scholarly journals On blowup for gain-term-only classical and relativistic Boltzmann equations

2004 ◽  
Vol 27 (18) ◽  
pp. 2231-2240 ◽  
Author(s):  
Håkan Andréasson ◽  
Simone Calogero ◽  
Reinhard Illner
Keyword(s):  
Boltzmann Equations ◽  
Gain Term

scholarly journals Complete leading-order standard model corrections to quantum leptogenesis

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Paul Frederik Depta ◽  
Andreas Halsch ◽  
Janine Hütig ◽  
Sebastian Mendizabal ◽  
Owe Philipsen
Keyword(s):  
Standard Model ◽  
Gauge Coupling ◽  
Thermal Bath ◽  
Leading Order ◽  
Boltzmann Equations ◽  
The Standard Model ◽  
Majorana Neutrinos ◽  
Infinite Loop ◽  
First Time ◽  
The Universe

Abstract Thermal leptogenesis, in the framework of the standard model with three additional heavy Majorana neutrinos, provides an attractive scenario to explain the observed baryon asymmetry in the universe. It is based on the out-of-equilibrium decay of Majorana neutrinos in a thermal bath of standard model particles, which in a fully quantum field theoretical formalism is obtained by solving Kadanoff-Baym equations. So far, the leading two-loop contributions from leptons and Higgs particles are included, but not yet gauge corrections. These enter at three-loop level but, in certain kinematical regimes, require a resummation to infinite loop order for a result to leading order in the gauge coupling. In this work, we apply such a resummation to the calculation of the lepton number density. The full result for the simplest “vanilla leptogenesis” scenario is by $$ \mathcal{O} $$ O (1) increased compared to that of quantum Boltzmann equations, and for the first time permits an estimate of all theoretical uncertainties. This step completes the quantum theory of leptogenesis and forms the basis for quantitative evaluations, as well as extensions to other scenarios.

Bracket formulation for discrete two-velocity Boltzmann equations

1987 ◽  
Vol 122 (3-4) ◽  
pp. 149-152 ◽  
Author(s):  
G. Baumann ◽  
T.F. Nonnenmacher
Keyword(s):  
Boltzmann Equations

scholarly journals Cutoff-type Boltzmann equations: Convergence of the solution

1987 ◽  
Vol 8 (1) ◽  
pp. 98-107 ◽  
Author(s):  
René Ferland ◽  
Gaston Giroux
Keyword(s):  
Boltzmann Equations

scholarly journals Boltzmann Equations

Nature ◽  
1969 ◽  
Vol 223 (5210) ◽  
pp. 1081-1082
Author(s):  
T. G. COWLING
Keyword(s):  
Boltzmann Equations

Development of the LBM non-isothermal flows with arbitrarily large Mach number

2021 ◽  
pp. 62-71
Author(s):  
Елизавета Вячеславовна Зипунова ◽  
Анастасия Юрьевна Перепёлкина ◽  
Андрей Владимирович Закиров
Keyword(s):  
Mach Number ◽  
High Speed ◽  
Classical Method ◽  
Discrete Distribution ◽  
Explicit Calculation ◽  
Time Layer ◽  
Boltzmann Equations ◽  
On Demand ◽  
Small Flow ◽  
Lattice Boltzmann Equations

При решении задач динамики жидкостей и газов в области малых скоростей потока и при изотермических условиях с успехом применяется метод решеточных уравнений Больцмана (LBM). Для решения дискретного уравнения Больцмана может быть использован новый метод Particles-on-Demand (PonD), в котором в каждой точке сетки дискретизация функции распределения в пространстве скоростей центрирована относительно текущей скорости потока. В отличие от классического LBM, метод PonD применим не только для задач с малыми скоростями потока и при изотермических условиях. В данной работе реализован метод PonD D1Q5 с итерационным расчетом скорости переноса и явным расчетом первых трех моментов, включая скорости переноса. Показано, что рассмотренная модификация метода PonD хоть и накладывает ограничения на параметры, позволяет проводить расчеты в большем диапазоне допустимых скоростей. The purpose of the paper is to demonstrate applicability of the Particle on Demand (PonD) D1Q5 method with the explicit calculation of the first three moments to problem with high speed of the flow. The standard LBM is applicable for small flow velocities. Thus to overcome this limitation we use PonD. In this work, we use conservative version of PonD - the D1Q5 method with the explicit calculation of the first three moments. Methodology. The Pond over LBM was applied to the Riemann problem in order to demonstrate the advantage of the method. In this work, we choose the case when contact discontinuities could propagate at variable speed. Findings. If the interpolation pattern is fixed relative to the point at which there is a current update of the discrete distribution function, then the transfer step can be written explicitly, thus the scheme is conservative. On the other hand, this imposes additional restrictions on the temperature and the flow rate. But even if the PonD scheme is limited to a fixed interpolation pattern, it is possible to simulate flows with larger values of the Mach number than in the case when the classical method of lattice Boltzmann equations is used. Originality/value. In the described particular case of the PonD method, it is possible to avoid iterations by calculating the temperature and velocity values directly at a new time layer. In this work, we have investigated the properties and the range of applicability (admissible values of temperature and velocity) of such modification of PonD.

scholarly journals Completely positive Bloch-Boltzmann equations

2003 ◽  
Vol 68 (1) ◽  
Author(s):  
Robert Alicki ◽  
Stanisław Kryszewski
Keyword(s):  
Boltzmann Equations ◽  
Completely Positive
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