Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    The Broadwell model for initial values inL + 1 (ℝ) (1984)
    Springer
    Communications in mathematical physics 93 (1984), S. 341-353 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The Cauchy problem for the Broadwell model is shown to have a global mild solution for initial data inL + 1 (ℝ) with smallL 1-norm, and a local solution for arbitrary initial data inL + 1 (ℝ). For data which are small inL 1(ℝ), the asymptotic behaviour of the solutions ast→∞ is determined. Moreover, it is shown that a global solution exists for all initial values inL + 1 (ℝ) with finite entropy if theH-Theorem holds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01258533
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    The Boltzmann equation: Global existence for a rare gas in an infinite vacuum (1984)
    Springer
    Communications in mathematical physics 95 (1984), S. 217-226 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Solutions of the Boltzmann equation are proved to exist, globally in time, under conditions that include the case of a finite volume of gas in an infinite vacuum when the mean free path of the gas is large enough. It is also proved, as might be expected in this case, that the density of the gas at each point in space goes to zero as time goes to infinity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01468142
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Global validity of the Boltzmann equation for a two-dimensional rare gas in vacuum (1986)
    Springer
    Communications in mathematical physics 105 (1986), S. 189-203 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider a system ofN hard disks in ℝ2 in the Boltzmann-Grad limit (i.e.N → ∞,d ↘ 0,N·d → λ−1〉0, whered is the diameter of the disks). If λ is sufficiently small and if the joint distribution densities factorize at time zero, we prove that the time-evolved one-particle distribution converges for all times to the solution of the Boltzmann equation with the same initial datum.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01211098
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    A boundary value problem for the two dimensional Broadwell model (1988)
    Springer
    Communications in mathematical physics 114 (1988), S. 687-698 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that a certain boundary value problem for the steady two-dimensional Broadwell model on a rectangle has a solution. The boundary conditions specify the ingoing particle densities on each side of the rectangle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01229460
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    Measure solutions of the steady Boltzmann equation in a slab (1991)
    Springer
    Communications in mathematical physics 142 (1991), S. 285-296 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that the steady Boltzmann equation in a slab [0,a] has solutionsx→μ x such that the ingoing boundary measuresμ 0∣{ξ〉0} andμ α∣{ξ〈0} can be prescribed a priori. The collision kernel is truncated such that particles with smallx-component of the velocity have a reduced collision rate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02102064
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    Collision operators as generators of Markov processes and their spectra (1979)
    Springer
    Journal of statistical physics 20 (1979), S. 303-316 
    Details
    ISSN: 1572-9613
    Keywords: Brownian motion ; Markov processes ; collision and transport operators ; Fokker-Planck equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The Markovian description of diffusion in velocity space involves a semigroup, which because of detailed balance is conveniently interpreted in a weightedL 2-space. The collision operatorC, defined by the corresponding generator, is positive semidefinite in this space. For a jump process and a continuous process we obtain the collision operators of the linear Boltzmann and Fokker-PIanck equations, respectively. If in the latter case the friction tensor has a nonvanishing limit asυ → ∞, the spectrum ofC is discrete. The Fourier-transformed transport operatorT k=C+ik·v is studied as a holomorphic family of sectorial operators. In the stated Fokker-Planck example, the spectrum ofT k remains discrete for arbitrary k.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01011939
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    On information-processing abilities of chaotic dynamical systems (1992)
    Springer
    Journal of statistical physics 66 (1992), S. 549-561 
    Details
    ISSN: 1572-9613
    Keywords: Information processing ; chaotic dynamical systems ; Lorenz attractor
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A mechanism is suggested to explain the information processing abilities of simple natural brains, which, by experimental evidence, display behavior like chaotic dynamical systems while at rest. The Lorenz system of equations is dealt with as a case study, and a comparison of the suggested mechanism with the standard theory of neural networks is made.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01060080
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    Collision Integrals for Attractive Potentials (1999)
    Springer
    Journal of statistical physics 95 (1999), S. 633-649 
    Details
    ISSN: 1572-9613
    Keywords: attractive power potential ; scattering angle ; collision integral ; coagulation integral
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Motivated by previous discussions of particle interactions under the Manev potential U(r)=−α/r−ε/r 2, we construct the collision integrals for attractive potentials U(r) satisfying the condition U(r) r 2→−ε as r→0 with ε≥0. For ε=0, we obtain a Boltzmann-type integral with a collision law allowing “spiral” interactions and nonunique correspondence between impact parameter and scattering angle. For ε〉0, an additional Smoluchowski-type coagulation integral arises. All these integrals are derived and possible applications are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004543325973
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    On nonlinear stationary half-space problems in discrete kinetic theory (1988)
    Springer
    Journal of statistical physics 52 (1988), S. 885-896 
    Details
    ISSN: 1572-9613
    Keywords: Boltzmann equation ; steady discrete velocity models ; half-space problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We show that every steady discrete velocity model of the Boltzmann equation on the real line,ξ i·(d/dx)f i=C i(f), which satisfies anH-theorem and for which allξ i≠0, has solutions on the half-line (0, ∞) which take prescribed non-negativef i(O) ifξ i〉0 and approach a certain manifold of Maxwellians asx→∞. Such solutions give the density distribution in a Knudsen boundary layer in the discrete velocity case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01019733
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    A random discrete velocity model and approximation of the Boltzmann equation (1993)
    Springer
    Journal of statistical physics 70 (1993), S. 773-792 
    Details
    ISSN: 1572-9613
    Keywords: Discrete velocity models ; Boltzmann equation ; simulation methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An approximation procedure for the Boltzmann equation based on random choices of collision pairs from a fixed velocity set and on discrete velocity models is designed. In a suitable limit, the procedure is shown to converge to the time-discretized and spatially homogeneous Boltzmann equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01053594
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...