A variational derivation of the velocity distribution functions for nonequilibrium, multispecies, weakly interacting, spherically symmetric many-body systems

1982 ◽  
Vol 29 (4) ◽  
pp. 803-812 ◽  
Author(s):  
S. Cuperman ◽  
I. Weiss ◽  
M. Dryer
Keyword(s):  
Velocity Distribution ◽  
Distribution Functions ◽  
Spherically Symmetric ◽  
Many Body ◽  
Weakly Interacting ◽  
Velocity Distribution Functions ◽  
Many Body Systems

scholarly journals On the Formation of Small Groups of Galaxies at High Redshifts

2000 ◽  
Vol 174 ◽  
pp. 412-422
Author(s):  
William C. Saslaw
Keyword(s):  
Velocity Distribution ◽  
Small Groups ◽  
High Redshift ◽  
Distribution Functions ◽  
Many Body ◽  
Redshift Distribution ◽  
Groups Of Galaxies ◽  
Velocity Distribution Functions ◽  
Free Parameters

AbstractCosmological many-body clustering agrees with the spatial and velocity distribution functions of galaxies at low redshifts, and it can be extended to high redshifts z ≈ 3 or more. The high redshift distribution functions are predicted to have a particular form. In the simplest case, there are no free parameters in this prediction, but the degree of clustering depends sensitively on Ω0. Current observations of small groups at high redshifts suggest that Ω0 = 0.3 ± 0.2 for Einstein-Friedmann cosmologies.

Subgrid modelling of ion pitch-angle scattering for magnetosheath waves in a global hybrid-Vlasov simulation

2021 ◽  
Author(s):  
Maxime Dubart ◽  
Urs Ganse ◽  
Adnane Osmane ◽  
Andreas Johlander ◽  
Markus Battarbee ◽  
...  
Keyword(s):  
Velocity Distribution ◽  
Numerical Simulations ◽  
Spatial Resolution ◽  
Pitch Angle ◽  
Space Physics ◽  
Distribution Functions ◽  
Cyclotron Instability ◽  
Angle Scattering ◽  
Velocity Distribution Functions ◽  
Proton Cyclotron

<p>Numerical simulations are widely used in modern space physics and are an essential tool to understand or discover new phenomena which cannot be observed using spacecraft measurements. However, numerical simulations are limited by the space grid resolution of the system and the computational costs of having a high spatial resolution. Therefore, some physics may be unresolved in part of the system due to its low spatial resolution. We have previously identified, using Vlasiator, that the proton cyclotron instability is not resolved for grid cell sizes larger than four times the inertial length in the solar wind, for waves in the downstream of the quasi-perpendicular shock in the magnetosheath of a global hybrid-Vlasov simulation. This leads to unphysically high perpendicular temperature and a dominance of the mirror mode waves. In this study, we use high-resolution simulations to measure and quantify how the proton cyclotron instability diffuses and isotropizes the velocity distribution functions. We investigate the process of pitch-angle scattering during the development of the instability and propose a method for the sub-grid modelling of the diffusion process of the instability at low resolution. This allows us to model the isotropization of the velocity distribution functions and to reduce the temperature anisotropy in the plasma while saving computational resources.</p>

scholarly journals On the Determination of Kappa Distribution Functions from Space Plasma Observations

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 212 ◽  
Author(s):  
Georgios Nicolaou ◽  
George Livadiotis ◽  
Robert T. Wicks
Keyword(s):  
Distribution Function ◽  
Velocity Distribution ◽  
Space Plasma ◽  
Distribution Functions ◽  
Specific Method ◽  
Kappa Distribution ◽  
Kappa Index ◽  
Velocity Distribution Functions ◽  
Bulk Parameters ◽  
Plasma Bulk

The velocities of space plasma particles, often follow kappa distribution functions. The kappa index, which labels and governs these distributions, is an important parameter in understanding the plasma dynamics. Space science missions often carry plasma instruments on board which observe the plasma particles and construct their velocity distribution functions. A proper analysis of the velocity distribution functions derives the plasma bulk parameters, such as the plasma density, speed, temperature, and kappa index. Commonly, the plasma bulk density, velocity, and temperature are determined from the velocity moments of the observed distribution function. Interestingly, recent studies demonstrated the calculation of the kappa index from the speed (kinetic energy) moments of the distribution function. Such a novel calculation could be very useful in future analyses and applications. This study examines the accuracy of the specific method using synthetic plasma proton observations by a typical electrostatic analyzer. We analyze the modeled observations in order to derive the plasma bulk parameters, which we compare with the parameters we used to model the observations in the first place. Through this comparison, we quantify the systematic and statistical errors in the derived moments, and we discuss their possible sources.

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