## 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