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1.
O. V. Muzychuk 《Radiophysics and Quantum Electronics》1999,42(9):811-818
We propose a numerical method for analyzing the relaxation of coordinate moments of the Brownian motion of a system described
by a stochastic Liouville equation of the 1st or 2nd order with moderate-order polynomial nonlinearity. Using exact or approximate
recurrence relations for the stationary values, at a certain step, we break the chain of equations for the moments of the
Brownian motion. The evolution of the model probability distribution of coordinates is found from the numerical solution of
the differential equations of relaxation of moments.
This method is used for analyzing the nonstationary probability characteristics of a system with nonlinear rigidity described
by a third-degree polynomial. The relaxation of moments and of the model probability distribution is plotted and tabulated.
The results obtained allow us to draw certain conclusions on the statistical dynamics of the Brownian motion of the systems
studied.
Nizhny Novgorod Architecture and Civil Engineering University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh
Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 9, pp. 922–930, September 1999 相似文献
2.
O. V. Muzychuk 《Radiophysics and Quantum Electronics》2000,43(5):422-431
We consider an oscillator with nonlinear elasticity and nonlinear damping under the action of a Gaussian delta-correlated
random force. The oscillator is treated as a Brownian particle in the corresponding potential profile. We analyze the problem
using the analytical-numerical method based on solving the chain of differential equations for the statistical moments, which
is broken in a certain manner. For the case of nonlinear elasticity, we find the dependence of the relaxation times of the
mean values and variances of both the coordinates and velocities on the system parameters and noise intensity. By analogy,
the relaxation of the probability characteristics of the oscillation amplitude is studied for a system with nonlinear damping.
In both cases, the evolution of the Gaussian or Rayleigh probability distributions is described on the basis of the moment
relaxation.
Nizhny Novgorod Architectural and Construction University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh
Zavedenii, Radiofizika, Vol. 43, No. 4, pp. 468–478, September, 2000. 相似文献
3.
We consider the relaxation of the moments of the coordinates of one-dimensional Brownian motion of particles in a symmetric potential profile under the action of a Gaussian, exponentially correlated random force. An analytical-numerical method of analysis based on obtaining and numerically solving a chain of differential equations for joint cumulants of some functions of particle coordinates and a random force is used. A priori constraints on the intensity and correlation time of noise are not imposed. Numerical procedure is checked by comparison with analytical results, which can be found in the limiting cases of delta-correlated and quasistatic random force. The dependence of the relaxation of the average value and variance on the intensity and spectrum of a random force and the character of the initial distribution of particles is elucidated. In particular, the presence of a variance minimum during distribution relaxation is established. The evolution of the model probability distribution of particle coordinates is constructed on the basis of the moment relaxation. 相似文献
4.
O. V. Muzychuk 《Radiophysics and Quantum Electronics》1998,41(10):874-881
Some probability characteristics of the Brownian motion in a symmetric potential profile with two equilibrium states subjected
to a random force are obtained. Two types of potential fluctuations are considered: the delta-correlated Gaussian noise and
the stochastic telegraph process with Poisson statistics of jumps. The stationary probability distributions of the particle
coordinate are found, and the dependence on the properties of parametric and additive noise is studied. It is shown that nonzero
equilibrium states approach each other and vanish as a result of strong potential fluctuations. Relaxation of intensity and
variance of coordinate fluctuations are studied numerically for the case of delta-correlated random forces. The influence
of the value of parametric and additive noise, system nonlinearity, and initial conditions on the relaxation process is determined.
Architectural and Civil Engineering University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii,
Radiofizika, Vol. 41, No. 10, pp. 1290–1300, October 1998. 相似文献
5.
N. G. Fytas A. Malakis 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,50(1-2):39-43
The three-dimensional bimodal random-field Ising model is studied
via a new finite temperature numerical approach. The methods of
Wang-Landau sampling and broad histogram are implemented in a
unified algorithm by using the N-fold version of the Wang-Landau
algorithm. The simulations are performed in dominant energy
subspaces, determined by the recently developed critical minimum
energy subspace technique. The random-fields are obtained from a
bimodal distribution, that is we consider the discrete
(±Δ) case and the model is studied on cubic lattices with
sizes 4≤L ≤20. In order to extract information for the
relevant probability distributions of the specific heat and
susceptibility peaks, large samples of random-field realizations
are generated. The general aspects of the model's scaling behavior
are discussed and the process of averaging finite-size anomalies
in random systems is re-examined under the prism of the lack of
self-averaging of the specific heat and susceptibility of the
model. 相似文献
6.
