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Sergey N. Dorogovtsev

in Lectures on Complex Networks

Published in print:
2010
Published Online:
May 2010
ISBN:
9780199548927
eISBN:
9780191720574
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199548927.003.0015
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In this concluding section of the text, the three major milestones marking the history of the exploration of networks are indicated. These are: Leonhard Euler's work (1735), the introduction of ... More


RELATIVISTIC HYDRODYNAMICS

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/9780199205677.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter presents the derivation of dynamical equations governing the motion of a perfect fluid, known as the Euler equations, both in the special and general relativistic cases. It considers ... More


Equilibrium and Non-Equilibrium Collisional Regimes

Raymond Brun

in Introduction to Reactive Gas Dynamics

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199552689
eISBN:
9780191720277
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199552689.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter defines collisional regimes of gaseous flows, including equilibrium and non-equilibrium situations which are described with Euler equations. It examines monatomic and diatomic gas flows, ... More


Nonlinear Bending of Straight Beams

J. N. REDDY

in An Introduction to Nonlinear Finite Element Analysis

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198525295
eISBN:
9780191711671
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525295.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter considers the application of the finite element method to the analysis of a slightly more complicated one-dimensional nonlinear problem: the bending of straight beams. When the applied ... More


The Stochastic Simulation Method

Heinz-Peter Breuer and Francesco Petruccione

in The Theory of Open Quantum Systems

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199213900
eISBN:
9780191706349
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213900.003.07
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The formulation of the dynamics of open quantum systems by means of stochastic processes in Hilbert space leads to efficient Monte–Carlo simulation techniques which are introduced and examined in ... More


Mathematical Tools

Hans-Peter Eckle

in Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz

Published in print:
2019
Published Online:
September 2019
ISBN:
9780199678839
eISBN:
9780191878589
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199678839.003.0019
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

Chapter 19 introduces the mathematical techniques required to extract analytic infor- mation from the Bethe ansatz equations for a Heisenberg quantum spin chain of finite length. It discusses how the ... More


Point Transformations in Lagrangian Mechanics

Peter Mann

in Lagrangian and Hamiltonian Dynamics

Published in print:
2018
Published Online:
August 2018
ISBN:
9780198822370
eISBN:
9780191861253
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198822370.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses point transformations in Lagrangian mechanics. Sometimes, when solving problems, it is useful to change coordinates in velocity phase space to better suit and simplify the ... More


Differential Equations

Peter Mann

in Lagrangian and Hamiltonian Dynamics

Published in print:
2018
Published Online:
August 2018
ISBN:
9780198822370
eISBN:
9780191861253
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198822370.003.0035
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter presents the general formulation of the calculus of variations as applied to mechanics, relativity and field theories. The calculus of variations is a common mathematical technique used ... More


Lagrangian Mechanics

David D. Nolte

in Introduction to Modern Dynamics: Chaos, Networks, Space, and Time

Published in print:
2019
Published Online:
November 2019
ISBN:
9780198844624
eISBN:
9780191880216
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198844624.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Dynamical systems follow trajectories for which the mechanical action integrated along the trajectory is an extremum. The action is defined as the time average of the difference between kinetic and ... More


Introduction to Differential Equations

David P. Feldman

in Chaos and Fractals: An Elementary Introduction

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199566433
eISBN:
9780191774966
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199566433.003.0029
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter focuses on differential equations, dynamical systems that change continuously, with the variable of interest having a value at every instant. It first provides an overview of discrete ... More


Two‐Dimensional Differential Equations

David P. Feldman

in Chaos and Fractals: An Elementary Introduction

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199566433
eISBN:
9780191774966
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199566433.003.0031
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter deals with two-dimensional differential equations and examines whether they are capable of a richer set of behaviours compared with their one-dimensional counterparts. It begins by ... More


Finite Heisenberg Quantum Spin Chain

Hans-Peter Eckle

in Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz

Published in print:
2019
Published Online:
September 2019
ISBN:
9780199678839
eISBN:
9780191878589
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199678839.003.0020
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

The Bethe ansatz genuinely considers a finite system. The extraction of finite-size results from the Bethe ansatz equations is of genuine interest, especially against the background of the results of ... More


The Consequences of Extensivity

Robert H. Swendsen

in An Introduction to Statistical Mechanics and Thermodynamics

Published in print:
2019
Published Online:
February 2020
ISBN:
9780198853237
eISBN:
9780191887703
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198853237.003.0013
Subject:
Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

While not all thermodynamic systems are extensive, those that are homogeneous satisfy the useful postulate of extensivity. In this chapter we return to the thermodynamic postulates and consider the ... More


Prologue

Cristopher Moore and Stephan Mertens

in The Nature of Computation

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199233212
eISBN:
9780191775079
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199233212.003.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This prologue begins by considering three examples to demonstrate that in order to solve different problems, fundamentally different kinds of search and different types of proof are required. The ... More


Two-Dimensional and Geophysical Fluid Mechanics

A. Campa, T. Dauxois, D. Fanelli, and S. Ruffo

in Physics of Long-Range Interacting Systems

Published in print:
2014
Published Online:
October 2014
ISBN:
9780199581931
eISBN:
9780191787140
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199581931.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In this Chapter the statistical mechanics theory of long-range interactions is applied to hydrodynamics problems. The Euler equation is derived as a limiting case of the two dimensional Navier-Stokes ... More


Functions and methods

Andrew M. Steane

in Thermodynamics: A complete undergraduate course

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198788560
eISBN:
9780191830426
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198788560.003.0013
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The fundamental relation of thermodynamics is given, and general methods introduced and applied. The thermodynamics potentials, Euler relation, Gibbs–Duhem relation, and Maxwell relations are all ... More


The Stationary Action Principle

Peter Mann

in Lagrangian and Hamiltonian Dynamics

Published in print:
2018
Published Online:
August 2018
ISBN:
9780198822370
eISBN:
9780191861253
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198822370.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This crucial chapter focuses on the stationary action principle. It introduces Lagrangian mechanics, using first-order variational calculus to derive the Euler–Lagrange equation, and the inverse ... More


Introduction

Laurent Baulieu, John Iliopoulos, and Roland Sénéor

in From Classical to Quantum Fields

Published in print:
2017
Published Online:
May 2017
ISBN:
9780198788393
eISBN:
9780191830310
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198788393.003.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

General introduction with a review of the principles of Hamiltonian and Lagrangian mechanics. The connection between symmetries and conservation laws, with a presentation of Noether’s theorem, is ... More


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