共查询到20条相似文献,搜索用时 31 毫秒
1.
Ramachandran S Sunil Kumar PB Pagonabarraga I 《The European physical journal. E, Soft matter》2006,20(2):151-158
We present a Lattice-Boltzmann method for simulating self-propelling (active) colloidal particles in two dimensions. Active
particles with symmetric and asymmetric force distribution on their surface are considered. The velocity field generated by
a single active particle, changing its orientation randomly, and the different time scales involved are characterized in detail.
The steady-state speed distribution in the fluid, resulting from the activity, is shown to deviate considerably from the equilibrium
distribution. 相似文献
2.
P. H. Chavanis M. Lemou 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,59(2):217-247
We develop the kinetic theory of point vortices in two-dimensional
hydrodynamics and illustrate the main results of the
theory with numerical simulations. We first consider the evolution of
the system “as a whole” and show that the evolution of the
vorticity profile is due to resonances between different orbits of the
point vortices. The evolution stops when the profile of angular
velocity becomes monotonic even if the system has not reached the
statistical equilibrium state (Boltzmann distribution). In that case,
the system remains blocked in a quasi stationary state with a non
standard distribution. We also study the relaxation of a test vortex
in a steady bath of field vortices. The relaxation of the test vortex
is described by a Fokker-Planck equation involving a diffusion term
and a drift term. The diffusion coefficient, which is proportional to
the density of field vortices and inversely proportional to the shear,
usually decreases rapidly with the distance. The drift is proportional
to the gradient of the density profile of the field vortices and is
connected to the diffusion coefficient by a generalized Einstein
relation. We study the evolution of the tail of the distribution
function of the test vortex and show that it has a front structure. We
also study how the temporal auto-correlation function of the position
of the test vortex decreases with time and find that it usually
exhibits an algebraic behavior with an exponent that we compute
analytically. We mention analogies with other systems with long-range
interactions. 相似文献
3.
Angsula Ghosh 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,62(3):271-275
We discuss thermalization of a test particle schematized as
a harmonic oscillator and coupled to a Boltzmann heat bath of finite size
and with a finite bandwidth for the frequencies of its particles.
We find that complete thermalization only occurs when the test particle frequency is within a certain range of the bath particle
frequencies, and for a certain range of mass ratios between the test particle and the bath particles. These results have implications
for the study of classical and quantum behaviour of high-frequency nanomechanical resonators. 相似文献
4.
We study relaxation towards a stationary out-of-equilibrium state by analyzing a one-dimensional stochastic process followed
by a particle accelerated by an external field and propagating through a thermal bath. The effect of collisions is described
within one-dimensional formulation of Boltzmann’s kinetic theory. We present analytical solutions for the Maxwell gas and
for the very hard particle model. The exponentially fast relaxation of the velocity distribution towards the stationary form
is demonstrated. In the reference frame moving with constant drift velocity the hydrodynamic diffusive mode is shown to govern
the distribution in the position space. We show that the exact value of the diffusion coefficient for any value of the field
is correctly predicted by the Green-Kubo autocorrelation formula generalized to the stationary state. 相似文献
5.
P. H. Chavanis 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,70(3):413-433
We discuss the distribution of the gravitational force
created by a Poissonian distribution of field sources (stars,
galaxies,...) in different dimensions of space d. In d = 3, when
the particle number N →+∞, it is given by a Lévy
law called the Holtsmark distribution. It presents an algebraic
tail for large fluctuations due to the contribution of the nearest
neighbor. In d = 2, for large but finite values of N, it is given
by a marginal Gaussian distribution intermediate between Gaussian
and Lévy laws. It presents a Gaussian core and an algebraic
tail. In d = 1, it is exactly given by the Bernouilli distribution
(for any particle number N) which becomes Gaussian for N ≫
1. Therefore, the dimension d = 2 is critical regarding the
statistics of the gravitational force. We generalize these results
for inhomogeneous systems with arbitrary power-law density profile
and arbitrary power-law force in a d-dimensional universe. 相似文献
6.
