2,082 research outputs found
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&
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
Non-universal dynamics of dimer growing interfaces
A finite temperature version of body-centered solid-on-solid growth models
involving attachment and detachment of dimers is discussed in 1+1 dimensions.
The dynamic exponent of the growing interface is studied numerically via the
spectrum gap of the underlying evolution operator. The finite size scaling of
the latter is found to be affected by a standard surface tension term on which
the growth rates depend. This non-universal aspect is also corroborated by the
growth behavior observed in large scale simulations. By contrast, the
roughening exponent remains robust over wide temperature ranges.Comment: 11 pages, 7 figures. v2 with some slight correction
Poisson-noise induced escape from a metastable state
We provide a complete solution of the problems of the probability
distribution and the escape rate in Poisson-noise driven systems. It includes
both the exponents and the prefactors. The analysis refers to an overdamped
particle in a potential well. The results apply for an arbitrary average rate
of noise pulses, from slow pulse rates, where the noise acts on the system as
strongly non-Gaussian, to high pulse rates, where the noise acts as effectively
Gaussian
Validation of the Jarzynski relation for a system with strong thermal coupling: an isothermal ideal gas model
We revisit the paradigm of an ideal gas under isothermal conditions. A moving piston performs work on an ideal gas in a container that is strongly coupled to a heat reservoir. The thermal coupling is modeled by stochastic scattering at the boundaries. In contrast to recent studies of an adiabatic ideal gas with a piston [R.C. Lua and A.Y. Grosberg, J. Phys. Chem. B 109, 6805 (2005); I. Bena et al., Europhys. Lett. 71, 879 (2005)], the container and piston stay in contact with the heat bath during the work process. Under this condition the heat reservoir as well as the system depend on the work parameter lambda and microscopic reversibility is broken for a moving piston. Our model is thus not included in the class of systems for which the nonequilibrium work theorem has been derived rigorously either by Hamiltonian [C. Jarzynski, J. Stat. Mech. (2004) P09005] or stochastic methods [G.E. Crooks, J. Stat. Phys. 90, 1481 (1998)]. Nevertheless the validity of the nonequilibrium work theorem is confirmed both numerically for a wide range of parameter values and analytically in the limit of a very fast moving piston, i.e., in the far nonequilibrium regime
Diffusion at constant speed in a model phase space
We reconsider the problem of diffusion of particles at constant speed and
present a generalization of the Telegrapher process to higher dimensional
stochastic media (), where the particle can move along directions.
We derive the equations for the probability density function using the
``formulae of differentiation'' of Shapiro and Loginov. The model is an
advancement over similiar models of photon migration in multiply scattering
media in that it results in a true diffusion at constant speed in the limit of
large dimensions.Comment: Final corrected version RevTeX, 6 pages, 1 figur
Evolution equation for a model of surface relaxation in complex networks
In this paper we derive analytically the evolution equation of the interface
for a model of surface growth with relaxation to the minimum (SRM) in complex
networks. We were inspired by the disagreement between the scaling results of
the steady state of the fluctuations between the discrete SRM model and the
Edward-Wilkinson process found in scale-free networks with degree distribution
for [Pastore y Piontti {\it et al.},
Phys. Rev. E {\bf 76}, 046117 (2007)]. Even though for Euclidean lattices the
evolution equation is linear, we find that in complex heterogeneous networks
non-linear terms appear due to the heterogeneity and the lack of symmetry of
the network; they produce a logarithmic divergency of the saturation roughness
with the system size as found by Pastore y Piontti {\it et al.} for .Comment: 9 pages, 2 figure
Generalised Ornstein-Uhlenbeck processes
We solve a physically significant extension of a classic problem in the
theory of diffusion, namely the Ornstein-Uhlenbeck process [G. E. Ornstein and
L. S. Uhlenbeck, Phys. Rev. 36, 823, (1930)]. Our generalised
Ornstein-Uhlenbeck systems include a force which depends upon the position of
the particle, as well as upon time. They exhibit anomalous diffusion at short
times, and non-Maxwellian velocity distributions in equilibrium. Two approaches
are used. Some statistics are obtained from a closed-form expression for the
propagator of the Fokker-Planck equation for the case where the particle is
initially at rest. In the general case we use spectral decomposition of a
Fokker-Planck equation, employing nonlinear creation and annihilation operators
to generate the spectrum which consists of two staggered ladders.Comment: 24 pages, 2 figure
Analytically solvable model of a driven system with quenched dichotomous disorder
We perform a time-dependent study of the driven dynamics of overdamped
particles which are placed in a one-dimensional, piecewise linear random
potential. This set-up of spatially quenched disorder then exerts a dichotomous
varying random force on the particles. We derive the path integral
representation of the resulting probability density function for the position
of the particles and transform this quantity of interest into the form of a
Fourier integral. In doing so, the evolution of the probability density can be
investigated analytically for finite times. It is demonstrated that the
probability density contains both a -singular contribution and a
regular part. While the former part plays a dominant role at short times, the
latter rules the behavior at large evolution times. The slow approach of the
probability density to a limiting Gaussian form as time tends to infinity is
elucidated in detail.Comment: 18 pages, 5 figure
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