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Mathematical Methods for the Magnetohydrodynamics of Liquid Metals

Jean-Frédéric Gerbeau, Claude Le Bris, and Tony Lelièvre

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198566656
eISBN:
9780191718014
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566656.001.0001
Subject:
Mathematics, Mathematical Physics

This text focuses on mathematical and numerical techniques for the simulation of magnetohydrodynamic phenomena, with an emphasis on the magnetohydrodynamics of liquid metals, on two-fluid flows, and ... More


Hamilton’s Principle

Oliver Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.003.0006
Subject:
Physics, Atomic, Laser, and Optical Physics

The general calculus of variations discussed in the previous chapter may be used to derive variational principles in mechanics. Two different, but closely related, variational principles are ... More


NUMERICAL SIMULATION OF TWO-FLUID PROBLEMS

Jean-Frédéric Gerbeau, Claude Le Bris, and Tony Lelièvre

in Mathematical Methods for the Magnetohydrodynamics of Liquid Metals

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198566656
eISBN:
9780191718014
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566656.003.0005
Subject:
Mathematics, Mathematical Physics

This chapter deals with the discretization issues raised by multifluid magnetohydrodynamics problems. The additional difficulty compared to those in Chapter 3, is the presence of one (or many) free ... More


ADVECTION AND ADVECTION DIFFUSION

George Em Karniadakis and Spencer J. Sherwin

in Spectral/hp Element Methods for Computational Fluid Dynamics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528692
eISBN:
9780191713491
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528692.003.0006
Subject:
Mathematics, Numerical Analysis

This chapter focuses on the scalar advection equation and develops a Galerkin discretization using the techniques described in Chapter 4. It includes an extended presentation of the discontinuous ... More


Extremum principles

Mauro Fabrizio and Morro Angelo

in Electromagnetism of Continuous Media: Mathematical Modelling and Applications

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198527008
eISBN:
9780191713316
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527008.003.0009
Subject:
Mathematics, Applied Mathematics

This chapter shows various ways in which variational formulations can be established. Particular attention is given to the inverse problem, namely, to the determination of a variational formulation, ... More


Competitive Economies

Lars Peter Hansen and Thomas J. Sargent

in Recursive Models of Dynamic Linear Economies

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691042770
eISBN:
9781400848188
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691042770.003.0007
Subject:
Economics and Finance, History of Economic Thought

This chapter describes a decentralized economy. It assigns ownership and decision making to three distinct economic entities, a household and two kinds of firms. It defines a competitive equilibrium. ... More


Tonelli Lagrangians and Hamiltonians on Compact Manifolds

Alfonso Sorrentino

in Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691164502
eISBN:
9781400866618
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691164502.003.0001
Subject:
Mathematics, Applied Mathematics

This chapter introduces the basic setting: Tonelli Lagrangians and Hamiltonians on a compact manifold. It discusses their main properties and some examples, and provides the opportunity to recall ... More


From KAM Theory to Aubry-Mather Theory

Alfonso Sorrentino

in Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691164502
eISBN:
9781400866618
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691164502.003.0002
Subject:
Mathematics, Applied Mathematics

This chapter discusses an illustrative example, namely the properties of invariant probability measures and orbits on KAM tori (or more generally, on invariant Lagrangian graphs). This will prepare ... More


Lagrangian Mechanics with Time as a Coordinate

Oliver Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.003.0011
Subject:
Physics, Atomic, Laser, and Optical Physics

In traditional analytical mechanics, it is assumed that the system traces out a path (one-dimensional curved line) in a D dimensional configuration space that is defined by writing each of the ... More


The Conceptual Framework of Quantum Field Theory

Anthony Duncan

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199573264
eISBN:
9780191743313
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573264.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The book attempts to provide an introduction to quantum field theory emphasizing conceptual issues frequently neglected in more ‘utilitarian’ treatments of the subject. The book is divided into four ... More


Advanced Mechanics: From Euler's Determinism to Arnold's Chaos

S. G. Rajeev

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199670857
eISBN:
9780191775154
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199670857.001.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

This book begins with the ancient parts of classical mechanics: the variational principle, Lagrangian and Hamiltonian formalisms, and Poisson brackets. The simple pendulum provides a glimpse of the ... More


Introduction to beam physics

J. B. Rosenzweig

in Fundamentals of Beam Physics

Published in print:
2003
Published Online:
January 2010
ISBN:
9780198525547
eISBN:
9780191711725
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525547.003.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter begins by introducing particle accelerators in their scientific and historical context. It reviews methods in Lagrangian and Hamiltonian dynamics as well as special relativity in a ... More


Fluid Mechanics and the SPH Method: Theory and Applications

Damien Violeau

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199655526
eISBN:
9780191741227
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199655526.001.0001
Subject:
Physics, Condensed Matter Physics / Materials

This book aims at presenting the SPH method for fluid modelling from a theoretical and applied viewpoint. It comprises two parts that refer to each other. The first, dealing with the fundamentals of ... More


Lagrangian Theory of Constraints

Oliver Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.003.0003
Subject:
Physics, Atomic, Laser, and Optical Physics

One attractive feature of the Lagrangian method is the ease with which it solves so-called constraint problems. This chapter presents several different ways of solving such problems, with examples of ... More


Small Vibrations About Equilibrium

Oliver Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.003.0010
Subject:
Physics, Atomic, Laser, and Optical Physics

A number of interesting mechanical systems have one or more essentially stable equilibrium configurations. When disturbed slightly, they vibrate about equilibrium in characteristic patterns called ... More


Hamilton’s Principle and Noether’s Theorem

Oliver Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.003.0013
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter presents extended forms of Hamilton’s principle and the phase space Hamilton’s principle based on the extended Lagrangian and Hamiltonian methods developed earlier. It also discusses ... More


Particle Motion in Curved Spacetime

Valeri P. Frolov and Andrei Zelnikov

in Introduction to Black Hole Physics

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199692293
eISBN:
9780191731860
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199692293.003.0004
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Particle motion in a curved spacetime is considered. The Lagrangian and Hamiltonian form of the equation of motion of a relativistic particle are described. We discuss here also the Hamilton‐Jacobi ... More


Lattice gauge theory beyond the Standard Model

Thomas Appelquist and Ethan T. Neil

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

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199691609
eISBN:
9780191731792
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199691609.003.0012
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter gives an overview of methods and recent studies in the application of lattice gauge theory to physics beyond the standard model. It focuses on theories in which electroweak symmetry is ... More


Lagrangian and Hamiltonian mechanics

D. Violeau

in Fluid Mechanics and the SPH Method: Theory and Applications

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199655526
eISBN:
9780191741227
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199655526.003.0001
Subject:
Physics, Condensed Matter Physics / Materials

This chapter details the basics of Lagrangian and Hamiltonian mechanics. From the basic principles of mechanics (Galilean invariance, least action principle), the chapter builds the fundamental ... More


The Lazy Universe: An Introduction to the Principle of Least Action

Jennifer Coopersmith

Published in print:
2017
Published Online:
June 2017
ISBN:
9780198743040
eISBN:
9780191802966
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198743040.001.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, History of Physics

Action and the Principle of Least Action are explained: what Action is, why the Principle of Least Action works, why it underlies all physics, and what are the insights gained into energy, space, and ... More


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