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Modern Perspectives in Lattice QCD: Quantum Field Theory and High Performance Computing: Lecture Notes of the Les Houches Summer School: Volume 93, August 2009

Laurent Lellouch, Rainer Sommer, Benjamin Svetitsky, Anastassios Vladikas, and Leticia F. Cugliandolo (eds)

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199691609
eISBN:
9780191731792
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199691609.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The book is based on the lectures delivered at the XCIII Session of the ´Ecole de Physique des Houches, held in August, 2009. The aim of the event was to familiarize the new generation of Ph.D. ... More


Variational Principles

Joram Lindenstrauss, David Preiss, and Tiˇser Jaroslav

in Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153551
eISBN:
9781400842698
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153551.003.0007
Subject:
Mathematics, Analysis

This chapter describes smooth variational principles (of Ekeland type) as infinite two-player games. These variational principles are based on a simple but careful recursive choice of points where ... More


Direct human impacts on high-latitude lakes and rivers

Martin J. Riddle and Derek C.G. Muir

in Polar Lakes and Rivers: Limnology of Arctic and Antarctic Aquatic Ecosystems

Published in print:
2008
Published Online:
January 2009
ISBN:
9780199213887
eISBN:
9780191707506
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213887.003.0016
Subject:
Biology, Ecology, Aquatic Biology

This chapter reviews and compares possible causes of environmental impacts on lake and river systems in the Arctic and Antarctica, with emphasis on the direct effects of local human activities. ... More


Control of Locomotion: Lessons from Whole-body Biomechanical Analysis

Boris I. Prilutsky and Alexander N. Klishko

in Motor Control: Theories, Experiments, and Applications

Published in print:
2010
Published Online:
January 2011
ISBN:
9780195395273
eISBN:
9780199863518
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195395273.003.0009
Subject:
Neuroscience, Sensory and Motor Systems

Biomechanical analysis of whole-body locomotion in different conditions is a unique tool for exploring the effects of environmental demands on movement control. This chapter reviews data from the ... More


Asymptotic Fr echet ´Differentiability

Joram Lindenstrauss, David Preiss, and Tiˇser Jaroslav

in Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153551
eISBN:
9781400842698
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153551.003.0015
Subject:
Mathematics, Analysis

This chapter presents the current development of the first, unpublished proof of existence of points Fréchet differentiability of Lipschitz mappings to two-dimensional spaces. For functions into ... More


Perturbations and generalized solutions

Rafal Goebel, Ricardo G. Sanfelice, and Andrew R. Teel

in Hybrid Dynamical Systems: Modeling, Stability, and Robustness

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153896
eISBN:
9781400842636
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153896.003.0004
Subject:
Mathematics, Applied Mathematics

This chapter discusses the effect of state perturbations on solutions to a hybrid system. It shows that state perturbations, of arbitrarily small size, can dramatically change the behavior of ... More


Mathematical and computational modelling tools

Baltazar D. Aguda and Avner Friedman

in Models of Cellular Regulation

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198570912
eISBN:
9780191718717
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570912.003.0003
Subject:
Physics, Soft Matter / Biological Physics

This chapter reviews chemical kinetics to illustrate the formulation of model equations for a given reaction mechanism. For spatially uniform systems, these model equations are usually ordinary ... 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


GRAVITATIONAL WAVE EXTRACTION

Miguel Alcubierre

in Introduction to 3+1 Numerical Relativity

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199205677
eISBN:
9780191709371
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199205677.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Gravitational waves are one of the most important physical phenomena associated with the presence of strong and dynamic gravitational fields, and as such they are of great interest in numerical ... More


The absorption and stimulated emission of radiation

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/9780199211456.003.0009
Subject:
Physics, Atomic, Laser, and Optical Physics

Starting from the absorption of radiation by a classical electron oscillator, Einstein's A and B coefficients for spontaneous and stimulated transitions are introduced. Stimulated transition rates ... More


PECULIARITIES OF D = 1

Thierry Giamarchi

in Quantum Physics in One Dimension

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198525004
eISBN:
9780191711909
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525004.003.0001
Subject:
Physics, Condensed Matter Physics / Materials

This chapter provides an overview of the basic ideas of interacting electrons and the peculiarities of one dimension. Interactions among particles are what endows the one-dimensional world with its ... More


Tunneling Phenomenon

C. Julian Chen

in Introduction to Scanning Tunneling Microscopy: Second Edition

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199211500
eISBN:
9780191705991
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199211500.003.0002
Subject:
Physics, Condensed Matter Physics / Materials

This chapter presents basic experimental methods and the basic theory of tunneling. The classical metal-insulator-metal tunneling junction experiment of Giaever, designed to verify the ... More


Atomic Forces

C. Julian Chen

in Introduction to Scanning Tunneling Microscopy: Second Edition

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199211500
eISBN:
9780191705991
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199211500.003.0004
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses the physics and properties of four types of atomic forces occurring in STM and AFM: the van der Waals force, the hard core repulsion, the ionic bond, and the covalent bond. The ... More


REGULARIZATION OF FIELD THEORY AND CHIRAL ANOMALIES

Kazuo Fujikawa and Hiroshi Suzuki

in Path Integrals and Quantum Anomalies

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198529132
eISBN:
9780191712821
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198529132.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter illustrates the regularization of field theory by taking quantum electrodynamics (QED) as an example, showing that the mass of the photon remains at 0 even after higher-order quantum ... More


Time-independent perturbation expansion

Efstratios Manousakis

in Practical Quantum Mechanics: Modern Tools and Applications

Published in print:
2015
Published Online:
December 2015
ISBN:
9780198749349
eISBN:
9780191813474
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198749349.003.0020
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter discusses time-indendent perturbation theory. It discusses the non-degenerate case first and then the case of application of perturbation theory for the case in which the state is ... More


Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis

Klaus Boehmer

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577040
eISBN:
9780191595172
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577040.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Nonlinear elliptic problems play an increasingly important role in mathematics, science and engineering, and create an exciting interplay. Other books discuss nonlinearity by a very few important ... More


Atom—Field Interactions

Stephen C. Rand

in Lectures on Light: Nonlinear and Quantum Optics using the Density Matrix

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199574872
eISBN:
9780191722219
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199574872.003.0003
Subject:
Physics, Atomic, Laser, and Optical Physics

In Chapter 3 the interaction Hamiltonian which determines the way light interacts with matter is derived. Simple perturbative analysis is applied to see if basic dynamics of atoms can be explained. ... More


Scale Matters

Christopher Pincock

in Mathematics and Scientific Representation

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199757107
eISBN:
9780199932313
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199757107.003.0005
Subject:
Philosophy, Philosophy of Science

This chapter considers the complicated interactions between mathematics and the scale of a scientific representation. Some aspects of scale echo the contributions found in chapters 3 and 4. Others ... More


A general discretization theory

Klaus Böhmer

in Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577040
eISBN:
9780191595172
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577040.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

A new general discretization theory unifies the generalized Petrov-Galerkin method and one of the classical methods. Linearization is a main tool: the derivative of the operator in the exact solution ... More


Hexatonic Cycles

Richard Cohn

in Audacious Euphony: Chromatic Harmony and the Triad's Second Nature

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199772698
eISBN:
9780199932238
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199772698.003.0002
Subject:
Music, Theory, Analysis, Composition

Chapter 2 presents the first of two preliminary models of the triadic universe, based on voice-leading proximity, On this conception, the most proximate triads are those whose roots are related by ... More


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