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  • Articles  (12)
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  • Boltzmann equation
  • Springer  (12)
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  • 2020-2022
  • 1975-1979  (10)
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  • Physics  (12)
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  • Articles  (12)
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  • Springer  (12)
  • American Association for the Advancement of Science
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  • Physics  (12)
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  • 1
    Electronic Resource
    Electronic Resource
    A variational principle for boundary value problems in kinetic theory (1969)
    Springer
    Journal of statistical physics 1 (1969), S. 297-311 
    Details
    ISSN: 1572-9613
    Keywords: kinetic theory ; boundary value problems ; variational principles ; Couette flow ; transition regime ; Boltzmann equation ; rarefied gas dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A variational principle which applies directly to the integrodifferential form of the linearized Boltzmann equation is introduced. Extremely general boundary conditions and collision terms are allowed. For a class of interesting problems, the value of the functional to be varied is shown to be closely related to quantities of great physical interest. The formalism is applied to the treatment of plane Couette flow for different forms of the collision term (BGK model, rigid spheres, Maxwell's molecules).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01007482
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  • 2
    Electronic Resource
    Electronic Resource
    Theory of kinetic equations for systems with production and absorption of particles (1976)
    Springer
    Journal of statistical physics 14 (1976), S. 249-262 
    Details
    ISSN: 1572-9613
    Keywords: Nonequilibrium systems ; Boltzmann equation ; Langevin equation ; time correlations ; systems with nuclear reactions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper is concerned with systems which are not in thermal equilibrium because of production and absorption of particles. On the basis of a new Hamiltonian describing such a nonequilibrium system, we develop a method for deriving kinetic equations for singlet density, time correlations of density, etc., including all the higher order interactions necessary to describe the production and absorption of particles. The foundations of the Boltzmann and Langevin equations for neutron distributions are studied. The time-correlation function is shown to obey a kinetic equation identical to that for the singlet density. It is also shown that the description of density fluctuations based on the Langevin equation is equivalent to the simplest decoupling of the rigorous hierarchy of equations for correlation functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01023627
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  • 3
    Electronic Resource
    Electronic Resource
    On a class of solutions of nonlinear Boltzmann equations (1979)
    Springer
    Journal of statistical physics 20 (1979), S. 115-119 
    Details
    ISSN: 1572-9613
    Keywords: Boltzmann equation ; special cross section ; exact solution ; moment equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In a recent paper by Krook and Wu, the nonlinear Boltzmann equation for an infinite, spatially homogeneous, isotropic monoatomic gas of constant density and kinetic energy and with an elastic differential cross section that varies inversely as relative speed has been reduced to an infinite sequence of moment equations. The present note observes that the moment equations are successively integrable and shows that as time goes to infinity, the distribution tends to be Maxwellian.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01013749
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  • 4
    Electronic Resource
    Electronic Resource
    Long-time behavior of the Lorentz electron gas in a constant, uniform electric field (1979)
    Springer
    Journal of statistical physics 21 (1979), S. 549-559 
    Details
    ISSN: 1572-9613
    Keywords: Lorentz gas ; Boltzmann equation ; distribution function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The long-time behavior of the Lorentz electron gas is studied in the presence of a uniform external field. A discussion of the rigorous solution of the one-dimensional Boltzmann equation is followed by the derivation of the asymptotic form of the velocity distribution in an arbitrary number of dimensions. The system is shown to absorb energy from the field without bounds, which excludes the usually assumed steady state with finite thermal energy density.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01011167
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  • 5
    Electronic Resource
    Electronic Resource
    Velocity-space contours of collision integrals (1969)
    Springer
    Journal of statistical physics 1 (1969), S. 585-593 
    Details
    ISSN: 1572-9613
