## 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