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  • Articles  (6)
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  • Articles: DFG German National Licenses  (6)
  • Boltzmann equation
  • Springer  (6)
  • American Association for the Advancement of Science
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  • Physics  (6)
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  • Articles  (6)
  • Other Sources
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  • Articles: DFG German National Licenses  (6)
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  • Springer  (6)
  • American Association for the Advancement of Science
  • American Meteorological Society
  • American Physical Society
  • Blackwell Publishing Ltd
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  • 2020-2022
  • 1990-1994  (6)
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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
    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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  • 3
    Electronic Resource
    Electronic Resource
    Relaxation and transport in FCHC lattice gases (1994)
    Springer
    Journal of statistical physics 74 (1994), S. 1085-1115 
    Details
    ISSN: 1572-9613
    Keywords: Lattice gas automata ; transport coefficients ; non-detailed balance ; staggered invariants ; Boltzmann equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract FCHC lattice gases are the basic models for studying flow problems in three-dimensional systems. This paper presents a self-contained theoretical analysis and some computer simulations of such lattice gases, extended to include an arbitrary number of rest particles, with special emphasis on non-semi-detailed balance (NSDB) models. The special FCHC lattice symmetry guarantees isotropy of the Navier-Stokes equations, and enumerates the 12 spurious conservation laws (staggered momenta). The kinetic theory is based on the mean field approximation or the nonlinear Boltzmann equation. It is shown how calculation of the eigenvalues of the linearized Boltzmann equation offers a simple alternative to the Chapman-Enskog method or the multi-time-scale methods for calculating transport coefficients and relaxation rates. The simulated values for the speed of sound in NSDB models slightly disagree with the Boltzmann prediction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02188218
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  • 4
    Electronic Resource
    Electronic Resource
    Two linearization procedures for the Boltzmann equation in ak=0 Robertson-Walker space-time (1994)
    Springer
    Journal of statistical physics 76 (1994), S. 1415-1437 
    Details
    ISSN: 1572-9613
    Keywords: Boltzmann equation ; Robertson-Walker space-times ; linearization procedures ; asymptotic kinetic equations ; convergence to equilibrium ; dust model ; hydrodynamic description
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract It is the aim of this paper to describe two different linearization procedures for the Boltzmann equation in ak=0 Robertson-Walker space-time. These procedures are discussed with a view to obtaining an asymptotic form of the Boltzmann equation for the late stages of cosmic expansion where the behavior appropriate to a nonrelativistic gas is encountered. Using the asymptotic kinetic equations, a necessary and sufficient condition is formulated under which every small perturbation of the equilibrium distribution function, either classical or relativistic, decays to zero as time goes on. The same condition can be extracted from each of two linearization procedures, and in this sense a comparison is made of these approaches which reveals mutual agreement. Also, applying an asymptotic theory of the Einstein-Boltzmann system, we show that the final state of a gas is dust (i.e., a fluid with zero temperature and pressure). Comparison with the predictions of the Eckart fluid model is briefly presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187069
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  • 5
    Electronic Resource
    Electronic Resource
    Observation of quantum particles on a large space-time scale (1994)
    Springer
    Journal of statistical physics 77 (1994), S. 259-309 
    Details
    ISSN: 1572-9613
    Keywords: Lorentz gas ; Boltzmann equation ; Landau equation ; Van Hove limit ; weak-coupling limit ; random potential ; quantum trajectories
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A quantum particle observed on a sufficiently large space-time scale can be described by means of classical particle trajectories. The joint distribution for large-scale multiple-time position and momentum measurements on a nonrelativistic quantum particle moving freely inR v is given by straight-line trajectories with probabilities determined by the initial momentum-space wavefunction. For large-scale toroidal and rectangular regions the trajectories are geodesics. In a uniform gravitational field the trajectories are parabolas. A quantum counting process on free particles is also considered and shown to converge in the large-space-time limit to a classical counting process for particles with straight-line trajectories. If the quantum particle interacts weakly with its environment, the classical particle trajectories may undergo random jumps. In the random potential model considered here, the quantum particle evolves according to a reversible unitary one-parameter group describing elastic scattering off static randomly distributed impurities (a quantum Lorentz gas). In the large-space-time weak-coupling limit a classical stochastic process is obtained with probability one and describes a classical particle moving with constant speed in straight lines between random jumps in direction. The process depends only on the ensemble value of the covariance of the random field and not on the sample field. The probability density in phase space associated with the classical stochastic process satisfies the linear Boltzmann equation for the classical Lorentz gas, which, in the limith→0, goes over to the linear Landau equation. Our study of the quantum Lorentz gas is based on a perturbative expansion and, as in other studies of this system, the series can be controlled only for small values of the rescaled time and for Gaussian random fields. The discussion of classical particle trajectories for nonrelativistic particles on a macroscopic spacetime scale applies also to relativistic particles. The problem of the spatial localization of a relativistic particle is avoided by observing the particle on a sufficiently large space-time scale.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02186843
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  • 6
    Electronic Resource
    Electronic Resource
    On diffuse reflection at the boundary for the Boltzmann equation and related equations (1994)
    Springer
    Journal of statistical physics 77 (1994), S. 1051-1077 
    Details
    ISSN: 1572-9613
    Keywords: Boltzmann equation ; BGK equation ; diffuse reflection ; boundary value problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The paper considers diffuse reflection at the boundary with nonconstant boundary temperature and unbounded velocities. The solutions obtained are proved to conserve mass at the boundary. After a preliminary study of the collisionless case, the main results obtained are existence for the Boltzmann equation in a “DiPerna-Lions framework” with the above boundary conditions in a bounded measure sense, and existence together with uniqueness for the BGK equation with Maxwellian diffusion on the boundary in anL ∞ framework.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02183152
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