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  • Articles  (63)
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  • Boltzmann equation
  • Springer  (63)
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  • Articles  (63)
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  • Springer  (63)
  • American Association for the Advancement of Science
  • American Meteorological Society
  • American Physical Society
  • Blackwell Publishing Ltd
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  • 1
    Electronic Resource
    Electronic Resource
    Boltzmann equation approach to the N-body problem with masses varying according to the Eddington-Jeans law (1994)
    Springer
    Celestial mechanics and dynamical astronomy 59 (1994), S. 201-208 
    Details
    ISSN: 1572-9478
    Keywords: Variable mass ; Boltzmann equation ; Galaxies ; Star clusters
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study special aspects of the N-body problem with masses varying according to the Eddington-Jeans law with powers n=2 and 3. Our main result is that a particular set of variables can be found that allows one to write the pertinent Boltzmann and Poisson equations in a fashion similar to that corresponding to the usual fixed mass situation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00692871
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  • 2
    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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  • 3
    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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  • 4
    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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  • 5
    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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  • 6
    Electronic Resource
    Electronic Resource
    Derivation of Slip boundary conditions for the Navier-Stokes system from the Boltzmann equation (1989)
    Springer
    Journal of statistical physics 54 (1989), S. 829-857 
    Details
    ISSN: 1572-9613
    Keywords: Boltzmann equation ; Knudsen layer ; Navier-Stokes equations ; slip boundary conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Rarefied gas flow behavior is usually described by the Boltzmann equation, the Navier-Stokes system being valid when the gas is less rarefied. Slip boundary conditions for the Navier-Stokes equations are derived in a rigorous and systematic way from the boundary condition at the kinetic level (Boltzmann equation). These slip conditions are explicitly written in terms of asymptotic behavior of some linear half-space problems. The validity of this analysis is established in the simple case of the Couette flow, for which it is proved that the right boundary conditions are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01019777
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  • 7
    Electronic Resource
    Electronic Resource
    Nonlinear transport in a dilute binary mixture of mechanically different particles (1994)
    Springer
    Journal of statistical physics 75 (1994), S. 797-816 
    Details
    ISSN: 1572-9613
    Keywords: Boltzmann equation ; Maxwell molecules ; nonlinear transport ; mutual diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The hierarchy of moments of the Boltzmann equation for a binary mixture of mechanically different Maxwell molecules is exactly solved. The solution corresponds to a nonequilibrium homogeneous steady state generated by an external force that accelerates particles of each species (or “color”) along opposite directions. As a consequence, macroscopic fluxes are induced in spite of the absence of concentration gradients. Explicit expressions for the fluxes of mass and momentum as functions of the field strength, the mass ratio, the molar fractions, and the interaction constant ratio are obtained. In particular, the color conductivity coefficient reduces to the mutual diffusion coefficient in the zero-field limit. Some physically interesting limiting cases are discussed. The maximum-entropy method is used to construct an approximate velocity distribution function from the exact knowledge of the mass and momentum fluxes. This distribution is exact up to second order in the color field and also in the limit of large color field.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02186744
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  • 8
    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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  • 9
    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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  • 10
    Electronic Resource
    Electronic Resource
    Lorentz gas shear viscosity via nonequilibrium molecular dynamics and Boltzmann's equation (1985)
    Springer
    Journal of statistical physics 38 (1985), S. 973-988 
    Details
    ISSN: 1572-9613
    Keywords: Boltzmann equation ; nonequilibrium ; viscosity ; molecular dynamics ; irreversibility
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract When nonequilibrium molecular dynamics is used to impose isothermal shear on a two-body periodic system of hard disks or spheres, the equations of motion reduce to those describing a Lorentz gas under shear. In this shearing Lorentz gas a single particle moves, isothermally, through a spatially periodic shearing crystal of infinitely massive scatterers. The curvilinear trajectories are calculated analytically and used to measure the dilute Lorentz gas viscosity at several strain rates. Simulations and solutions of Boltzmann's equation exhibit shear thinning resembling that found inN-body nonequilibrium simulations. For the three-dimensional Lorentz gas we obtained an exact expression for the viscosity which is valid at all strain rates. In two dimensions this is not possible due to the anisotropy of the scattering.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01010425
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