## 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