Evolution Equation and Transport Coefficients of Swarms in Short Time Development of Initial Relaxation Processes

1987 ◽  
pp. 109-110
Author(s):  
Keiichi Kondo
Keyword(s):  
Evolution Equation ◽  
Transport Coefficients ◽  
Time Development ◽  
Relaxation Processes ◽  
Short Time

scholarly journals Evolution Equation and Transport Coefficients of Swarms in Initial Relaxation Processes

1987 ◽  
Vol 40 (3) ◽  
pp. 367 ◽  
Author(s):  
Keiichi Kondo
Keyword(s):  
Evolution Equation ◽  
Transport Coefficients ◽  
Collision Operator ◽  
Operator Method ◽  
Time Dependent ◽  
Relaxation Processes ◽  
Projection Operator Method ◽  
Model Collision ◽  
The Difference ◽  
Dependent Transport

The problem of a swarm approaching the hydrodynamic regime is studied by using the projection operator method. An evolution equation for the density and the related time-dependent transport coefficient are derived. The effects of the initial condition on the transport characteristics of a swarm are separated from the intrinsic evolution of the swarms, and the difference from the continuity equation with time-dependent transport coefficients introduced by Tagashira et al. (1977, 1978) is discussed. To illustrate this method, calculations on the relaxation model collision operator have been carried out. The results are found to agree with the analysis by Robson (1975).

scholarly journals A parabolic flow of balanced metrics

2017 ◽  
Vol 2017 (723) ◽  
Author(s):  
Lucio Bedulli ◽  
Luigi Vezzoni
Keyword(s):  
Vector Bundle ◽  
Evolution Equation ◽  
Existence And Uniqueness ◽  
General Criterion ◽  
Balanced Metrics ◽  
Time Solution ◽  
Parabolic Flow ◽  
Short Time

AbstractWe prove a general criterion to establish existence and uniqueness of a short-time solution to an evolution equation involving “closed” sections of a vector bundle, generalizing a method used by Bryant and Xu [

The Homogeneous Flow

2018 ◽  
Author(s):  
Ercüment H. Ortaçgil
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Second Order ◽  
Initial Condition ◽  
Homogeneous Flow ◽  
Short Time

In this chapter, a second-order nonlinear evolution equation is constructed that starts with any parallelism as initial condition and flows in the direction of a parallelism with vanishing curvature. The existence of unique short-time solutions is proved.

scholarly journals Kinetic Theory of Charged Particle Swarms in Neutral Gases

1980 ◽  
Vol 33 (2) ◽  
pp. 343 ◽  
Author(s):  
Kailash Kumar ◽  
HR Skullerud ◽  
RE Robson
Keyword(s):  
Kinetic Theory ◽  
Transport Coefficients ◽  
Time Development ◽  
Processes And Reactions ◽  
Particle Swarms ◽  
Neutral Gas ◽  
Test Particles ◽  
Electric And Magnetic Fields ◽  
Charged Test ◽  
Inelastic Processes

The kinetic theory of charged test particles in a neutral gas, in the presence of static and uniform electric and magnetic fields, is reviewed. The effects of inelastic processes and reactions are included. The general space-time development of the swarms is considered and the relation between the nonhydrodynamic anQ hydrodynamic developments is pointed out. The transport coefficients are identified as statistical averages over the configuration-space and phase-space distributions. The evaluation of these averages by computer simulations is briefly discussed.

The quantum mechanical Landau equation

1983 ◽  
Vol 388 (1795) ◽  
pp. 393-400 ◽  
Keyword(s):  
Landau Equation ◽  
Time Development ◽  
Feynman Diagrams ◽  
Quantum Mechanical ◽  
Number Density ◽  
Short Discussion ◽  
Mechanical Effects ◽  
Quantum Mechanical Effects ◽  
Apparent Similarity ◽  
Short Time

The significance of quantum mechanical effects on the short time development of the Landau equation is examined. The analysis is undertaken using the density diagram technique of Prigogine and Balescu. Owing to the apparent similarity that exists between the density diagrams and the more familiar Feynman diagrams derived from generalized Green functions a short discussion of both techniques is presented. The solution is undertaken for small h/m and does not necessarily apply to electrons. It is found that quantum mechanical effects may become significant at a number density around 10 14 , which is the lower bound in density that an earlier analysis suggested. Non-Markovian effects may be significant.

Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results

1994 ◽  
Vol 271 ◽  
pp. 311-339 ◽  
Author(s):  
Anthony J. C. Ladd
Keyword(s):  
Colloidal Particles ◽  
Transport Coefficients ◽  
Computational Cost ◽  
Reynolds Numbers ◽  
General Technique ◽  
Particulate Suspensions ◽  
Time Dynamics ◽  
Creeping Flows ◽  
Short Time ◽  
Number Of Particles

A new and very general technique for simulating solid–fluid suspensions has been described in a previous paper (Part 1); the most important feature of the new method is that the computational cost scales linearly with the number of particles. In this paper (Part 2), extensive numerical tests of the method are described; results are presented for creeping flows, both with and without Brownian motion, and at finite Reynolds numbers. Hydrodynamic interactions, transport coefficients, and the short-time dynamics of random dispersions of up to 1024 colloidal particles have been simulated.

An inhomogeneous Landau-like equation

1981 ◽  
Vol 378 (1774) ◽  
pp. 385-400 ◽  
Keyword(s):  
Power Series ◽  
Statistical Mechanics ◽  
Weak Coupling ◽  
Landau Equation ◽  
Time Development ◽  
Sample Problem ◽  
Homogeneous Plasma ◽  
Vector Generation ◽  
Short Time ◽  
Infinite Temperature

The problem of the mixing of two plasmas is very difficult to solve if the methods of statistical mechanics are used. When both plasmas are homogeneous in space, and the limit of weak coupling is appropriate, the Landau equation describes the motion. An equation, similar to the Landau equation, is developed for the case when one of the plasmas is initially inhomogeneous in space. The equation is a power series in time and involves wave vectors in space. The short-time-after-mixing limit is considered, which restricts the number of wave vectors. A sample problem is presented of the short time development of an infinite-temperature spike interacting with a homogeneous plasma. The spike is found to move very rapidly from the origin owing to the long range of the forces. Extension of the time development past the initial short time requires consideration of destructive wave vectors in addition to the wave vector generation considered here.

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