共查询到20条相似文献,搜索用时 31 毫秒
1.
T.?Bauer F.?H?fling T.?Munk E.?Frey T.?Franosch 《The European physical journal. Special topics》2010,189(1):103-118
We investigate the dynamics of a single tracer particle performing Brownian motion in a two-dimensional course of randomly
distributed hard obstacles. At a certain critical obstacle density, the motion of the tracer becomes anomalous over many decades
in time, which is rationalized in terms of an underlying percolation transition of the void space. In the vicinity of this
critical density the dynamics follows the anomalous one up to a crossover time scale where the motion becomes either diffusive
or localized. We analyze the scaling behavior of the time-dependent diffusion coefficient D(t) including corrections to scaling. Away from the critical density, D(t) exhibits universal hydrodynamic long-time tails both in the diffusive as well as in the localized phase. 相似文献
2.
In this paper we study the asymptotics of the probability distribution function for a certain model of freely decaying passive scalar transport. In particular we prove rigorous large n, or semiclassical, asymptotics for the eigenvalues of the covariance of a fractional Brownian motion. Using these asymptotics, along with some standard large deviations results, we are able to derive tight asymptotics for the rate of decay of the tails of the probability density for a generalization of the Majda model of scalar intermittency originally due to Vanden Eijnden. We are also able to derive asymptotically tight estimates for the closely related problem of small L2 ball probabilities for a fractional Brownian motion. 相似文献
3.
A. M. Berezhkovskii Yu. A. Makhnovskii R. A. Suris 《Journal of statistical physics》1989,57(1-2):333-346
The statistical characteristics of a spatial region visited by a spherical Brownian particle during timet (Wiener sausage) are investigated. The expectation value and dispersion of this quantity are obtained for a space of arbitrary dimension. In the one-dimensional case the distribution of probability density and the moments of any order are determined for this quantity. 相似文献
4.
In several studies of actin-based cellular motility, the barbed ends of actin filaments have been observed to be attached
to moving obstacles. Filament growth in the presence of such filament-obstacle interactions is studied via Brownian dynamics
simulations of a three-dimensional energy-based model. We find that with a binding energy greater than 24k
B
T and a highly directional force field, a single actin filament is able to push a small obstacle for over a second at a speed
of half of the free filament elongation rate. These results are consistent with experimental observations of plastic beads
in cell extracts. Calculations of an external force acting on a single-filament-pushed obstacle show that for typical in vitro free-actin concentrations, a 3pN pulling force maximizes the obstacle speed, while a 4pN pushing force almost stops the obstacle.
Extension of the model to treat beads propelled by many filaments suggests that most of the propulsive force could be generated
by attached filaments. 相似文献
5.
《Physica A》1996,225(2):221-234
We study the effect of a field on the span of a particle diffusing on a line, i.e., the length covered by a Brownian particle which moves on a line for time t in the presence of a constant field. This is the one-dimensional analog of the Wiener sausage volume. Exact expressions are found for the probability density for the span together with the first two moments. Our results indicate that at very short times the dominant effect is diffusion while at very long times the field plays the dominant role. 相似文献
6.
Tom Kennedy 《Journal of statistical physics》2008,131(5):803-819
We simulate several models of random curves in the half plane and numerically compute the stochastic driving processes that
produce the curves through the Loewner equation. Our models include models whose scaling limit is the Schramm-Loewner evolution
(SLE) and models for which it is not. We study several tests of whether the driving process is Brownian motion, as it is for
SLE. We find that testing only the normality of the process at a fixed time is not effective at determining if the random
curves are an SLE. Tests that involve the independence of the increments of Brownian motion are much more effective. We also
study the zipper algorithm for numerically computing the driving function of a simple curve. We give an implementation of
this algorithm which runs in a time O(N
1.35) rather than the usual O(N
2), where N is the number of points on the curve. 相似文献
7.
