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Random Processes in Physics and Finance

Melvin Lax, Wei Cai, and Min Xu

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198567769
eISBN:
9780191718359
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567769.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book discusses random processes in physics, from basic probability theory to the Fokker-Planck process and Langevin equation for the Fokker Planck process and diffusion. It includes diverse ... More


MATHEMATICAL ANALYSIS 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/9780198566656.003.0004
Subject:
Mathematics, Mathematical Physics

This chapter deals with the theoretical aspects of multifluid magnetohydrodynamics problems. In addition to the coupling between hydrodynamics and electromagnetics examined in Chapter 2, the high ... More


Coherent X-ray imaging

David M. Paganin

in Coherent X-Ray Optics

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198567288
eISBN:
9780191717963
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567288.003.0004
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter draws on material from all preceding chapters to give an overview of the field of coherent X-ray imaging. It opens with an introduction to the operator theory of imaging, this being the ... More


FLUCTUATION TRANSPORT

Anatoly Larkin and Andrei Varlamov

in Theory of Fluctuations in Superconductors

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528159
eISBN:
9780191713521
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528159.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

The time-dependent Ginzburg-Landau equation is phenomenologically introduced in relation to the order parameter relaxation in quasi-stationary approximation. This is applied to the fluctuation ... More


Collective dynamics in plasmas—I. Hydrodynamics and transport

Abraham Bers

in Plasma Physics and Fusion Plasma Electrodynamics

Published in print:
2016
Published Online:
November 2016
ISBN:
9780199295784
eISBN:
9780191749063
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199295784.003.0002
Subject:
Physics, Nuclear and Plasma Physics, Particle Physics / Astrophysics / Cosmology

This chapter presents simple, illustrative descriptions of collective dynamics in plasmas—in particular, in fully-ionized plasmas. These descriptions entail choices of collective plasma models, and ... More


Analytical solution of the elastic transport equation

Melvin Lax, Wei Cai, and Min Xu

in Random Processes in Physics and Finance

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198567769
eISBN:
9780191718359
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567769.003.0014
Subject:
Physics, Theoretical, Computational, and Statistical Physics

An example of a random process is the propagation of a particle (or photons, or acoustic wave) in a turbid medium, where particles undergo multiple scattering by randomly distributed scatterers in ... More


Metals and quantum wires

Helmut Hofmann

in The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198504016
eISBN:
9780191708480
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504016.003.0015
Subject:
Physics, Nuclear and Plasma Physics

This chapter discusses conductivity in metals and semiconductor heterostructures. It aims to exhibit the similarities to nuclear transport problems. Semi-classical transport equations are used and ... More


TRANSPORT PROPERTIES OF CHARGE CARRIERS AT LOW TEMPERATURE

A.F. Borghesani

in Ions and electrons in liquid helium

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199213603
eISBN:
9780191707421
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213603.003.0005
Subject:
Physics, Condensed Matter Physics / Materials

This chapter describes the main experimental techniques used to measure the drift velocity in superfluid 4He at low temperature. The experimental results are then presented by showing the ... More


Transport and evolution of classical and quantum ensembles

Sandip Tiwari

in Semiconductor Physics: Principles, Theory and Nanoscale

Published in print:
2020
Published Online:
November 2020
ISBN:
9780198759867
eISBN:
9780191820830
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198759867.003.0008
Subject:
Physics, Condensed Matter Physics / Materials

This chapter explores the evolution of an ensemble of electrons under stimulus, classically and quantum-mechanically. The classical Liouville description is derived, and then reformed to the quantum ... More


NEGATIVE IONS IN NORMAL LIQUID 3HE FOR T < 1 K

A.F. Borghesani

in Ions and electrons in liquid helium

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199213603
eISBN:
9780191707421
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213603.003.0021
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses the studies of the electron bubble mobility in normal liquid 3He. The high temperature measurements are extended into the milliKelvin range down to the superfluid transition at ... More