    Keywords: Kinetic theory of gases ; Boltzmann equation ; collision integrals ; nonequilibrium in hard-sphere gases ; numerical analysis of collision integrals ; exact results for collision integrals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Based on the recently found closed-form expressions of the Boltzmann collision integrals in a rigid-sphere gas for multi-Maxwellian distributions, a few typical sets of contour surfaces of the integrals in the space of molecular velocities are presented. These show graphically the tendency toward equilibrium under the influence of collisions. A brief preliminary comparison with Monte Carlo results is also given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01024133
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  • 6
    Electronic Resource
    Electronic Resource
    On the theory of brownian motion. VIII. A Brownian particle in a dilute gas with inelastic collisions (1975)
    Springer
    Journal of statistical physics 12 (1975), S. 427-436 
    Details
    ISSN: 1572-9613
    Keywords: Brownian motion ; Fokker-Planck equation ; Boltzmann equation ; diffuse scattering ; inelastic collisions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The Fokker-Planck equation for a heavy particle in a dilute gas of light particles is derived from a Boltzmann equation. Inelastic collisions between the heavy and light particles are considered, and explicit quadratures for the frictional coefficients are given in terms of the scattering kernels. It is shown that the general formulation reduces properly to known results in the cases of pure elastic and pure diffuse scattering, respectively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01012886
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  • 7
    Electronic Resource
    Electronic Resource
    On the extension of the Boltzmann equation to include pair correlations (1975)
    Springer
    Journal of statistical physics 13 (1975), S. 379-384 
    Details
    ISSN: 1572-9613
    Keywords: Boltzmann equation ; pair correlations ; kinetic equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The derivation of kinetic equations, including the effects of pair correlations, for a gas of particles interacting via purely repulsive forces is reported. An additional assumption on the form of the two-particle distribution function yields the Enskog equation for a dense hard-sphere gas. However, the true two-particle distribution function is not of this form.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01013114
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  • 8
    Electronic Resource
    Electronic Resource
    Nonequilibrium kinetics: Exact and approximate solutions (1976)
    Springer
    Journal of statistical physics 14 (1976), S. 469-481 
    Details
    ISSN: 1572-9613
    Keywords: Chemical kinetics ; nonequilibrium statistical mechanics ; correlation functions ; Boltzmann equation ; Chapman-Enskog solutions ; inelastic relaxation ; projection operator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The relaxation of an internal state distribution in the presence of an excess of an inert gas is considered. The explicit time dependence of the nonequilibrium contributions to the transition rate coefficients is approximated using the Kapral-Hudson-Ross method. The resulting solution contains cross-correlation terms which do not appear when a single reaction is considered. It is shown that the first term of a perturbation expansion of an exact formal solution gives the Kapral-Hudson-Ross solution for short times, and the Chapman-Enskog solution at long times if there is a wide separation in time scales. The Kapral-Hudson-Ross, Chapman-Enskog, and exact solutions are compared for a two-state, hard-sphere model system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01012846
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  • 9
    Electronic Resource
    Electronic Resource
    Global solutions of the Boltzmann equation on a lattice (1979)
    Springer
    Journal of statistical physics 20 (1979), S. 449-462 
    Details
    ISSN: 1572-9613
    Keywords: Boltzmann equation ; partial differential equations ; global solutions ; mild solutions ; lattice ; semigroup
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The nonlinear Boltzmann equation with a discretized spatial variable is studied in a Banach space of absolutely integrable functions of the velocity variables. Conservation laws and positivity are utilized to extend weak local solutions to a global solution. This is shown to be a strong solution by analytic semigroup techniques.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01011781
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  • 10
    Electronic Resource
    Electronic Resource
    Discretized Boltzmann equation: Lattice limit and non-Maxwellian gases (1979)
    Springer
    Journal of statistical physics 21 (1979), S. 649-657 
    Details
    ISSN: 1572-9613
    Keywords: Boltzmann equation ; finite-difference approximation ; lattice limit ; global solutions ; non-Maxwellian gases
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We continue the study of a discrete model of the Boltzmann equation, in which the spatial variable is replaced by a finite periodic lattice. Using a weak compactness criterion forL 1, the existence of a lattice limit as the lattice spacing tends to zero is proved. The case of unbounded collision kernels (non-Maxwellian gases) is also treated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01107907
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