The extinction coefficient of atmospheric aerosol particles influences the earth’s radiation balance directly or indirectly,
and it can be determined by the scattering and absorption characteristics of aerosol particles. The problem of estimating
the change of extinction coefficient due to time evolution of bimodal particle size distribution is studied, and two improved
methods for calculating the Brownian coagulation coefficient and the condensation growth rate are proposed, respectively.
Through the improved method based on Otto kernel, the Brownian coagulation coefficient can be expressed simply in powers of
particle volume for the entire particle size regime based on the fitted polynomials of the mean enhancement function. Meanwhile,
the improved method based on Fuchs–Sutugin kernel is developed to obtain the condensation growth rate for the entire particle
size regime. And then, the change of the overall extinction coefficient of bimodal distributions undergoing Brownian coagulation
and condensation can be estimated comprehensively for the entire particle size regime. Simulation experiments indicate that
the extinction coefficients obtained with the improved methods coincide fairly well with the true values, which provide a
simple, reliable, and general method to estimate the change of extinction coefficient for the entire particle size regime
during the bimodal particle dynamic processes. 相似文献
7.
S. Duhot R. Mélin 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,51(2):257-266
The three-dimensional bimodal random-field Ising model
is investigated using the N-fold version of the Wang-Landau
algorithm. The essential energy subspaces are determined by the
recently developed critical minimum energy subspace technique, and
two implementations of this scheme are utilized. The random fields
are obtained from a bimodal discrete (±Δ) distribution,
and we study the model for various values of the disorder strength
Δ, Δ=0.5,1,1.5 and 2, on cubic lattices with
linear sizes L=4–24. We extract information for the probability
distributions of the specific heat peaks over samples of random
fields. This permits us to obtain the phase diagram and present
the finite-size behavior of the specific heat. The question of
saturation of the specific heat is re-examined and it is shown
that the open problem of universality for the random-field Ising
model is strongly influenced by the lack of self-averaging of the
model. This property appears to be substantially depended on the
disorder strength. 相似文献
8.
Marcin Magdziarz Sebastian Orzeł Aleksander Weron 《Journal of statistical physics》2011,145(1):187-203
The earliest model of stock prices based on Brownian diffusion is the Bachelier model. In this paper we propose an extension
of the Bachelier model, which reflects the subdiffusive nature of the underlying asset dynamics. The subdiffusive property
is manifested by the random (infinitely divisible) periods of time, during which the asset price does not change. We introduce
a subdiffusive arithmetic Brownian motion as a model of stock prices with such characteristics. The structure of this process
agrees with two-stage scenario underlying the anomalous diffusion mechanism, in which trapping random events are superimposed
on the Langevin dynamics. We find the corresponding fractional Fokker-Planck equation governing the probability density function
of the introduced process. We construct the corresponding martingale measure and show that the model is incomplete. We derive
the formulas for European put and call option prices. We describe explicit algorithms and present some Monte-Carlo simulations
for the particular cases of α-stable and tempered α-stable distributions of waiting times. 相似文献
9.
Verhulst model with Lévy white noise excitation 总被引:1,自引:0,他引:1
A. A. Dubkov B. Spagnolo 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,65(3):361-367
The transient dynamics of the Verhulst model perturbed by arbitrary non-Gaussian white noise is investigated. Based on the
infinitely divisible distribution of the Lévy process we study the nonlinear relaxation of the population density for three
cases of white non-Gaussian noise: (i) shot noise; (ii) noise with a probability density of increments expressed in terms
of Gamma function; and (iii) Cauchy stable noise. We obtain exact results for the probability distribution of the population
density in all cases, and for Cauchy stable noise the exact expression of the nonlinear relaxation time is derived. Moreover
starting from an initial delta function distribution, we find a transition induced by the multiplicative Lévy noise, from
a trimodal probability distribution to a bimodal probability distribution in asymptotics. Finally we find a nonmonotonic behavior
of the nonlinear relaxation time as a function of the Cauchy stable noise intensity. 相似文献
10.
