86,149 research outputs found
The Kolmogorov-Sinai Entropy for Dilute Gases in Equilibrium
We use the kinetic theory of gases to compute the Kolmogorov-Sinai entropy
per particle for a dilute gas in equilibrium. For an equilibrium system, the KS
entropy, h_KS is the sum of all of the positive Lyapunov exponents
characterizing the chaotic behavior of the gas. We compute h_KS/N, where N is
the number of particles in the gas. This quantity has a density expansion of
the form h_KS/N = a\nu[-\ln{\tilde{n}} + b + O(\tilde{n})], where \nu is the
single-particle collision frequency and \tilde{n} is the reduced number density
of the gas. The theoretical values for the coefficients a and b are compared
with the results of computer simulations, with excellent agreement for a, and
less than satisfactory agreement for b. Possible reasons for this difference in
b are discussed.Comment: 15 pages, 2 figures, submitted to Phys. Rev.
Global Continua of Positive Equilibria for some Quasilinear Parabolic Equation with a Nonlocal Initial Condition
This paper is concerned with a quaslinear parabolic equation including a
nonlinear nonlocal initial condition. The problem arises as equilibrium
equation in population dynamics with nonlinear diffusion. We make use of global
bifurcation theory to prove existence of an unbounded continuum of positive
solutions
Model Study of Three-Body Forces in the Three-Body Bound State
The Faddeev equations for the three-body bound state with two- and three-body
forces are solved directly as three-dimensional integral equation. The
numerical feasibility and stability of the algorithm, which does not employ
partial wave decomposition is demonstrated. The three-body binding energy and
the full wave function are calculated with Malfliet-Tjon-type two-body
potentials and scalar Fujita-Miyazawa type three-body forces. The influence of
the strength and range of the three-body force on the wave function, single
particle momentum distributions and the two-body correlation functions are
studied in detail. The extreme case of pure three-body forces is investigated
as well.Comment: 25 pages, 15 postscript figure
Three-Body Scattering without Partial Waves
The Faddeev equation for three-body scattering at arbitrary energies is
formulated in momentum space and directly solved in terms of momentum vectors
without employing a partial wave decomposition. In its simplest form the
Faddeev equation for identical bosons is a three-dimensional integral equation
in five variables, magnitudes of relative momenta and angles. The elastic
differential cross section, semi-exclusive d(N,N') cross sections and total
cross sections of both elastic and breakup processes in the intermediate energy
range up to about 1 GeV are calculated based on a Malfliet-Tjon type potential,
and the convergence of the multiple scattering series is investigated in every
case. In general a truncation in the first or second order in the two-body
t-matrix is quite insufficient.Comment: 3 pages, Oral Contribution to the 19th European Few-Body Conference,
Groningen Aug. 23-27, 200
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