3,807 research outputs found
Transient rectification of Brownian diffusion with asymmetric initial distribution
In an ensemble of non-interacting Brownian particles, a finite systematic
average velocity may temporarily develop, even if it is zero initially. The
effect originates from a small nonlinear correction to the dissipative force,
causing the equation for the first moment of velocity to couple to moments of
higher order. The effect may be relevant when a complex system dissociates in a
viscous medium with conservation of momentum
Dark matter density profiles: A comparison of nonextensive theory with N-body simulations
Density profiles of simulated galaxy cluster-sized dark matter haloes are
analysed in the context of a recently introduced nonextensive theory of dark
matter and gas density distributions. Nonextensive statistics accounts for
long-range interactions in gravitationally coupled systems and is derived from
the fundamental concept of entropy generalisation. The simulated profiles are
determined down to radii of ~1% of R_200. The general trend of the relaxed,
spherically averaged profiles is accurately reproduced by the theory. For the
main free parameter kappa, measuring the degree of coupling within the system,
and linked to physical quantities as the heat capacity and the polytropic index
of the self-gravitating ensembles, we find a value of -15. The significant
advantage over empirical fitting functions is provided by the physical content
of the nonextensive approach.Comment: 6 pages, 3 figures, accepted for publication in A&
Enlighting the roads of tomorrow:exploring road users' preferences of road lighting along highways in the Netherlands
Generalized Fokker-Planck equation, Brownian motion, and ergodicity
Microscopic theory of Brownian motion of a particle of mass in a bath of
molecules of mass is considered beyond lowest order in the mass ratio
. The corresponding Langevin equation contains nonlinear corrections to
the dissipative force, and the generalized Fokker-Planck equation involves
derivatives of order higher than two. These equations are derived from first
principles with coefficients expressed in terms of correlation functions of
microscopic force on the particle. The coefficients are evaluated explicitly
for a generalized Rayleigh model with a finite time of molecule-particle
collisions. In the limit of a low-density bath, we recover the results obtained
previously for a model with instantaneous binary collisions. In general case,
the equations contain additional corrections, quadratic in bath density,
originating from a finite collision time. These corrections survive to order
and are found to make the stationary distribution non-Maxwellian.
Some relevant numerical simulations are also presented
Anderson localization as a parametric instability of the linear kicked oscillator
We rigorously analyse the correspondence between the one-dimensional standard
Anderson model and a related classical system, the `kicked oscillator' with
noisy frequency. We show that the Anderson localization corresponds to a
parametric instability of the oscillator, with the localization length
determined by an increment of the exponential growth of the energy. Analytical
expression for a weak disorder is obtained, which is valid both inside the
energy band and at the band edge.Comment: 7 pages, Revtex, no figures, submitted to Phys. Rev.
An "All Possible Steps" Approach to the Accelerated Use of Gillespie's Algorithm
Many physical and biological processes are stochastic in nature.
Computational models and simulations of such processes are a mathematical and
computational challenge. The basic stochastic simulation algorithm was
published by D. Gillespie about three decades ago [D.T. Gillespie, J. Phys.
Chem. {\bf 81}, 2340, (1977)]. Since then, intensive work has been done to make
the algorithm more efficient in terms of running time. All accelerated versions
of the algorithm are aimed at minimizing the running time required to produce a
stochastic trajectory in state space. In these simulations, a necessary
condition for reliable statistics is averaging over a large number of
simulations. In this study I present a new accelerating approach which does not
alter the stochastic algorithm, but reduces the number of required runs. By
analysis of collected data I demonstrate high precision levels with fewer
simulations. Moreover, the suggested approach provides a good estimation of
statistical error, which may serve as a tool for determining the number of
required runs.Comment: Accepted for publication at the Journal of Chemical Physics. 19
pages, including 2 Tables and 4 Figure
Vlasov Equation In Magnetic Field
The linearized Vlasov equation for a plasma system in a uniform magnetic
field and the corresponding linear Vlasov operator are studied. The spectrum
and the corresponding eigenfunctions of the Vlasov operator are found. The
spectrum of this operator consists of two parts: one is continuous and real;
the other is discrete and complex. Interestingly, the real eigenvalues are
infinitely degenerate, which causes difficulty solving this initial value
problem by using the conventional eigenfunction expansion method. Finally, the
Vlasov equation is solved by the resolvent method.Comment: 15 page
1D quantum models with correlated disorder vs. classical oscillators with coloured noise
We perform an analytical study of the correspondence between a classical
oscillator with frequency perturbed by a coloured noise and the one-dimensional
Anderson-type model with correlated diagonal disorder. It is rigorously shown
that localisation of electronic states in the quantum model corresponds to
exponential divergence of nearby trajectories of the classical random
oscillator. We discuss the relation between the localisation length for the
quantum model and the rate of energy growth for the stochastic oscillator.
Finally, we examine the problem of electron transmission through a finite
disordered barrier by considering the evolution of the classical oscillator.Comment: 23 pages, LaTeX fil
Enhanced quantum tunnelling induced by disorder
We reconsider the problem of the enhancement of tunnelling of a quantum
particle induced by disorder of a one-dimensional tunnel barrier of length ,
using two different approximate analytic solutions of the invariant imbedding
equations of wave propagation for weak disorder. The two solutions are
complementary for the detailed understanding of important aspects of numerical
results on disorder-enhanced tunnelling obtained recently by Kim et al. (Phys.
rev. B{\bf 77}, 024203 (2008)). In particular, we derive analytically the
scaled wavenumber -threshold where disorder-enhanced tunnelling of an
incident electron first occurs, as well as the rate of variation of the
transmittance in the limit of vanishing disorder. Both quantities are in good
agreement with the numerical results of Kim et al. Our non-perturbative
solution of the invariant imbedding equations allows us to show that the
disorder enhances both the mean conductance and the mean resistance of the
barrier.Comment: 10 page
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