The cumulant method for the space-homogeneous Boltzmann equation

Seeger, S.; Hoffmann, K.
February 2005
Continuum Mechanics & Thermodynamics;Feb2005, Vol. 17 Issue 1, p51
Academic Journal
In this work we give a comparison of the exact Bobylev/Krook-Wu solution to the space-homogeneous Boltzmann equation and numerical results obtained by a implementation of the cumulant method for the space-homogeneous case. We find excellent agreement of the numerical solution to the cumulant equations with the exact solution of the space-homogeneous Boltzmann equation as long as the exact, non-linear production terms are used. If a linearized variant of the production terms is used, relaxation rates may be underestimated due to convergence to the solution of the linearized equations.


Related Articles

  • Exponential Rates of Convergence in the Ergodic Theorem: A Constructive Approach. Bosco, G. G.; Machado, F. P; Ritchie, Thomas Logan // Journal of Statistical Physics;May2010, Vol. 139 Issue 3, p367 

    We prove that, once an algorithm of perfect simulation for a stationary and ergodic random field F taking values in $S^{\mathbb{Z}^{d}}$, S a bounded subset of R n, is provided, the speed of convergence in the mean ergodic theorem occurs exponentially fast for F. Applications from...

  • Quantum mechanical transition state theory and tunneling corrections. Thompson, Ward H. // Journal of Chemical Physics;3/1/1999, Vol. 110 Issue 9, p4221 

    Presents an efficient implementation of the quantum mechanical transition state theory proposed by Hansen and Andersen. Approximation of the flux-flux autocorrelation function by using short-time information to fit an assumed functional form; Exploitation of the low rank of the...

  • Enhanced sampling via strong coupling to a heat bath: Relationship between Tsallis and multicanonical algorithms. Morishita, Tetsuya; Mikami, Masuhiro // Journal of Chemical Physics;7/21/2007, Vol. 127 Issue 3, p034104 

    We show that Tsallis and multicanonical statistical mechanics are equivalent under specific conditions and that they describe a system strongly coupled to a heat bath. The concept of the strong coupling to a heat bath, in which energy fluctuation is larger than that in the canonical ensemble [J....

  • On the Quantum Boltzmann Equation. Erdös, László; Salmhofer, Manfred; Horng-Tzer Yau // Journal of Statistical Physics;Aug2004, Vol. 116 Issue 1-4, p367 

    We give a nonrigorous derivation of the nonlinear Boltzmann equation from the Schrödinger evolution of interacting fermions. The argument is based mainly on the assumption that a quasifree initial state satisfies a property called restricted quasifreeness in the weak coupling limit at any...

  • Polymer Transport in Random Flow. Celani, A.; Musacchio, S.; Vincenzi, D. // Journal of Statistical Physics;Feb2005, Vol. 118 Issue 3/4, p531 

    The dynamics of polymers in a random smooth flow is investigated in the framework of the Hookean dumbbell model. The analytical expression of the time-dependent probability density function of polymer elongation is derived explicitly for a Gaussian, rapidly changing flow. When polymers are in...

  • Tutorial Series on Brain-Inspired Computing: Part 5: Statistical Mechanics of Communication and Computation. Kabashima, Yoshiyuki // New Generation Computing;2006, Vol. 24 Issue 4, p403 

    Statistical mechanics (SM) is a branch of theoretical physics that explores cooperative phenomena observed in many body systems. For a long time, applications of SM were limited to material objects such as gases, liquids, metals, magnets, and semi-conductors. However, about a decade ago,...

  • Linear Response Theory for Thermally Driven Quantum Open Systems. Jak�ic, V.; Ogata, Y.; Pillet, C.-A. // Journal of Statistical Physics;May2006, Vol. 123 Issue 3, p547 

    This note is a continuation of our recent paper [V. Jak�ic Y. Ogata, and C.-A. Pillet, The Green-Kubo formula and Onsager reciprocity relations in quantum statistical mechanics. Commun. Math. Phys. in press.] where we have proven the Green-Kubo formula and the Onsager reciprocity relations...

  • The Spin-Echo System Reconsidered. Lavis, D. A. // Foundations of Physics;Apr2004, Vol. 34 Issue 4, p669 

    Simple models have played an important role in the discussion of foundational issues in statistical mechanics. Among them the spin-echo system is of particular interest since it can be realized experimentally. This has led to inferences being drawn about approaches to the foundations of...

  • On the Definition of Temperature in FPU Systems. Carati, A.; Cipriani, P.; Galgani, L. // Journal of Statistical Physics;May2004, Vol. 115 Issue 3/4, p1101 

    It is usually assumed, in classical statistical mechanics, that the temperature should coincide, apart from a suitable constant factor, with the mean kinetic energy of the particles. We show that this is not the case for Fermi–Pasta–Ulam systems, in conditions in which energy...


Read the Article


Sign out of this library

Other Topics