We consider the solution of the equation r(t) = W(r(t)), r(0) = r
0 > 0 where W(⋅) is a fractional Brownian motion (f.B.m.) with the Hurst exponent α∈ (0,1). We show that for almost all realizations of
W(⋅) the trajectory reaches in finite time the nearest equilibrium point (i.e. zero of the f.B.m.) either to the right or to
the left of r
0, depending on whether W(r
0) is positive or not. After reaching the equilibrium the trajectory stays in it forever. The problem is motivated by studying
the separation between two particles in a Gaussian velocity field which satisfies a local self-similarity hypothesis. In contrast
to the case when the forcing term is a Brownian motion (then an analogous statement is a consequence of the Markov property
of the process) we show our result using as the principal tools the properties of time reversibility of the law of the f.B.m.,
see Lemma 2.4 below, and the small ball estimate of Molchan, Commun. Math. Phys.
205 (1999) 97–111. 相似文献
8.
We consider the trajectoryQ
M(t) of a Brownian particle of massM in an ideal gas of identical particles of mass 1 and of density 1 in equilibrium at inverse temperature 1 (the dynamics is uniform motion plus elastic collisions with the Brownian particle). Our theory, in dimension one, describes a variety of limiting processes — containing the Wiener process and the Ornstein-Uhlenbeck process — forA
–1/2
Q
M(A)(At) depending on the asymptotic behaviour ofM(A). Part of the theory is hypothetical while another part relies upon known results. We also prove that, ifA
1/2+M(A)A, thenA
–1/2
Q
M(A) (At) converges to a Wiener process whose variance is known from papers of Sinai-Soloveichik and of the present authors. 相似文献
9.
T. Nishiyama S. Yasuda T. Inamuro 《The European physical journal. Special topics》2009,171(1):145-149
The deformation and breakup processes of a particle-cluster aggregate under shear flows are investigated by the two-phase
lattice Boltzmann method. In the simulation the particle is modeled by a hard droplet with large viscosity and strong surface
tension. The van der Waals attraction force is taken into account for the interaction between the particles. Also, the Brownian
motion is considered for nano-particles. Two important dimensionless parameters are introduced in order to classify calculated
results. One is the ratio of fluid force to the maximum inter-particle force, Y, and the other is the Péclet number which is the ratio of the rate of diffusion by a shear flow to the rate of diffusion
by Brownian motion. It is found that Y is the key factor in dispersion and that the Brownian motion retards the dispersion. 相似文献
10.
This paper reports on studies of the behaviour of a Brownian walker that diffuses in a bidimensional non-homogeneous medium constituted by immobile spherical adsorbing obstacles residing in a continuous solvent. Results show that the probability that the random walker is adsorbed, for a given adsorbing interaction potential between the walker and the surface, depends only on the full adsorbing surface S in the reaction medium, and does not show any appreciable dependence on the size of the adsorbing obstacles. Also, the diffusion coefficient of the random walker depends only on the value of S (for a given adsorbed interaction) if the adsorption energy is large enough. In contrast, when the adsorption energy between the walker and the surface of the adsorbing obstacles is zero, the diffusion coefficient decays exponentially with the volume fraction occupied for the obstacles. The efficiency of the walker to visit all obstacles in the simulation cell depends strongly on the concentration of obstacles and on the adsorbing interaction energy, decreasing quickly to zero with an increase in these parameters. 相似文献
11.
Krzysztof Burdzy Robert Hołyst Peter March 《Communications in Mathematical Physics》2000,214(3):679-703
We consider a model with a large number N of particles which move according to independent Brownian motions. A particle which leaves a domain D is killed; at the same time, a different particle splits into two particles. For large N, the particle distribution density converges to the normalized heat equation solution in D with Dirichlet boundary conditions. The stationary distributions converge as N→∞ to the first eigenfunction of the Laplacian in D with the same boundary conditions.
Received: 11 November 1999 / Accepted: 19 May 2000 相似文献
12.
