HIGH-FIELD LIMIT OF THE VLASOV–POISSON–FOKKER–PLANCK SYSTEM: A COMPARISON OF DIFFERENT PERTURBATION METHODS

A reduced drift-diffusion (Smoluchowski–Poisson) equation is found for the electric charge in the high-field limit of the Vlasov–Poisson–Fokker–Planck system, both in one and three dimensions. The corresponding electric field satisfies a Burgers equation. Three methods are compared in the one-dimensional case: Hilbert expansion, Chapman–Enskog procedure and closure of the hierarchy of equations for the moments of the probability density. Of these methods, only the Chapman–Enskog method is able to systematically yield reduced equations containing terms of different order.

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Statistical Mechanics of Thermotransport of a Heavy Impurity in an Insulating Solid

Zeitschrift für Naturforschung A ◽

10.1515/zna-1971-0103 ◽

1971 ◽

Vol 26 (1) ◽

pp. 10-17 ◽

Cited By ~ 17

Author(s):

A. R. Allnatt

Keyword(s):

Heat Flux ◽

Time Correlation ◽

Three Dimensions ◽

Time Correlation Functions ◽

Single Vacancy ◽

One Dimensional ◽

Enthalpy Of Activation ◽

Heavy Impurity ◽

The One ◽

Non Equilibrium

AbstractA kinetic equation is derived for the singlet distribution function for a heavy impurity in a lattice of lighter atoms in a temperature gradient. In the one dimensional case the equation can be solved to find formal expressions for the jump probability and hence the heat of transport, q*. for a single vacancy jump of the impurity, q* is the sum of the enthalpy of activation, a term involving only averaging in an equilibrium ensemble, and two non-equilibrium terms involving time correlation functions. The most important non-equilibrium term concerns the correlation between the force on the impurity and a microscopic heat flux. A plausible extension to three dimensions is suggested and the relation to earlier isothermal and non-isothermal theories is indicated

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Integration of one-dimensional equations of motions

Exploring Classical Mechanics ◽

10.1093/oso/9780198853787.003.0014 ◽

2020 ◽

pp. 79-90

Author(s):

Gleb L. Kotkin ◽

Valeriy G. Serbo

Keyword(s):

Potential Energy ◽

Field Change ◽

One Dimensional ◽

System A ◽

Small Correction ◽

The Law ◽

The One ◽

The Given ◽

Equations Of Motions

If the potential energy is independent of time, the energy of the system remains constant during the motion of a closed system. A system with one degree of freedom allows for the determination of the law of motion in quadrature. In this chapter, the authors consider motion of the particles in the one-dimensional fields. They discuss also how the law and the period of a particle moving in the potential field change due to adding to the given field a small correction.

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On the Recovery of 3D Spatial Statistics of Particles from 1D Measurements: Implications for Airborne Instruments

Journal of Atmospheric and Oceanic Technology ◽

10.1175/jtech-d-14-00004.1 ◽

2014 ◽

Vol 31 (10) ◽

pp. 2078-2087 ◽

Cited By ~ 6

Author(s):

Michael L. Larsen ◽

Clarissa A. Briner ◽

Philip Boehner

Keyword(s):

Point Processes ◽

Pair Correlation ◽

Three Dimensional ◽

Three Dimensions ◽

Dimensional System ◽

Cloud Droplets ◽

Sampling Variability ◽

One Dimensional ◽

Natural Sampling ◽

The One

Abstract The spatial positions of individual aerosol particles, cloud droplets, or raindrops can be modeled as a point processes in three dimensions. Characterization of three-dimensional point processes often involves the calculation or estimation of the radial distribution function (RDF) and/or the pair-correlation function (PCF) for the system. Sampling these three-dimensional systems is often impractical, however, and, consequently, these three-dimensional systems are directly measured by probing the system along a one-dimensional transect through the volume (e.g., an aircraft-mounted cloud probe measuring a thin horizontal “skewer” through a cloud). The measured RDF and PCF of these one-dimensional transects are related to (but not, in general, equal to) the RDF/PCF of the intrinsic three-dimensional systems from which the sample was taken. Previous work examined the formal mathematical relationship between the statistics of the intrinsic three-dimensional system and the one-dimensional transect; this study extends the previous work within the context of realistic sampling variability. Natural sampling variability is found to constrain substantially the usefulness of applying previous theoretical relationships. Implications for future sampling strategies are discussed.