We develop a kinetic theory of systems with long-range interactions taking collective effects and spatial inhomogeneity into account. Starting from the Klimontovich equation and using a quasilinear approximation, we derive a Lenard–Balescu-type kinetic equation written in angle–action variables. We confirm the result obtained by Heyvaerts [Heyvaerts, Mon. Not. R. Astron. Soc. 407, 355 (2010)] who started from the Liouville equation and used the BBGKY hierarchy truncated at the level of the two-body distribution function (i.e., neglecting three-body correlations). When collective effects are ignored, we recover the Landau-type kinetic equation obtained in our previous papers [P.H. Chavanis, Physica A 377, 469 (2007); J. Stat. Mech., P05019 (2010)]. We also consider the relaxation of a test particle in a bath of field particles. Its stochastic motion is described by a Fokker–Planck equation written in angle–action variables. We determine the diffusion tensor and the friction force by explicitly calculating the first and second order moments of the increment of action of the test particle from its equations of motion, taking collective effects into account. This generalizes the expressions obtained in our previous works. We discuss the scaling with N of the relaxation time for the system as a whole and for a test particle in a bath. 相似文献
7.
A model for self-propulsion of a colloidal particle--the osmotic motor--immersed in a dispersion of "bath" particles is presented. The nonequilibrium concentration of bath particles induced by a surface chemical reaction creates an osmotic pressure imbalance on the motor causing it to move. The ratio of the speed of reaction to that of diffusion governs the bath particle distribution which is employed to calculate the driving force on the motor, and from which the self-induced osmotic velocity is determined. For slow reactions, the self-propulsion is proportional to the reaction velocity. When surface reaction dominates over diffusion the osmotic velocity cannot exceed the diffusive speed of the bath particles. Implications of these features for different bath particle volume fractions and motor sizes are discussed. Theoretical predictions are compared with Brownian dynamics simulations. 相似文献
8.
9.
Our interest goes to the behavior of a tracer particle, accelerated by a constant and uniform external field, when the energy injected by the field is redistributed through collision to a bath of unaccelerated particles. A non equilibrium steady state is thereby reached. Solutions of a generalized Boltzmann-Lorentz equation are analyzed analytically, in a versatile framework that embeds the majority of tracer-bath interactions discussed in the literature. These results??mostly derived for a one dimensional system??are successfully confronted to those of three independent numerical simulation methods: a direct iterative solution, Gillespie algorithm, and the Direct Simulation Monte Carlo technique. We work out the diffusion properties as well as the velocity tails: large v, and either large ?v, or v in the vicinity of its lower cutoff whenever the velocity distribution is bounded from below. Particular emphasis is put on the cold bath limit, with scatterers at rest, which plays a special role in our model. 相似文献
10.
Eli Barkai 《Journal of statistical physics》2004,115(5-6):1537-1565
To obtain further insight on possible power law generalizations of Boltzmann equilibrium concepts, we consider stochastic collision models. The models are a generalization of the Rayleigh collision model, for a heavy one dimensional particle M interacting with ideal gas particles with a mass m<<M. Similar to previous approaches we assume elastic, uncorrelated, and impulsive collisions. We let the bath particle velocity distribution function to be of general form, namely we do not postulate a specific form of power-law equilibrium. We show, under certain conditions, that the velocity distribution function of the heavy particle is Lévy stable, the Maxwellian distribution being a special case. We demonstrate our results with numerical examples. The relation of the power law equilibrium obtained here to thermodynamics is discussed. In particular we compare between two models: a thermodynamic and an energy scaling approaches. These models yield insight into questions like the meaning of temperature for power law equilibrium, and into the issue of the universality of the equilibrium (i.e., is the width of the generalized Maxwellian distribution functions obtained here, independent of coupling constant to the bath). 相似文献
11.
