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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


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