Based on the model of the Brownian diffusion in an arbitrary two-well potential profile, the main spectral characteristics of the process of noise-induced switchings of a bistable system from one stable condition into another are considered. It is shown that the maximum value and the band of the spectrum of the random switching process are determined by the times of relaxation of the nonequilibrium probability densities of the Brownian particle coordinate to the equilibrium (Boltzmann) distribution.State University, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, Nos. 1–2, pp. 88–93, January–February, 1995. 相似文献
11.
The compositional relaxation in random copolymer systems on a macroscopic scale is considered in theory. A set of diffusion
equations is derived that describes the motion of chains of different composition and then converted into coupled equations
for statistical moments of the compositional distribution. Several ways to solve the closure problem for these equations are
discussed. The simplest is the situation when the shape of the transient compositional distribution can be predicted a priori, for example, a bimodal distribution is kept during interdiffusion of two copolymers that are not very close in composition.
For a general case, it is shown that the cumulant-neglect closure based on the truncation of high-order cumulants is an effective
method to get an approximate solution in terms of the time-dependent local mean composition and its dispersion. This method
is applied to non-homogeneous compatible polymer systems, such as a random copolymer AB of a composition varying in space,
a bilayer of Bernoullian copolymers AB of different composition, and a bilayer of homopolymers A and B, in which an autocatalytic
polymer-analogous reaction A → B takes place, with possibility of the neighbor group effect. It is found that the interdiffusion
can lead to a substantial broadening of the local compositional distribution, which, in turn, accelerates the system dynamics
and promotes chemical reactions. 相似文献
12.
M. Fähnle 《Applied Physics A: Materials Science & Processing》1980,23(3):267-272
For binary alloys with only one sort of magnetic atoms we have calculated, by means of computer simulations, the distribution
of magnetic dipole fields at regular lattice sites and suitably defined interstitial sites for the magnetic ground state of
amorphous ferromagnetic and speromagnetic alloys and crystalline and amorphous spin glasses. Thereby we have considered spatially
random arrangements of atoms and have neglected all magnetic correlations in the case of speromagnets and spin glasses. We
have derived symmetric and isotropic distribution functions, which are fairly well described by Gaussian distributions for
large concentrations of magnetic atoms only. The distribution functions are characterized by their second moments, which are
important for the discussion of NMR and μ+ SR relaxation rates in these materials. 相似文献
13.
Patrick Valageas 《Journal of statistical physics》2009,134(3):589-640
We study the one-dimensional Burgers equation in the inviscid limit for Brownian initial velocity (i.e. the initial velocity
is a two-sided Brownian motion that starts from the origin x=0). We obtain the one-point distribution of the velocity field in closed analytical form. In the limit where we are far from
the origin, we also obtain the two-point and higher-order distributions. We show how they factorize and recover the statistical
invariance through translations for the distributions of velocity increments and Lagrangian increments. We also derive the
velocity structure functions and we recover the bifractality of the inverse Lagrangian map. Then, for the case where the initial
density is uniform, we obtain the distribution of the density field and its n-point correlations. In the same limit, we derive the n-point distributions of the Lagrangian displacement field and the properties of shocks. We note that both the stable-clustering
ansatz and the Press-Schechter mass function, that are widely used in the cosmological context, happen to be exact for this
one-dimensional version of the adhesion model. 相似文献
14.
Yu. E. Kuzovlev 《Journal of Experimental and Theoretical Physics》1997,84(6):1138-1144
This paper examines the relationships that exist between low-frequency fluctuations of the rate of dissipation in nonequilibrium
thermodynamic systems and higher-order multitime statistical moments of equilibrium noise. In particular, it studies the relationships
between internal friction fluctuations in the phonon system being excited and low-frequency fluctuations of Raman scattering
of light in an equilibrium phonon system. We show that both processes are related to strong fluctuations in the phase diffusion
rate and the relaxation of phonon modes generated, in turn, by the exponential instability of the dynamical paths of the system.
