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Asymptotic Relaxation Laws

Wolfgang Götze

in Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory

Published in print:
2008
Published Online:
May 2009
ISBN:
9780199235346
eISBN:
9780191715600
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199235346.003.0006
Subject:
Physics, Condensed Matter Physics / Materials

In order to identify the essential items of the mode-coupling-theory scenarios, this chapter describes asymptotic expansions of the correlation functions for small frequencies and small separations ... More


Computations, Transition Formulae, and the Local Index Formula

Simon Scott

in Traces and Determinants of Pseudodifferential Operators

Published in print:
2010
Published Online:
January 2011
ISBN:
9780198568360
eISBN:
9780191594748
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568360.003.0004
Subject:
Mathematics, Analysis

In this chapter the constructions of chapters 1 and 2 for are illustrated with explicit computations. The first part of the chapter presents various methods of computation commonly used in the ... More


Perturbation Methods

Anatoly I. Ruban

in Fluid Dynamics: Part 2: Asymptotic Problems of Fluid Dynamics

Published in print:
2015
Published Online:
October 2015
ISBN:
9780199681747
eISBN:
9780191761614
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199681747.003.0002
Subject:
Physics, Soft Matter / Biological Physics

Chapter 1 discusses the mathematical aspects of the asymptotic theory. It starts with basic definitions, using for this purpose the so-called coordinate asymptotic expansions. Then the chapter turns ... More


Functions of a complex variable

Chun Wa Wong

in Introduction to Mathematical Physics: Methods & Concepts

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199641390
eISBN:
9780191747786
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641390.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Functions of a complex variable are shown to be more complete and rigid than functions of a real variable. Analytic functions with well defined derivatives satisfy two Cauch–Riemann conditions. ... More


Hyper-asymptotic expansions and instantons

Jean Zinn-Justin

in From Random Walks to Random Matrices

Published in print:
2019
Published Online:
August 2019
ISBN:
9780198787754
eISBN:
9780191829840
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198787754.003.0024
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 24 examines the topic of hyper–asymptotic expansions and instantons. A number of quantum mechanics and quantum field theory (QFT) examples exhibit degenerate classical minima connected by ... More


Small-Volume Expansions of the Displacement Fields

Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab

in Mathematical Methods in Elasticity Imaging

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691165318
eISBN:
9781400866625
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691165318.003.0004
Subject:
Mathematics, Applied Mathematics

This chapter deals with small-volume expansions of the displacement fields. It first introduces the notion of elastic moment tensor, a geometric quantity associated with a small-volume inclusion, ... More


DYNAMICS OF IMPERFECT LATTICES

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/9780198507802.003.0011
Subject:
Physics, Condensed Matter Physics / Materials

Defects and impurities affect the vibrations of a solid, and hence properties such as infra-red spectra and thermal conductivity. There can be new, high-frequency, local modes; there can be new, ... More


Boundary Perturbations due to the Presence of Small Cracks

Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab

in Mathematical Methods in Elasticity Imaging

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691165318
eISBN:
9781400866625
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691165318.003.0005
Subject:
Mathematics, Applied Mathematics

This chapter considers the perturbations of the displacement (or traction) vector that are due to the presence of a small crack with homogeneous Neumann boundary conditions in an elastic medium. It ... More


Resonant Wave Interactions and Resonant Excitation of Wave-guide Modes

Vladimir Zeitlin

in Geophysical Fluid Dynamics: Understanding (almost) everything with rotating shallow water models

Published in print:
2018
Published Online:
April 2018
ISBN:
9780198804338
eISBN:
9780191842627
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198804338.003.0012
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

The idea of resonant nonlinear interactions of waves, and of resonant wave triads, is first explained using the example of Rossby waves, and then used to highlight a mechanism of excitation of ... More


Elasticity Equations with High Contrast Parameters

Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab

in Mathematical Methods in Elasticity Imaging

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691165318
eISBN:
9781400866625
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691165318.003.0003
Subject:
Mathematics, Applied Mathematics

This chapter presents some recent results on the elasticity equations with high contrast coefficients. It first sets up the problems for finite and extreme moduli before discussing the incompressible ... More


The Spicules of Sponges

Marjorie Senechal

in I Died for Beauty: A Biography of Dorothy Wrinch

Published in print:
2012
Published Online:
March 2015
ISBN:
9780199732593
eISBN:
9780190254353
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:osobl/9780199732593.003.0009
Subject:
History, History of Science, Technology, and Medicine

This chapter describes the papers Dot presented to the University of London for her graduate degrees. While the papers were pure mathematics, sponges had shaped her work just as they shaped their ... More


Optimal Control Imaging of Extended Inclusions

Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab

in Mathematical Methods in Elasticity Imaging

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691165318
eISBN:
9781400866625
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691165318.003.0010
Subject:
Mathematics, Applied Mathematics

This chapter describes the use of time-reversal imaging techniques for optimal control of extended inclusions. It first considers the problem of reconstructing shape deformations of an extended ... More


Getting Rid of Fast Waves: Slow Dynamics

Vladimir Zeitlin

in Geophysical Fluid Dynamics: Understanding (almost) everything with rotating shallow water models

Published in print:
2018
Published Online:
April 2018
ISBN:
9780198804338
eISBN:
9780191842627
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198804338.003.0005
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

After analysis of general properties of horizontal motion in primitive equations and introduction of principal parameters, the key notion of geostrophic equilibrium is introduced. Quasi-geostrophic ... More


Geostrophic Adjustment and Wave–Vortex (Non)Interaction

Vladimir Zeitlin

in Geophysical Fluid Dynamics: Understanding (almost) everything with rotating shallow water models

Published in print:
2018
Published Online:
April 2018
ISBN:
9780198804338
eISBN:
9780191842627
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198804338.003.0008
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

The fundamental process of geostrophic adjustment is treated by the method of multi-scale asymptotic expansions in Rossby number and fast-time averaging (which is explained), first in the barotropic ... More


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