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On the Stochastic Burgers Equation and Some Applications to Turbulence and Astrophysics

A.D. Neate and A. Truman

in Analysis and Stochastics of Growth Processes and Interface Models

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199239252
eISBN:
9780191716911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199239252.003.0013
Subject:
Mathematics, Probability / Statistics, Analysis

This chapter summarises a selection of results on the inviscid limit of the stochastic Burgers equation emphasising geometric properties of the caustic, Maxwell set and Hamilton-Jacobi level surfaces ... More


Singular X-ray optics

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/9780198567288.003.0005
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter acquaints the reader with the nascent field of singular X-ray optics, dealing with the singularities of X-ray wave fields, particularly phase singularities (phase vortices). The concept ... More


Intertheoretic Relations—Optics

Robert W. Batterman

in The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence

Published in print:
2001
Published Online:
November 2003
ISBN:
9780195146479
eISBN:
9780199833078
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195146476.003.0006
Subject:
Philosophy, Philosophy of Science

This chapter discusses limiting correspondence relations between the wave theory of light and the ray theory of light. The limit is singular and there is no reductive relation between the theories. ... More


Introduction

John A. Adam

in Rays, Waves, and Scattering: Topics in Classical Mathematical Physics

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691148373
eISBN:
9781400885404
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691148373.003.0001
Subject:
Mathematics, Applied Mathematics

This book deals with rays, waves, and scattering and covers many of the mathematical concepts, structures, and techniques used to study them. The subject of rays is explored in an ... More


Diffraction Catastrophes

John A. Adam

in Rays, Waves, and Scattering: Topics in Classical Mathematical Physics

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691148373
eISBN:
9781400885404
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691148373.003.0006
Subject:
Mathematics, Applied Mathematics

This chapter discusses the mathematics of diffraction catastrophes, focusing on the wavefront associated with a monochromatic wave with Q(x, y, f (x, y)) as a point on the wavefront surface and P (X, ... More


The classical S matrix

M. S. Child

in Semiclassical Mechanics with Molecular Applications

Published in print:
2014
Published Online:
October 2014
ISBN:
9780199672981
eISBN:
9780191783227
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199672981.003.0010
Subject:
Physics, Atomic, Laser, and Optical Physics

The classical S matrix is a natural multidimensional extension of the semiclassical phase shift. It is most naturally interpreted as a contraction of the Feynman path integral propagator, between ... More


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