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The Porous Medium Equation: Mathematical Theory

Juan Luis Vazquez

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198569039
eISBN:
9780191717468
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198569039.001.0001
Subject:
Mathematics, Mathematical Physics

The heat equation is one of the three classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it ... More


Multi-dimensional hyperbolic partial differential equations: First-order systems and applications

Sylvie Benzoni-Gavage and Denis Serre

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199211234
eISBN:
9780191705700
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199211234.001.0001
Subject:
Mathematics, Applied Mathematics

This book presents a view of the state of the art in multi-dimensional hyperbolic partial differential equations, with a particular emphasis on problems in which modern tools of analysis have proved ... More


Computational Methods for the Study of Dynamic Economies

Ramon Marimon and Andrew Scott (eds)

Published in print:
2001
Published Online:
November 2003
ISBN:
9780199248278
eISBN:
9780191596605
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0199248273.001.0001
Subject:
Economics and Finance, Macro- and Monetary Economics

Macroeconomics increasingly uses stochastic dynamic general equilibrium models to understand theoretical and policy issues. Unless very strong assumptions are made, understanding the properties of ... More


Isochronous Systems

Francesco Calogero

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199535286
eISBN:
9780191715853
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535286.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

A classical dynamical system is called isochronous if it features in its phase space an open, fully dimensional sector where all its solutions are periodic in all their degrees of freedom with the ... More


Intense Terahertz Excitation of Semiconductors

Sergey Ganichev and Willi Prettl

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528302
eISBN:
9780191713637
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528302.001.0001
Subject:
Physics, Condensed Matter Physics / Materials

This book presents high-power terahertz applications to semiconductors and semiconductor structures. It aims to bridge the gap between optics and microwave physics. It focuses on a core topic of ... More


Nonlinear Finite-Amplitude Dynamics

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/9780691141725.003.0004
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter modifies the numerical code by adding the nonlinear terms to produce finite-amplitude simulations. The nonlinear terms are calculated using a Galerkin method in spectral space. After ... More


Postprocessing

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/9780691141725.003.0005
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter explains how to write a postprocessing code, and more specifically how to study the nonlinear simulations using computer graphics and analysis. It first considers how to compute and ... More


Double-Diffusive Convection

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/9780691141725.003.0007
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses double-diffusive convection, with a particular focus on the initial instability and eventual nonlinear evolution. It first considers the “salt-fingering” instability and then ... More


Forbidden Areas and Anchor Points

Rein Taagepera

in Making Social Sciences More Scientific: The Need for Predictive Models

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199534661
eISBN:
9780191715921
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199534661.003.0008
Subject:
Political Science, Comparative Politics, Political Economy

The outcomes of sociopolitical processes often depend on the factor in shortest supply; this makes multiplication of factors superior to their addition. Naïve linear regression may not detect all ... More


An Introduction to Nonlinear Finite Element Analysis

J. N. Reddy

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198525295
eISBN:
9780191711671
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525295.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book presents the theory and computer implementation of the finite element method as applied to nonlinear problems of heat transfer and similar field problems, fluid mechanics (flows of ... More


Introduction

Juan Luis Vázquez

in Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199202973
eISBN:
9780191707919
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199202973.003.0001
Subject:
Mathematics, Applied Mathematics

This introductory chapter opens with an explanation of the purpose of the book, which is to obtain basic estimates for some particular nonlinear parabolic equations and to derive consequences about ... More


Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers

Robert C. Hilborn

Published in print:
2000
Published Online:
January 2010
ISBN:
9780198507239
eISBN:
9780191709340
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507239.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book introduces the full range of activity in the rapidly growing field of nonlinear dynamics. Using a step-by-step introduction to dynamics and geometry in state space as the central focus of ... More


Relaxation Processes in Micromagnetics

Harry Suhl

Published in print:
2007
Published Online:
January 2010
ISBN:
9780198528029
eISBN:
9780191713545
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528029.001.0001
Subject:
Physics, Condensed Matter Physics / Materials

Electrons in solids behave like microscopic bar magnets, and in certain solids these align to produce macroscopic magnetizations. This book deals with the dynamics of this magnetization field. It ... More


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

Joram Lindenstrauss, David Preiss, and Jaroslav Tier

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153551
eISBN:
9781400842698
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153551.001.0001
Subject:
Mathematics, Analysis

This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the ... More


Hybrid Dynamical Systems: Modeling, Stability, and Robustness

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

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153896
eISBN:
9781400842636
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153896.001.0001
Subject:
Mathematics, Applied Mathematics

Hybrid dynamical systems exhibit continuous and instantaneous changes, having features of continuous-time and discrete-time dynamical systems. Filled with a wealth of examples to illustrate concepts, ... More


Regression and Model Fitting

Andrew J. Connolly, Jacob T. VanderPlas, Alexander Gray, Andrew J. Connolly, Jacob T. VanderPlas, and Alexander Gray

in Statistics, Data Mining, and Machine Learning in Astronomy: A Practical Python Guide for the Analysis of Survey Data

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691151687
eISBN:
9781400848911
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691151687.003.0008
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Regression is a special case of the general model fitting and selection procedures discussed in chapters 4 and 5. It can be defined as the relation between a dependent variable, y, and a set of ... More


Time Integration Schemes

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/9780691141725.003.0008
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter focuses on time integration schemes, including fourth-order accurate Runge–Kutta and predictor-corrector schemes as well as schemes that allow larger time steps (and therefore fewer ... More


Magnetic Field

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/9780691141725.003.0011
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter focuses on magnetoconvection, which refers to thermal convection of an electrically conducting fluid within a background magnetic field maintained by some external mechanism. It first ... More


Non‐Linear Hyperbolic Rigid Heat Conductor of The Coleman Type

Józef Ignaczak and Martin Ostoja‐Starzewski

in Thermoelasticity with Finite Wave Speeds

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199541645
eISBN:
9780191716164
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199541645.003.0013
Subject:
Mathematics, Applied Mathematics, Mathematical Physics

While all previous chapters are devoted to linear hyperbolic theories of thermoelasticity, this one concerns a rigid but nonlinear hyperbolic heat conductor due to Coleman et al. (1982, 1983, 1986). ... More


Psychophysiological Recording

Robert M. Stern, William J. Ray, and Karen S. Quigley

Published in print:
2000
Published Online:
March 2012
ISBN:
9780195113594
eISBN:
9780199846962
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195113594.001.0001
Subject:
Psychology, Health Psychology

This text contains a revised edition of a book on psychophysiological recording. The book includes information on the most up-to-date equipment used today to do brain scanning and discusses other ... More


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