scholarly journals Conservative discretization of the Landau collision integral

2017 ◽  
Vol 24 (3) ◽  
pp. 032121 ◽  
Author(s):  
E. Hirvijoki ◽  
M. F. Adams
Keyword(s):  
Collision Integral ◽  
Conservative Discretization

scholarly journals Relaxation of quasi-stationary states in long range interacting systems and a classification of the range of pair interactions

Open Physics ◽  
2012 ◽  
Vol 10 (3) ◽  
Author(s):  
Bruno Marcos ◽  
Andrea Gabrielli ◽  
Michael Joyce
Keyword(s):  
Long Range ◽  
Asymptotic Form ◽  
Pair Interaction ◽  
Collision Integral ◽  
Stationary States ◽  
Long Range Interactions ◽  
Interacting Systems ◽  
Dynamical Properties ◽  
Number Of Particles

AbstractSystems of particles interacting with long range interactions present generically ”quasi-stationary states” (QSS), which are approximately time-independent out of equilibrium states. In this proceedings, we explore the generalization of the formation of such QSS and their relaxation from the much studied case of gravity to a generic pair interaction with the asymptotic form of the potential v(r) ∼ 1/r γ with γ > 0 in d dimensions. We compute analytic estimations of the relaxation time calculating the rate of two body collisionality in a virialized system approximated as homogeneous. We show that for γ < (d − 1/2), the collision integral is dominated by the size of the system, while for γ > (d − 1/2), it is dominated by small impact parameters. In addition, the lifetime of QSS increases with the number of particles if γ < d − 1 (i.e. the force is not integrable) and decreases if γ > d − 1. Using numerical simulations we confirm our analytic results. A corollary of our work gives a ”dynamical” classification of interactions: the dynamical properties of the system depend on whether the pair force is integrable or not.

Calculation of boltzmann equation collision integral and accurate solution of relaxation problem

1978 ◽  
Vol 12 (5) ◽  
pp. 749-757
Author(s):  
I. N. Kolyshkin ◽  
A. Ya. �nder ◽  
I. A. �nder
Keyword(s):  
Boltzmann Equation ◽  
Accurate Solution ◽  
Collision Integral ◽  
Relaxation Problem

Covariant form for the collision integral

2007 ◽  
Vol 73 (4) ◽  
pp. 599-611 ◽  
Author(s):  
D. B. MELROSE
Keyword(s):  
Quantum Electrodynamics ◽  
Relativistic Effects ◽  
Collision Integral ◽  
Covariant Theory ◽  
Debye Screening ◽  
Coulomb Interactions ◽  
Small Momentum Transfer ◽  
Moller Scattering ◽  
Transverse Current ◽  
Charge Interaction

AbstractThe collision integral that describes the evolution of a distribution of particles in a plasma due to Coulomb interactions between themselves or with other particles is generalized to include relativistic effects and the current–current interaction (in addition to the charge–charge interaction). This is achieved through a covariant version of a conventional derivation based on correlation functions for fluctuations in the plasma. The covariant theory is used to distinguish between longitudinal (charge–charge) and transverse (current–current) interactions. For highly relativistic particles, the current–current contribution is half the charge–charge contribution when Debye screening is unimportant, and is unaffected by Debye screening. It is shown that the classical theory is reproduced by a quantum electrodynamics calculation for electron–electron (Møller) scattering in the limit of small momentum transfer.

scholarly journals A deterministic-stochastic method for computing the Boltzmann collision integral in $\mathcal{O}(MN)$ operations

2018 ◽  
Vol 11 (5) ◽  
pp. 1211-1234 ◽  
Author(s):  
Alexander Alekseenko ◽  
◽  
Truong Nguyen ◽  
Aihua Wood ◽  
◽  
...  
Keyword(s):  
Collision Integral ◽  
Stochastic Method

scholarly journals Modeling of formation of carbon cluster groups in electric arc discharge plasma

2018 ◽  
Vol 80 (2) ◽  
pp. 108-113 ◽  
Author(s):  
A. N. Gavrilov
Keyword(s):  
Carbon Nanostructures ◽  
Arc Discharge ◽  
Experimental Studies ◽  
Particle Method ◽  
Cost Effective ◽  
Carbon Cluster ◽  
Collision Integral ◽  
Numerical Calculations ◽  
Plasma Synthesis ◽  
Interelectrode Space

The problem of modeling complex resource-intensive processes of plasma synthesis of carbon nanostructures (CNS) on the basis of mathematical and numerical methods of solution, focused on the use of parallel and distributed computing for processing large amounts of data, allowing to investigate the relationship and characteristics of processes to obtain an effective, cost-effective method of synthesis of CNS (fullerenes, nanotubes), is an actual theoretical and practical problem. This article deals with the problem of mathematical modeling of motion and interaction of charged particles in a multicomponent plasma based on the Boltzmann equation for the synthesis of ONS by thermal sublimation of graphite. The derivation of the collision integral is presented allowing to perform a numerical solution of the Boltzmann - Maxwell equations system with respect to the arc synthesis of CNS. The high order of particles and the number of their interactions involved simultaneously in the process of synthesis of CNS requires significant costs of machine resources and time to perform numerical calculations on the constructed model. Application of the large particle method makes it possible to reduce the amount of computing and hardware requirements without affecting the accuracy of numerical calculations. The use of parallel computing technology on the CPU and GPU with the use of Nvidia CUDA technology allows you to organize all the General-purpose calculations for the developed model based on the graphics processor of the personal computer graphics card, without the use of supercomputers or computing clusters. The results of experimental studies and numerical calculations confirming the adequacy of the developed model are presented. Obtained quantitative characteristics of the total pairwise interactions between the carbon particles and interactions with the formation of clusters of carbon with various types of ties in the plasma of the interelectrode space which are the basis of the synthesized nanostructures. The formation of carbon clusters occurs in the entire interelectrode space of the plasma with different intensity and depends on the process parameters.

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