5,071 research outputs found
Stochastically perturbed flows: Delayed and interrupted evolution
We present analytical expressions for the time-dependent and stationary
probability distributions corresponding to a stochastically perturbed
one-dimensional flow with critical points, in two physically relevant
situations: delayed evolution, in which the flow alternates with a quiescent
state in which the variate remains frozen at its current value for random
intervals of time; and interrupted evolution, in which the variate is also
re-set in the quiescent state to a random value drawn from a fixed
distribution. In the former case, the effect of the delay upon the first
passage time statistics is analyzed. In the latter case, the conditions under
which an extended stationary distribution can exist as a consequence of the
competition between an attractor in the flow and the random re-setting are
examined. We elucidate the role of the normalization condition in eliminating
the singularities arising from the unstable critical points of the flow, and
present a number of representative examples. A simple formula is obtained for
the stationary distribution and interpreted physically. A similar
interpretation is also given for the known formula for the stationary
distribution in a full-fledged dichotomous flow.Comment: 27 pages; no figures. Submitted to Stochastics and Dynamic
Analytic calculation of energy transfer and heat flux in a one-dimensional system
In the context of the problem of heat conduction in one-dimensional systems,
we present an analytical calculation of the instantaneous energy transfer
across a tagged particle in a one-dimensional gas of equal-mass, hard-point
particles. From this, we obtain a formula for the steady-state energy flux, and
identify and separate the mechanical work and heat conduction contributions to
it. The nature of the Fourier law for the model, and the nonlinear dependence
of the rate of mechanical work on the stationary drift velocity of the tagged
particle, are analyzed and elucidated.Comment: 17 pages including title pag
Wave packet dynamics of the matter wave field of a Bose-Einstein condensate
We show in the framework of a tractable model that revivals and fractional
revivals of wave packets afford clear signatures of the extent of departure
from coherence and from Poisson statistics of the matter wave field in a
Bose-Einstein condensate, or of a suitably chosen initial state of the
radiation field propagating in a Kerr-like medium.Comment: 10 pages, 4 figures, RevTeX
Rate coefficients for rovibrational transitions in H_2 due to collisions with He
We present quantum mechanical and quasiclassical trajectory calculations of
cross sections for rovibrational transitions in ortho- and para-H_2 induced by
collisions with He atoms. Cross sections were obtained for kinetic energies
between 10^-4 and 3 eV, and the corresponding rate coefficients were calculated
for the temperature range 100<T<4000 K. Comparisons are made with previous
calculations.Comment: 21 pages, 2 figures, AAS, eps
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