Different initial and boundary value problems for the equation of vibrations of rods (also called Fresnel equation) are solved
by exploiting the connection with Brownian motion and the heat equation. The equation of vibrations of plates is considered
and the case of circular vibrating disks C
R
is investigated by applying the methods of planar orthogonally reflecting Brownian motion within C
R
. The analysis of the fractional version (of order ν) of the Fresnel equation is also performed and, in detail, some specific cases, like ν=1/2, 1/3, 2/3, are analyzed. By means of the fundamental solution of the Fresnel equation, a pseudo-process F(t), t>0 with real sign-varying density is constructed and some of its properties examined. The composition of F with reflecting Brownian motion B yields the law of biquadratic heat equation while the composition of F with the first passage time T
t
of B produces a genuine probability law strictly connected with the Cauchy process. 相似文献
13.
In non-equilibrium statistical mechanics, the entropy production is used to describe flowing in or pumping out of the entropy
of a time-dependent system. Even if a system is in a steady state (invariant in time), Prigogine suggested that there should
be a positive entropy production if it is open. In 1979, the first author of this paper and Qian Min-Ping discovered that
the entropy production describes the irreversibility of stationary Markov chains, and proved the circulation decomposition
formula of the entropy production. They also obtained the entropy production formula for drifted Brownian motions on Euclidean
space R
n
(see a report without proof in the Proc. 1st World Congr. Bernoulli Soc.). By the topological triviality of R
n
, there is no discrete circulation associated to the diffusion processes on $R^n$. In this paper, the entropy production formula
for stationary drifted Brownian motions on a compact Riemannian manifold M is proved. Furthermore, the entropy production is decomposed into two parts – in addition to the first part analogous to
that of a diffusion process on R
n
, some discrete circulations intrinsic to the topology of M appear! The first part is called the hidden circulation and is then explained as the circulation of a lifted process on M×S
1 around the circle S
1. The main result of this paper is the circulation decomposition formula which states that the entropy production of a stationary
drifted Brownian motion on M is a linear sum of its circulations around the generators of the fundamental group of M and the hidden circulation.
Received: 4 November 1998 / Accepted: 7 April 1999 相似文献
14.
We study the rolling motion of a small solid sphere on a fibrillated rubber substrate in an external field in the presence
of a Gaussian noise. From the nature of the drift and the evolution of the displacement fluctuation of the ball, it is evident
that the rolling is controlled by a complex non-linear friction at a low velocity and a low noise strength (K), but by a linear kinematic friction at a high velocity and a high noise strength. This transition from a non-linear to a
linear friction control of motion can be discerned from another experiment in which the ball is subjected to a periodic asymmetric
vibration in conjunction with a random noise. Here, as opposed to that of a fixed external force, the rolling velocity decreases
with the strength of the noise suggesting a progressive fluidization of the interface. A state (K) and rate (V) dependent friction model is able to explain both the evolution of the displacement fluctuation as well as the sigmoidal
variation of the drift velocity with K. This research sets the stage for studying friction in a new way, in which it is submitted to a noise and then its dynamic
response is studied using the tools of statistical mechanics. Although more works would be needed for a fuller realization
of the above-stated goal, this approach has the potential to complement direct measurements of friction over several decades
of velocities and other state variables. It is striking that the non-Gaussian displacement statistics as observed with the
stochastic rolling is similar to that of a colloidal particle undergoing Brownian motion in contact with a soft microtubule. 相似文献
15.
Jianping Jiang 《Journal of statistical physics》2014,156(1):177-188
Wiener measures are measures on curves that are derived from two-dimensional Brownian motion. We prove a relationship between two types of Wiener measures: measures on paths with fixed starting point (say the origin \(0\) ) and fixed time duration (say \(1\) ); and measures on paths with fixed endpoints (say \(0\) and \(i\) ). The relationship is that if we take a curve from the first type, weight it by a suitable power of the distance to the endpoint of the curve and then apply the conformal map that takes the endpoint to \(i\) , then we get the curve from the second type. 相似文献
16.
The multiplayer dynamics of a football game is analyzed to unveil self-similarities in the time evolution of player and ball positioning. Temporal fluctuations in both the team-turf boundary and the ball location are uncovered to follow the rules of fractional Brownian motion with a Hurst exponent of H ~ 0.7. The persistence time below which self-similarity holds is found to be several tens of seconds, implying a characteristic time scale that governs far-from-equilibrium motion on a playing field. 相似文献
17.
