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1.
This research focuses on numerically investigating the self-diffusion coefficient and velocity autocorrelation function (VACF) of a dissipative particle dynamics (DPD) fluid as a function of the conservative interaction strength. Analytic solutions to VACF and self-diffusion coefficients in DPD were obtained by many researchers in some restricted cases including ideal gases, without the account of conservative force. As departure from the ideal gas conditions are accentuated with increasing the relative proportion of conservative force, it is anticipated that the VACF should gradually deviate from its normally expected exponentially decay. This trend is confirmed through numerical simulations and an expression in terms of the conservative force parameter, density and temperature is proposed for the self-diffusion coefficient. As it concerned the VACF, the equivalent Langevin equation describing Brownian motion of particles with a harmonic potential is adapted to the problem and reveals an exponentially decaying oscillatory pattern influenced by the conservative force parameter, dissipative parameter and temperature. Although the proposed model for obtaining the self-diffusion coefficient with consideration of the conservative force could not be verified due to computational complexities, nonetheless the Arrhenius dependency of the self-diffusion coefficient to temperature and pressure permits to certify our model over a definite range of DPD parameters. 相似文献
2.
Robert M. Mazo 《Journal of statistical physics》1969,1(1):89-99
The molecular theory of the Brownian motion of heavy particles in a homogeneous solvent of light particles is extended to cover the case of interactions between the Brownian particles. This will have physical effects in the concentration dependence of the Brownian particle self-diffusion coefficient. A density expansion for the Brownian particle friction coefficient is derived, and an approximation permitting the first density correction to be calculated is suggested.This work, part of research supported by NSF Grant GP-8497, was done under the tenure of a National Science Foundation Senior Postdoctoral Fellowship, and of a sabbatical leave granted by the University of Oregon. 相似文献
3.
The formalism, developed in two earlier papers, for the dynamics of interacting Brownian particles is applied to a system of charged spherical particles in solution. Memory-type transport equations are derived for the propagators of collective and self-diffusion. The memory function for collective diffusion can be related, in the hydrodynamic limit, to the viscosity of the “fluid” of Brownian particles. The memory functions are calculated for a Debye-Hückel system, from an experimentally determined static structure factor S(k), and for an overdamped one-component plasma (OCP). In the two latter cases satisfactory agreement is found with dynamical light scattering results on solutions of polystyrene spheres; in particular, the deviation of the dynamical structure factor from a simple exponential decay can be related to memory effects. With regard to self-diffusion the velocity autocorrelation function, the mean square displacement of one particle and from it the self-diffusion coefficient Ds are calculated. Using S(k) for an actual system, is obtained, where D0 is the free diffusion constant. The calculations on the basis of the overdamped OCP-model show that the dynamical properties of the experimentally investigated systems of charged polystyrene spheres can be described by this model for a wide range of scattering angles. 相似文献
4.
Dramatic change of the self-diffusions of colloidal ellipsoids by hydrodynamic interactions in narrow channels 下载免费PDF全文
《中国物理 B》2019,(7)
The self-diffusion problem of Brownian particles under the constraint of quasi-one-dimensional(q1 D) channel has raised wide concern.The hydrodynamic interaction(HI) plays an important role in many practical problems and two-body interactions remain dominant under q1D constraint.We measure the diffusion coefficient of individual ellipsoid when two ellipsoidal particles are close to each other by video-microscopy measurement.Meanwhile, we obtain the numerical simulation results of diffusion coefficient using finite element software.We find that the self-diffusion coefficient of the ellipsoid decreases exponentially with the decrease of their mutual distance X when X X_0, where X_0 is the maximum distance of the ellipsoids to maintain their mutual influence, X_0 and the variation rate are related to the aspect ratio p = a/b.The mean squared displacement(MSD) of the ellipsoids indicates that the self-diffusion appears as a crossover region, in which the diffusion coefficient increases as the time increases in the intermediate time regime, which is proven to be caused by the spatial variations affected by the hydrodynamic interactions.These findings indicate that hydrodynamic interaction can significantly affect the self-diffusion behavior of adjacent particles and has important implications to the research of microfluidic problems in blood vessels and bones, drug delivery, and lab-on-chip. 相似文献
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In this paper, the analytical solutions of Schr¨odinger equation for Brownian motion in a double well potential are acquired by the homotopy analysis method and the Adomian decomposition method. Double well potential for Brownian motion is always used to obtain the solutions of Fokker–Planck equation known as the Klein–Kramers equation, which is suitable for separation and additive Hamiltonians. In essence, we could study the random motion of Brownian particles by solving Schr¨odinger equation. The analytical results obtained from the two different methods agree with each other well. The double well potential is affected by two parameters, which are analyzed and discussed in details with the aid of graphical illustrations. According to the final results, the shapes of the double well potential have significant influence on the probability density function. 相似文献
7.