We integrate the lattice Boltzmann method (LBM) and immersed boundary method (IBM) to capture the coupling between a rigid boundary surface and the hydrodynamic response of an enclosed particle laden fluid. We focus on a rigid box filled with a Newtonian fluid where the drag force based on the slip velocity at the wall and settling particles induces the interaction. We impose an external harmonic oscillation on the system boundary and found interesting results in the sedimentation behavior. Our results reveal that the sedimentation and particle locations are sensitive to the boundary walls oscillation amplitude and the subsequent changes on the enclosed flow field. Two different particle distribution analyses were performed and showed the presence of an agglomerate structure of particles. Despite the increase in the amplitude of wall motion, the turbulence level of the flow field and distribution of particles are found to be less in quantity compared to the stationary walls. The integrated LBM-IBM methodology promised the prospect of an efficient and accurate dynamic coupling between a non-compliant bounding surface and flow field in a wide-range of systems. Understanding the dynamics of the fluid-filled box can be particularly important in a simulation of particle deposition within biological systems and other engineering applications. 相似文献
12.
13.
With the PDPA (Phase Doppler Particle Analyzer) measurement technology, the probability distributions of particle impact and
lift-off velocities on bed surface and the particle velocity distributions at different heights are detected in a wind tunnel.
The results show that the probability distribution of impact and lift-off velocities of sand grains can be expressed by a
log-normal function, and that of impact and lift-off angles complies with an exponential function. The mean impact angle is
between 28° and 39°, and the mean lift-off angle ranges from 30° to 44°. The mean lift-off velocity is 0.81–0.9 times the
mean impact velocity. The proportion of backward-impacting particles is 0.05–0.11, and that of backward-entrained particles
ranges from 0.04 to 0.13. The probability distribution of particle horizontal velocity at 4 mm height is positive skew, the
horizontal velocity of particles at 20 mm height varies widely, and the variation of the particle horizontal velocity at 80
mm height is less than that at 20 mm height. The probability distribution of particle vertical velocity at different heights
can be described as a normal function.
Supported by the National Natural Science Foundation of China (Grant No. 10532030) and the National Basic Research Program
of China (Grant No. G2000048702) 相似文献
14.
We study the deterministic dynamics of non‐interacting classical gas particles confined to a one‐dimensional box as a pedagogical toy model for the relaxation of the Boltzmann distribution towards equilibrium. Hard container walls alone induce a uniform distribution of the gas particles at large times. For the relaxation of the velocity distribution we model the dynamical walls by independent scatterers. The Markov property guarantees a stationary but not necessarily thermal velocity distribution for the gas particles at large times. We identify the conditions for physical walls where the stationary velocity distribution is the Maxwell distribution. For our numerical simulation we represent the wall particles by independent harmonic oscillators. The corresponding dynamical map for oscillators with a fixed phase (Fermi–Ulam accelerator) is chaotic for mesoscopic box dimensions. 相似文献
15.
Vladimir K. Mukhomorov 《Journal of nanoparticle research》2011,13(11):6113-6120
One-dimensional and quasi one-dimensional electron structures are of applied interest. For example, in one-dimensional (nano-capillary)
electroneutral metal–ammonia systems, exotic electron properties are observed, such as a drastic (by several orders of magnitude)
drop of the electrical conductivity with decreasing temperature, which resembles the superconductivity transition. In this
work, we studied the possibility of one-dimensional filamentary polaron nano-structure in insulating media. It was established
that the interpolaron pair potential for large polarons offers attraction properties. It is known that attraction between
the particles may alter the collective properties of a many-particle system. We demonstrated that the initially uniform distribution
of the particles becomes unstable in one-dimensional systems and may change to the nonuniform structured state under specific
conditions imposed on the temperature, particle concentration, and parameters of the pair interpolaron potential. The possibility
of existence of a periodic one-dimensional structure of small-amplitude polarons that is imposed on the polaron uniform distribution
is estimated in terms of temperature and concentration criteria. A dispersion relation between existence of the one-dimensional
polaron structure and translational velocity of the polarons is found. The upper limit of the translational velocity when
the periodic contribution to the distribution vanishes is determined. Periodic contribution disappears virtually stepwise
as the velocity approaches its critical value. It is shown that this specific polaron–polaron interaction leads to results
that are in principal different from those observed for classical Coulomb electron interaction. 相似文献
16.