Zh. éksp. Teor. Fiz. 111, 2086–2098 (June 1997) 相似文献
15.
We consider the relaxation of rms characteristics of the coordinates of particles during their Brownian motion in a symmetric potential profile under the action of a dichotomous random force. An analytical-numerical method of analysis based on the numerical solution of a chain of differential equations for coordinate moments and joint correlations is used. The calculation procedure is checked using exact results which can be found in the limiting cases of delta-correlated and quasi-static random action. The dependence of the distribution variance and its relaxation time on the intensity and correlation time of noise is elucidated. 相似文献
16.
Two-dimensional loop-erased random walks (LERWs) are random planar curves whose scaling limit is known to be a Schramm-Loewner
evolution SLE
κ
with parameter κ=2. In this note, some properties of an SLE
κ
trace on doubly-connected domains are studied and a connection to passive scalar diffusion in a Burgers flow is emphasised.
In particular, the endpoint probability distribution and winding probabilities for SLE2 on a cylinder, starting from one boundary component and stopped when hitting the other, are found. A relation of the result
to conditioned one-dimensional Brownian motion is pointed out. Moreover, this result permits to study the statistics of the
winding number for SLE2 with fixed endpoints. A solution for the endpoint distribution of SLE4 on the cylinder is obtained and a relation to reflected Brownian motion pointed out. 相似文献
17.
《Physica A》2006,368(2):362-376
The longitudinal relaxation time and the complex dielectric polarizability of rod-like molecules with dipole moment parallel to the long axis in a biaxial nematic liquid crystal are calculated using as model the rotational Brownian motion in a mean field potential so reducing the problem to a solution of a set of linear differential-recurrence relations for statistical moments (the appropriate equilibrium orientational correlation functions). The solution of this set is obtained by matrix continued fractions. Moreover, simple analytic equations (based on the exponential separation of the time scales of the intrawell and overbarrier (interwell) relaxation processes), allowing one to understand the qualitative behavior of the system and accurately predicting the longitudinal complex polarizability for wide range of the barrier height and anisotropy parameters, are proposed. 相似文献
18.
In this paper, we construct an intermediate distribution linking the Gaussian and the Cauchy distribution. We provide the probability density function and the corresponding characteristic function of the intermediate distribution. Because many kinds of distributions have no moment, we introduce weighted moments. Specifically, we consider weighted moments under two types of weighted functions: the cut-off function and the exponential function. Through these two types of weighted functions, we can obtain weighted moments for almost all distributions. We consider an application of the probability density function of the intermediate distribution on the spectral line broadening in laser theory. Moreover, we utilize the intermediate distribution to the problem of the stock market return in quantitative finance. 相似文献
19.
An analytical representation of a random process with independent increments in some space (random walks introduced by Pearson)
is considered. The law of random walk distribution in space is derived from the general representation of stochastic elementary
hops (distribution law of hop probability) using Kadanoff’s concept of the unit increment as one hop. For limited hop laws
and laws of hop distributions with all moments there naturally arises Chandrasekhar’s result that describes ordinary physical
diffusion. For laws of hop distributions without the second and highest moments there also arise known Lévy walks (flights)
sometimes treated as superdiffusion. For the intermediate case, where the distributions of hops have at least the second moment
and not all finite moments (these hops are sometimes called truncated Lévy walks), the asymptotic form of the random walk
distribution was obtained for the first time. The results obtained are compared with the experimental laws known in econophysics.
Satisfactory agreement is observed between the developed theory and the empirical data for insufficiently studied truncated
Lévy walks. 相似文献
20.
Naofumi Muraki 《Communications in Mathematical Physics》1997,183(3):557-570
An example of noncommutative Brownian motion is constructed on the monotone Fock space which is a kind of “Fock space” generated
by all the decreasing finite sequences of positive real numbers. The probability distribution at time associated to this Brownian motion is shown to be the arcsine law normalized to mean 0 and variance t.
Received: 15 March 1996\,/\,Accepted: 2 July 1996 相似文献