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Numerical Method

Gary A. Glatzmaier

in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691141725
eISBN:
9781400848904
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691141725.003.0002
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter describes a numerical method for solving equations of thermal convection on a computer. It begins by introducing the vorticity-streamfunction formulation as a means of conserving mass. ... More


Ionic soft matter

Masao Doi

in Soft Matter Physics

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199652952
eISBN:
9780191774942
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199652952.003.0010
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Ionic soft matter includes suspensions of charged colloidal particles, polyelectrolyte solutions, polyelectrolyte gels, ionic micelles, etc. A common special feature in these materials is that they ... More


The Finite Element Method: A Review

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/9780198525295.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter reviews the basic steps involved in the development of the finite element method as applied to one- and two-dimensional problems described by typical second-order differential equations. ... More


The Poisson Equation

Howard C. Elman, David J. Silvester, and Andrew J. Wathen

in Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics

Published in print:
2014
Published Online:
September 2014
ISBN:
9780199678792
eISBN:
9780191780745
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199678792.003.0002
Subject:
Mathematics, Numerical Analysis, Computational Mathematics / Optimization

This chapter concerns the statement of the Poisson equation and its weak formulation. This is followed by a description of finite element discretization and properties of the discrete problem.


The evolution of the large-scale structure of the universe: beyond the linear regime

Francis Bernardeau

in Post-Planck Cosmology: Lecture Notes of the Les Houches Summer School: Volume 100, July 2013

Published in print:
2015
Published Online:
March 2015
ISBN:
9780198728856
eISBN:
9780191795794
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198728856.003.0002
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter introduces analytical tools, methods, and results describing the growth of large-scale structure beyond the linear regime. The presentation focuses on the single-flow regime of the ... More


Finite Difference Methods

S. G. Rajeev

in Fluid Mechanics: A Geometrical Point of View

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805021
eISBN:
9780191843136
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805021.003.0014
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

This chapter offers a peek at the vast literature on numerical methods for partial differential equations. The focus is on finite difference methods (FDM): approximating differential operators by ... More


Essentials of Electricity and Magnetism

Richard Freeman, James King, and Gregory Lafyatis

in Electromagnetic Radiation

Published in print:
2019
Published Online:
February 2019
ISBN:
9780198726500
eISBN:
9780191793325
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198726500.003.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

A review of the basic elements of electricity and magnetism is presented with an introduction to Maxwell’s equations for steady-state in a vacuum. The modifications to these equations necessary to ... More


Two-Dimensional Problems Involving a Single Variable

J. N. Reddy

in An Introduction to Nonlinear Finite Element Analysis, 2nd Edn: with applications to heat transfer, fluid mechanics, and solid mechanics

Published in print:
2014
Published Online:
June 2015
ISBN:
9780199641758
eISBN:
9780191789557
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641758.003.0006
Subject:
Physics, Condensed Matter Physics / Materials

This chapter presents the weak-form Galerkin finite element model of a generalized, nonlinear Poisson equation in two-dimensions for both steady-state and transient response. It discusses the ... More


The electrostatics of conductors

J. Pierrus

in Solved Problems in Classical Electromagnetism: Analytical and Numerical Solutions with Comments

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198821915
eISBN:
9780191861055
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198821915.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

This chapter begins by proving some important properties of (i) conductors in electrostatic equilibrium, and (ii) harmonic functions. These results underpin most of the remaining questions of Chapter ... More


Fourier Integral and Sobolev Space Hs

Fon-Che Liu

in Real Analysis

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198790426
eISBN:
9780191831676
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198790426.003.0007
Subject:
Mathematics, Analysis

The Fourier integral, which is often called a Fourier transform, is based on an idea of J. Fourier for resolving functions into basic harmonics in the treatment of heat conduction. The Fourier ... More


The law of gravitation

Nathalie Deruelle and Jean-Philippe Uzan

in Relativity in Modern Physics

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198786399
eISBN:
9780191828669
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198786399.003.0011
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter embarks on the study of Newton’s law of gravitation. It first discusses gravitational mass and inertial mass, a measure of the ‘resistance’ of the point particle to an applied force. The ... More


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