R.K. Varma 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2002,18(2):211-218
It has been shown earlier [3,6] that matter waves which are known to lie typically in the range of a few angstrom, can also
manifest in the macrodomain with a wave length of a few centimeters, for electrons propagating along a magnetic field. This
followed from the predictions of a probability amplitude theory by the author [1,2] in the classical macrodomain of the dynamics
of charged particles in a magnetic field. It is shown in this paper that this case constitutes only a special case of a generic
situation whereby composite systems such as atoms and molecules in their highly excited internal states, can exhibit matter
wave manifestation in macro and mesodomains, in one-dimensional scattering. The wave length of these waves is determined,
not by the mass of the particle as in the case of the de Broglie wave, but by the frequency ω, of the classical orbital motion
of the internal state in the correspondence limit, and is given by a nonquantal expression, λ = 2πv/ω, v being the velocity of the particle. For the electrons in a magnetic field the frequency corresponds to the gyrofrequency,
Ω and the nonquantal wave length is given by λ = 2πv
|| /Ω; v
|| being the velocity of electrons along the magnetic field.
Received 29 September 2001 / Received in final form 23 May 2002 Published online 19 July 2002 相似文献
17.
We present an insightful ‘derivation’ of the Langevin equation and the fluctuation dissipation theorem in the specific context
of a heavier particle moving through an ideal gas of much lighter particles. The Newton’s law of motion (mx = F) for the heavy particle reduces to a Langevin equation (valid on a coarser time-scale) with the assumption that the lighter
gas particles follow a Boltzmann velocity distribution. Starting from the kinematics of the random collisions we show that
(1) the average force 〈F〉 ∞ −x and (2) the correlation function of the fluctuating forceη = F — 〈F〉 is related to the strength of the average force.
Deceased 相似文献
18.
We investigate the settling of heavy particles in a steady, two-dimensional random velocity field, and find instances in which particle suspension occurs. This leads to a bimodal velocity distribution that may explain some apparently conflicting results reported in the literature. The bimodal distribution is typically smeared out by a time dependence of the ambient flow but, if the time variation is slow, the settling rates of some particles will be as well. The resulting broadbanded velocity distribution of the settling particles will have significance for processes such as rain drop formation, in which the spread of particle velocities affects the statistics of particle collisions. 相似文献
19.
M. Treiber D. Helbing 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,68(4):607-618
This contribution presents a derivation of the steady-state distribution of velocities and
distances of driven particles on a onedimensional periodic ring, using a Fokker-Planck formalism. We will compare two different
situations: (i) symmetrical interaction forces fulfilling Newton’s law
of “actio = reactio” and (ii) asymmetric, forwardly directed interactions as, for example
in vehicular traffic. Surprisingly, the steady-state velocity and distance distributions
for asymmetric interactions and driving terms agree with the equilibrium distributions of
classical many-particle systems with symmetrical interactions, if the system is large enough.
This analytical result is confirmed by computer simulations and
establishes the possibility of approximating the steady state
statistics in driven many-particle systems by Hamiltonian systems. Our finding is also
useful to understand the various departure time distributions of queueing systems as a possible
effect of interactions among the elements in the respective queue [Physica A 363, 62 (2006)]. 相似文献
20.
É. Falcon S. Fauve C. Laroche 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,7(2):183-186
We report experimental results on the behavior of an ensemble of inelastically colliding particles, excited by a vibrated
piston in a vertical cylinder. When the particle number is increased, we observe a transition from a regime where the particles
have erratic motions (“granular gas”) to a collective behavior where all the particles bounce like a nearly solid body. In
the gas-like regime, we measure the density of particles as a function of the altitude and the pressure as a function of the
number N of particles. The atmosphere is found to be exponential far enough from the piston, and the “granular temperature”, T, dependence on the piston velocity, V, is of the form , where is a decreasing function of N. This may explain previous conflicting numerical results.
Received 1 February 1999 相似文献