A mathematical model to predict large enhancement of thermal conductivity of nanofluids by considering the Brownian motion is proposed. The effect of the Brownian motion on the flow and heat transfer characteristics is examined. The computations were done for various types of nanoparticles such as CuO, Al2O3, and ZnO dispersed in a base fluid (water), volume fraction of nanoparticles ? in the range of 1 % to 6 % at a fixed Reynolds number Re = 450 and nanoparticle diameter dnp = 30 nm. Our results demonstrate that Brownian motion could be an important factor that enhances the thermal conductivity of nanofluids. Nanofluid of Al2O3 is observed to have the highest Nusselt number Nu among other nanofluids types, while nanofluid of ZnO nanoparticles has the lowest Nu. Effects of the square cylinder on heat transfer characteristics are significant with considering Brownian motion. Enhancement in the maximum value of Nu of 29 % and 26 % are obtained at the lower and the upper walls of the channel, respectively, by considering the Brownian effects, with square cylinder, compared with that in the case without considering the Brownian motion. On the other hand, results show a marked improvement in heat transfer compared to the base fluid, this improvement is more pronounced on the upper wall for higher ?. 相似文献
18.
S. Alessio L. Briatore R. Cremonini E Ferrero C. Giraud A. Longhetto O. Morra R. Purini 《Il Nuovo Cimento C》1995,18(6):603-627
Summary This paper presents the results of laboratory experiments designed to simulate some basic process of large-scale flows interacting
with obstacles, also in order to better understand details of subsynoptic disturbances that are created in the lee of large
topographic features. For this event, the experimental facilities of the Istituto di Cosmogeofisica of Consiglio Nazionale
delle Ricerche (CNR) were exploited, consisting in a hydraulic channel mounted on a rotating platform, along whose longitudinal
axis a hemispherical obstacle was towed at various speeds. Because of the conversion of potential vorticity, the experimental
results showed, as expected, the existence of a region of anticyclonic circulation, located above the obstacle; however, also
an asymmetric pattern of positive vorticity located downwind of the obstacle did appear, which cannot be interpreted in terms
of simple quasi-geostrophic inviscid dynamics. This behaviour is not surprising, if one considers that the real flow near
the obstacle could hardly ever match the conditions of inviscid quasi-geostrophy (Ro≪1,E∼0), but was similar to that characterising the zone close to the surface of the obstacle, where inertial and viscous effects
are not negligible. Finally, in order to investigate the importance of these effects on the interaction processes, simple
numerical and analytical models were applied, by which the consistency of some laboratory simulations, chosen among the most
significant ones, could be compared. 相似文献
19.
R. F. Streater 《Journal of statistical physics》1997,88(1-2):447-469
We consider a large number of particles on a one-dimensional latticel
Z in interaction with a heat particle; the latter is located on the bond linking the position of the particle to the point
to which it jumps. The energy of a single particle is given by a potentialV(x), x∈Z. In the continuum limit, the classical version leads to Brownian motion with drift. A quantum version leads to a local drift
velocity which is independent of the applied force. Both these models obey Einstein's relation between drift, diffusion, and
applied force. The system obeys the first and second laws of thermodynamics, with the time evolution given by a pair of coupled
non linear heat equations, one for the density of the Brownian particles and one for the heat occupation number; the equation
for a tagged Brownian particle can be written as a stochastic differential equation. 相似文献
20.
Motivated by discrete directed polymers in one space and one time dimension, we construct a continuum directed random polymer that is modeled by a continuous path interacting with a space-time white noise. The strength of the interaction is determined by an inverse temperature parameter β, and for a given β and realization of the noise the path is a Markov process. The transition probabilities are determined by solutions to the one-dimensional stochastic heat equation. We show that for all β>0 and for almost all realizations of the white noise the path measure has the same Hölder continuity and quadratic variation properties as Brownian motion, but that it is actually singular with respect to the standard Wiener measure on C([0,1]). 相似文献