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The factorization method for Maxwell's equations

Andreas Kirsch and Natalia Grinberg

in The Factorization Method for Inverse Problems

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199213535
eISBN:
9780191707629
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213535.003.0005
Subject:
Mathematics, Applied Mathematics

This chapter examines the time-harmonic Maxwell's equations for isotropic and non-magnetic but possibly inhomogeneous media. It begins by formulating the direct scattering problem for arbitrary ... More


Weighting, scaling, and missing values

J. C. Gower and G. B. Dijksterhuis

in Procrustes Problems

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198510581
eISBN:
9780191708961
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198510581.003.0008
Subject:
Mathematics, Probability / Statistics

This chapter introduces the different forms of weighting. One form of weighting is when the rows of X1 are weighted. It is also possible to weight the columns. In these cases the ... More


Domain of Influence Theorems

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/9780199541645.003.0004
Subject:
Mathematics, Applied Mathematics, Mathematical Physics

The first part of this chapter concerns a domain of influence theorem for a potential‐temperature problem, which is a particular form of a displacement‐temperature problem in the L‐S theory. The ... More


Dielectric Tensor of Superlattices

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/9780199234417.003.0008
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter presents calculations of dielectric tensor of superlattices. In consideration of superlattices having large periods compared to lattice constants, equations of macroscopical ... More


REPRINT THE STATISTICAL DYNAMICS OF HOMOGENEOUS TURBULENCE

S. F. Edwards

in Stealing the Gold: A celebration of the pioneering physics of Sam Edwards

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198528531
eISBN:
9780191713415
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528531.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter presents a paper which examines the problem of steady homogeneous isotropic turbulence under idealized conditions, allowing the for the exact form of the correlation functions to be ... More


STRUCTURE OF CRYSTALLINE SOLIDS AND THE “DEFECT STATE”

A. S. Argon

in Strengthening Mechanisms in Crystal Plasticity

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198516002
eISBN:
9780191705717
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198516002.003.0001
Subject:
Physics, Crystallography

What governs the state of order of a solid depends primarily on the type of atomic bonding and on the processing path. The interest in this book is almost entirely in solids in the crystalline state ... More


MATERIAL DEFORMATION

Nasr M. Ghoniem and Daniel D. Walgraef

in Instabilities and Self-Organization in Materials: Volume I: Fundamentals of Nanoscience, Volume II: Applications in Materials Design and Nanotechnology

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199298686
eISBN:
9780191720222
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199298686.003.0002
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses the main elements of continuum theory, which will be utilized further in later sections dealing with a variety of applications. First, a basic review of vector and tensor ... More


ELECTRON SPIN RESONANCE

A.M. Stoneham

in Theory of Defects in Solids: Electronic Structure of Defects in Insulators and Semiconductors

Published in print:
2001
Published Online:
September 2007
ISBN:
9780198507802
eISBN:
9780191709920
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507802.003.0013
Subject:
Physics, Condensed Matter Physics / Materials

Spin resonance is one of the major tools in the study of defect and impurity systems. This chapter describes how the key parameters of the spin Hamiltonian can be predicted, including a detailed ... More


Classification of Pseudo-reductive Groups (AM-191)

Brian Conrad and Gopal Prasad

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691167923
eISBN:
9781400874026
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691167923.001.0001
Subject:
Mathematics, Numerical Analysis

This book goes further than the exploration of the general structure of pseudo-reductive groups to study the classification over an arbitrary field. An Isomorphism Theorem proved here determines the ... More


The homogeneous and isotropic universe

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/9780199573639.003.0009
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

The universe, when observed on distance scales ≳100 Mpc, is homogeneous and isotropic. Hubble's discovery that the universe is expanding suggests strongly that it had a beginning. The estimate of the ... More


The Isotropic Micellar And Bicontinuous Phases

Antônio M. Figueiredo Neto and Silvio R. A. Salinas

in The Physics of Lyotropic Liquid Crystals: Phase Transitions and Structural Properties

