic wave equation are introduced. The electric and magnetic fields ... More

## Physical Aspects and Applications of Hyperbolic Thermoelasticity

*Józef Ignaczak and Martin Ostoja‐Starzewski*

### in Thermoelasticity with Finite Wave Speeds

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199541645
- eISBN:
- 9780191716164
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199541645.003.0012
- Subject:
- Mathematics, Applied Mathematics, Mathematical Physics

This chapter first provides a brief review of several other theories, all classified as generalized thermoelasticity and due to Green and Naghdi. Next follows a justification of the presence of a ... More

## Polarised electromagnetic waves

*S. R Cloude*

### in Polarisation: Applications in Remote Sensing

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199569731
- eISBN:
- 9780191721908
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199569731.003.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Geophysics, Atmospheric and Environmental Physics

This chapter considers a basic description of the generation, propagation and scattering of polarised electromagnetic waves. It assumes a starting familiarity with the basic form of Maxwell's ... More

## MATHEMATICAL ANALYSIS OF ONE-FLUID PROBLEMS

*Jean-Frédéric Gerbeau, Claude Le Bris, and Tony Lelièvre*

### in Mathematical Methods for the Magnetohydrodynamics of Liquid Metals

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198566656
- eISBN:
- 9780191718014
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566656.003.0002
- Subject:
- Mathematics, Mathematical Physics

This chapter focuses on the modelling of one-fluid magnetohydrodynamics problems. The crucial point under consideration is the coupling between hydrodynamics phenomena and electromagnetic phenomena. ... More

## Special Relativity

*Yvonne Choquet-Bruhat*

### in General Relativity and the Einstein Equations

- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199230723
- eISBN:
- 9780191710872
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230723.003.0002
- Subject:
- Mathematics, Applied Mathematics

This chapter begins with a discussion of Newton's mechanics. It then covers Maxwell's equations, Minkowski spacetime, Poincaré group, Lorentz group, special relativity, Newtonian law, relativistic ... More

## X-ray wave-fields in free space

*David M. Paganin*

### in Coherent X-Ray Optics

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198567288
- eISBN:
- 9780191717963
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567288.003.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter considers the theory of classical X-ray wave-fields in free space, taking the Maxwell equations as a starting point. Vacuum wave equations (d’Alembert equations) are developed for X-rays ... More

## Tensors in special relativity

*Ta-Pei Cheng*

### in Relativity, Gravitation and Cosmology: A Basic Introduction

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199573639
- eISBN:
- 9780191722448
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573639.003.0012
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

Tensors in a general coordinate system are introduced. When a tensor is expanded in terms of a set of basis (or inverse basis) vectors, the coefficients of expansion are its contravariant (or ... More

## Taking Charge

*Michael Munowitz*

### in Knowing: The Nature of Physical Law

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780195167375
- eISBN:
- 9780199787104
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195167375.003.0006
- Subject:
- Physics, History of Physics

This chapter considers the other great domain of classical physics, the macroscopic and deterministic world of electric charge. Here, the four Maxwell equations unite electricity with magnetism and ... More

## Theoretical basis

*Leon Mestel*

### in Stellar Magnetism: Second Edition

- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780199641741
- eISBN:
- 9780191738609
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199641741.003.0002
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses the following: Maxwell's equations and the magnetohydrodynamic approximation; properties of cosmical plasmas; macroscopic equations for a fully ionized gas and the two-fluid ... More

## A Kinetic-Theory Description of Fluids

*Luciano Rezzolla and Olindo Zanotti*

### in Relativistic Hydrodynamics

- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780198528906
- eISBN:
- 9780191746505
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528906.003.0002
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter illustrates how the foundations of the fluid description are rooted in statistical mechanics and in kinetic theory. This approach, which is appropriate for those systems composed of a ... More

## Fields—Maxwell’s Equations

*Nicholas Manton and Nicholas Mee*

### in The Physical World: An Inspirational Tour of Fundamental Physics

- Published in print:
- 2017
- Published Online:
- July 2017
- ISBN:
- 9780198795933
- eISBN:
- 9780191837111
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198795933.003.0004
- Subject:
- Physics, Condensed Matter Physics / Materials

Chapter 3 explores the concept of the field, which is necessary to describe forces without resorting to action at a distance, and uses it to describe electromagnetism, as encapsulated by the Maxwell ... More

## The Maxwell Equations and Constitutive Relations

*G. F. Roach, I. G. Stratis, and A. N. Yannacopoulos*

### in Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691142173
- eISBN:
- 9781400842650
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691142173.003.0002
- Subject:
- Mathematics, Applied Mathematics

This chapter first introduces the constitutive relations which are commonly used in electromagnetic theory for the mathematical modelling of complex electromagnetic media. These constitutive ... More

## Properties of the electromagnetic field— propagation and scattering

*ANDRÉ AUTHIER*

### in Dynamical Theory of X-Ray Diffraction

- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198528920
- eISBN:
- 9780191713125
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528920.003.0002
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter gives a theoretical description of the basic properties of electromagnetic radiation. Maxwell's equations are first reviewed; the expressions of electrodynamic potentials in the vacuum ... More

## Elements of Classical Electrodynamics

*John Weiner and Frederico Nunes*

### in Light-Matter Interaction: Physics and Engineering at the Nanoscale, Second Edition

- Published in print:
- 2017
- Published Online:
- March 2017
- ISBN:
- 9780198796664
- eISBN:
- 9780191837920
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198796664.003.0002
- Subject:
- Physics, Atomic, Laser, and Optical Physics, Condensed Matter Physics / Materials

Chapter 2 reacquaints the reader with electric and magnetic force fields and their interactions with ponderable media through Maxwell’s equations and the accompanying Lorentz force law. Macroscopic ... More

## Interaction of light with matter

*J. C. Garrison and R. Y. Chiao*

### in Quantum Optics

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198508861
- eISBN:
- 9780191708640
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508861.003.0005
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter begins with a review of the semi-classical model of the interaction of charged particles with light, and then proceeds to the full quantum theory by replacing the classical fields with ... More