Transport-Elliptic Estimates

Philip Isett

in Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691174822
eISBN:
9781400885428
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174822.003.0027
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter solves the underdetermined, elliptic equation ∂ⱼQsuperscript jl = Usuperscript l and Qsuperscript jl = Qsuperscript lj (Equation 1069) in order to eliminate the error term in the ... More


A Kinetic-Theory Description of Fluids

Luciano Rezzolla and Olindo Zanotti

in Relativistic Hydrodynamics

Published in print:
2013
Published Online:
January 2014
ISBN:
9780198528906
eISBN:
9780191746505
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528906.003.0002
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter illustrates how the foundations of the fluid description are rooted in statistical mechanics and in kinetic theory. This approach, which is appropriate for those systems composed of a ... More


Random walk of light in turbid media

Melvin Lax, Wei Cai, and Min Xu

in Random Processes in Physics and Finance

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198567769
eISBN:
9780191718359
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567769.003.0013
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The random motion of particles in a turbid medium, due to multiple elastic scattering, obeys the classic Boltzmann transport equation. This chapter shows how the center position and the diffusion ... More


Movement of charge carriers in electric and magnetic fields

Hermann Kolanoski and Norbert Wermes

in Particle Detectors: Fundamentals and Applications

Published in print:
2020
Published Online:
September 2020
ISBN:
9780198858362
eISBN:
9780191890710
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198858362.003.0004
Subject:
Physics, Atomic, Laser, and Optical Physics, Particle Physics / Astrophysics / Cosmology

For the detection of charged particles many detector principles exploit the ionisation in sensing layers and the collection of the generated charges by electrical fields on electrodes, from where the ... More


Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

Philip Isett

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691174822
eISBN:
9781400885428
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174822.001.0001
Subject:
Mathematics, Computational Mathematics / Optimization

Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if ... More


Scattering-constrained dynamics

Sandip Tiwari

in Semiconductor Physics: Principles, Theory and Nanoscale

Published in print:
2020
Published Online:
November 2020
ISBN:
9780198759867
eISBN:
9780191820830
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198759867.003.0009
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses the statics and dynamics of particle ensemble evolution under multiple stimuli—electrical, magnetic and thermal, particularly (thermoelectromagnetic interaction)—by developing ... More


Coupling Vapor Transport and Transformation of Volatile Organic Chemicals

Yassar H. El-Farhan and Kate M. Scow

in Vadose Zone Hydrology: Cutting Across Disciplines

Published in print:
1999
Published Online:
November 2020
ISBN:
9780195109900
eISBN:
9780197561058
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195109900.003.0013
Subject:
Earth Sciences and Geography, Oceanography and Hydrology

Volatile organic chemicals (VOCs) are the most prevalent group of organic goundwater contaminants and originate primarily from industrial sources (Westerick et al., 1984). Many VOCs are aliphatics, ... More


Kinetic theory of collisions and transport—I. Fully-ionized plasmas

Abraham Bers

in Plasma Physics and Fusion Plasma Electrodynamics

Published in print:
2016
Published Online:
November 2016
ISBN:
9780199295784
eISBN:
9780191749063
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199295784.003.0030
Subject:
Physics, Nuclear and Plasma Physics, Particle Physics / Astrophysics / Cosmology

This chapter explores the kinetic theory of collisions and transport for fully-ionized plasmas. It first derives the Fokker–Planck collision equation analyzed in previous chapters by presenting them ... More


Decay Estimates for α‎ and α‎ (Theorems M2, M3)

Sergiu Klainerman and Jérémie Szeftel

in Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations: (AMS-210)

Published in print:
2020
Published Online:
May 2021
ISBN:
9780691212425
eISBN:
9780691218526
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691212425.003.0006
Subject:
Mathematics, Geometry / Topology

This chapter investigates the proof for Theorems M2 and M3. It relies on the decay of q to prove the decay estimates for α‎ and α‎. More precisely, the chapter relies on the results of Theorem M1 to ... More


Transport Estimates

Philip Isett

in Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691174822
eISBN:
9781400885428
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174822.003.0017
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter derives estimates for quantities which are transported by the coarse scale flow and for their derivatives. It first considers the phase functions which satisfy the Transport equation, ... More


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