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198525509
eISBN:
9780191711756
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525509.003.0005
Subject:
Physics, Crystallography

A variety of structures of self-assembled molecules are present in the polymorphism of lyotropics. This chapter describes the structure and properties of micellar isotropic phases and bicontinuous ... More


Semi-ramified Quadrangles of Type E6, E7 and E8

Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss

in Descent in Buildings (AM-190)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691166902
eISBN:
9781400874019
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691166902.003.0012
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter deals with the case that the building at infinity of the Bruhat-Tits building Ξ‎ is a Moufang semi-ramified quadrangle of type E⁶, E₇ and E₈. The basic proposition is that Ξ‎ is a ... More


A little elementary acoustics

G. A. D. Briggs and O. V. Kolosov

in Acoustic Microscopy: Second Edition

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199232734
eISBN:
9780191716355
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232734.003.0006
Subject:
Physics, Condensed Matter Physics / Materials

Solids support both longitudinal and shear acoustic waves; fluids support only longitudinal waves, with attenuation proportional to the viscosity and to the square of the frequency. The longitudinal ... More


Fiber symmetry

David J. Steigmann

in Finite Elasticity Theory

Published in print:
2017
Published Online:
December 2017
ISBN:
9780198567783
eISBN:
9780191746536
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198567783.003.0005
Subject:
Mathematics, Applied Mathematics

This chapter develops the general constitutive equation for transversely isotropic, fiber-reinforced materials. Applications include composite materials and bio-elasticity.


Homogeneous, Isotropic Turbulence: Phenomenology, Renormalization and Statistical Closures

W. David McComb

Published in print:
2014
Published Online:
April 2014
ISBN:
9780199689385
eISBN:
9780191768255
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199689385.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The aim of this book is to elucidate, and help resolve, some of the outstanding issues in fundamental turbulence theory. Accordingly, it is restricted to homogeneous, isotropic turbulence (HIT). It ... More


Brain Soup

Suzana Herculano-Houzel

in The Human Advantage: A New Understanding of How Our Brain Became Remarkable

Published in print:
2016
Published Online:
September 2016
ISBN:
9780262034258
eISBN:
9780262333214
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262034258.003.0002
Subject:
Neuroscience, Behavioral Neuroscience

Why two brains of similar size probably don’t have similar numbers of neurons; 100 billion neurons in the human brain as an order-of-magnitude estimate; how to count cells in a brain; how to turn ... More


Criteria ensuring global existence

Hans Ringström

in On the Topology and Future Stability of the Universe

Published in print:
2013
Published Online:
September 2013
ISBN:
9780199680290
eISBN:
9780191760235
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199680290.003.0026
Subject:
Mathematics, Mathematical Physics, Geometry / Topology

In Chapter 26, we formulate criteria ensuring future global existence of solutions (in the spatially homogeneous setting). Moreover, we provide some rough conclusions concerning the asymptotics. ... More


Isotropic Baselines

Richard M. Christensen

in The Theory of Materials Failure

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199662111
eISBN:
9780191748387
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199662111.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

In considering the failure of isotropic materials, a general theory of failure must involve a minimal number of properties that then apply across all major types of materials from ductile metals to ... More


The Ductile/Brittle Transition for Isotropic Materials

Richard M. Christensen

in The Theory of Materials Failure

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199662111
eISBN:
9780191748387
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199662111.003.0008
Subject:
Physics, Condensed Matter Physics / Materials

There are few discipline areas that have been and are as challenging as that of predicting ductile versus brittle failure conditions. First, the traditional but inadequate means of characterizing ... More


Anisotropic Fiber Composite Laminates Failure

Richard M. Christensen

in The Theory of Materials Failure

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199662111
eISBN:
9780191748387
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199662111.003.0012
Subject:
Physics, Condensed Matter Physics / Materials

Fiber composite laminates pose an even higher degree of complexity than does the aligned fiber composite lamina of Chapter 11. First, the matter of scale must be considered. At what scale should the ... More


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