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Phase Space Reduction of the One-Dimensional Fokker-Planck (Kramers) Equation

Journal of Statistical Physics ◽

10.1007/s10955-012-0570-2 ◽

2012 ◽

Vol 148 (6) ◽

pp. 1135-1155 ◽

Cited By ~ 4

Author(s):

Pavol Kalinay ◽

Jerome K. Percus

Keyword(s):

Phase Space ◽

One Dimensional ◽

Space Reduction ◽

Kramers Equation ◽

The One ◽

Phase Space Reduction ◽

Fokker Planck

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On a Class of Models for the Yielding Behavior of Continuous and Composite Systems

Journal of Applied Mechanics ◽

10.1115/1.3607751 ◽

1967 ◽

Vol 34 (3) ◽

pp. 612-617 ◽

Cited By ~ 500

Author(s):

W. D. Iwan

Keyword(s):

Steady State ◽

Bauschinger Effect ◽

Three Dimensions ◽

Cyclic Behavior ◽

One Dimensional ◽

Composite Systems ◽

Yielding Behavior ◽

Nonsteady State ◽

The One ◽

Incremental Theory Of Plasticity

A class of one-dimensional models for the yielding behavior of materials and structures is presented. This class of models leads to stress-strain relations which exhibit a Bauschinger effect of the Massing type, and both the steady-state and nonsteady-state cyclic behavior are completely specified if the initial monotonic loading behavior is known. The concepts of the one-dimensional class of models are extended to three-dimensions and lead to a subsequent generalization of the customary concepts of the incremental theory of plasticity.

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Diffraction of Electrons by Two and Three Mutually Orthogonal Standing Light Waves

Canadian Journal of Physics ◽

10.1139/p75-023 ◽

1975 ◽

Vol 53 (2) ◽

pp. 157-164 ◽

Cited By ~ 1

Author(s):

F. Ehlotzky

Keyword(s):

Electron Scattering ◽

Light Wave ◽

Three Dimensional ◽

Three Dimensions ◽

Dimensional Problem ◽

One Dimensional ◽

Standing Light Wave ◽

Light Waves ◽

The One ◽

Rectangular Lattices

The one-dimensional problem of electron scattering by a standing light wave, known as the Kapitza–Dirac effect, is shown to be easily extendable to two and three dimensions, thus showing all characteristics of diffraction of electrons by simple two- and three-dimensional rectangular lattices.

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FISH-ing for captured contacts: towards reconciling FISH and 3C

10.1101/081448 ◽

2016 ◽

Cited By ~ 6

Author(s):

Geoff Fudenberg ◽

Maxim Imakaev

Keyword(s):

Genomic Sequence ◽

Three Dimensions ◽

Spatial Distance ◽

Chromosome Conformation ◽

One Dimensional ◽

Genome Wide ◽

Contact Frequency ◽

The One ◽

Chromosomal Loci

AbstractDeciphering how the one-dimensional information encoded in a genomic sequence is read out in three-dimensions is a pressing contemporary challenge. Chromosome conformation capture (3C) and fluorescence in-situ hybridization (FISH) are two popular technologies that provide important links between genomic sequence and 3D chromosome organization. However, how to integrate views from 3C, or genome-wide Hi-C, and FISH is far from solved. We first discuss what each of these methods measure by reconsidering available matched experimental data for Hi-C and FISH. Using polymer simulations, we then demonstrate that contact frequency is distinct from average spatial distance. We show this distinction can create a seemingly-paradoxical relationship between 3C and FISH. Finally, we consider how the measurement of specific interactions between chromosomal loci might be differentially affected by the two technologies. Together, our results have implications for future attempts to cross-validate and integrate 3C and FISH, as well as for developing models of chromosomes.

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