A kinetic equation for the motion of a particle of arbitrary size and mass through a moderately dense gas is derived and discussed. The “long-time tail” of the velocity correlation function is calculated and found to agree with existing results. For a Brownian particle, the theory gives the Stokes-Einstein law for the self-diffusion coefficient, with the shear viscosity given by its Enskog value. 相似文献
8.
The method of molecular dynamics is used to study the dynamic behavior of a nonideal system of particles interacting through screened Coulomb potential. The behavior of the self-diffusion coefficient of particles as a function of the nonideality parameter is investigated. The conditions of the crystallization of such a system are discussed, as well as the possibility of using the crystallization criterion, based on the dynamic characteristics of the system. 相似文献
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10.
研究具有幂律记忆性的带反馈耦合布朗马达的定向输运现象, 引入分数阶理论, 建立了带反馈的分数阶耦合布朗马达模型, 利用分数阶差分法求得模型数值解并分析了模型参数对合作定向输运性质的影响. 仿真结果表明, 系统的记忆性通过影响带反馈的棘齿势的打开和闭合而影响粒子的定向输运, 即当系统的阶数在较小的范围内, 系统的记忆性会使带反馈的棘齿势的开关频率增加, 从而增大定向流速; 当系统其他参数(势垒高度、噪声强度等)固定时, 输运速度随着阶数的变化出现广义随机共振现象. 相似文献
11.
GERHARD NÄGELE ADOLFO J. BANCHIO MARKUS KOLLMANN RAPHAËL PESCHÉ 《Molecular physics》2013,111(18):2921-2933
The static and dynamic properties of 2- and 3-dimensional dispersions of strongly interacting colloidal spheres are examined. Quasi-2-dimensional dispersions of particles interacting by long range electrostatic and dipolar magnetic forces, respectively, are investigated using Brownian dynamics computer simulations with hydrodynamic interactions included. The dynamics of 3-dimensional bulk dispersions of charge-stabilized and neutral colloidal spheres is determined from a fully self-consistent mode-coupling scheme. For systems with long range repulsive interactions the dynamic correlation functions are shown to obey dynamic scaling in terms of a characteristic relaxation time related to the mean particle distance. Hydrodynamic interactions introduce a second characteristic length scale, and they lead to more restricted scaling behaviour with an enhancement of self-diffusion and, for 2-dimensional systems, to the divergence of the short-time collective diffusion coefficient. As a consequence of dynamic scaling, a dynamic criterion for the onset of colloidal freezing related to long-time self-diffusion is shown to be equivalent to a static freezing criterion related to the 2- and 3-dimensional static structure factors. Alternative freezing criteria are given in terms of the long-time and the mean collective diffusion coefficients. 相似文献
12.
Brownian motion of the particles with repulsive interaction is investigated. When the potential condition is satisfied, the eigenvalue problem of interaction Fokker-Planck equation
under certain conditions can be transformed to that of a many-particle Schrödinger equation. Using the Green's function method,
we obtain the effective single-variable Fokker-Planck equation in the low density limit. We find that the diffusion of coupled Brownian particles in quenched disorder media is also anomalous in 2D. The Mittag-Leffler relaxation of pancake vortices is investigated by fractional Fokker-Planck equation. 相似文献
13.
Y. Zhang B. H. Lin J. C. Chen 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,53(4):481-485
Brownian particles moving in a spatially asymmetric but periodic
potential (ratchet), with an external load force and connected to an
alternating hot and cold reservoir, are modeled as a microscopic heat
engine, referred to as the Brownian heat engine. The heat flow via both the
potential energy and the kinetic energy of the particles are considered
simultaneously. The forward and backward particle currents are determined
using an Arrhenius' factor. Expressions for the power output and efficiency
are derived analytically. The maximum power output and efficiency are
calculated. It is expounded that the Brownian heat engine is always
irreversible and its efficiency cannot approach the efficiency ηC of
the Carnot heat engine even in quasistatic limit. The influence of the main
parameters such as the load, the barrier height of the potential, the
asymmetry of the potential and the temperature ratio of the heat reservoirs
on the performance of the Brownian heat engine is discussed in detail. It is
found that the Brownian heat engines may be controlled to operate in
different regions through variation of some parameters. 相似文献
14.
Szamel G 《Physical review letters》2004,93(17):178301
Using memory-function formalism we show that in sheared colloidal suspensions the fluctuation-dissipation theorem for self-diffusion, i.e., Einstein's relation between self-diffusion and mobility tensors, is violated and propose a new way to measure this violation in Brownian dynamics simulations. We derive mode-coupling expressions for the tagged particle friction tensor and for an effective, shear-rate dependent temperature. 相似文献
15.
We use the system-plus-reservoir approach to study the dynamics of a system composed of two independent Brownian particles. We present an extension of the well-known model of a bath of oscillators which is capable of inducing an effective coupling between the two particles depending on the choice made for the spectral function of the bath oscillators. The coupling is nonlinear in the variables of interest, and an exponential dependence on these variables is imposed in order to guarantee the translational invariance of the model if the two particles are not subject to any external potential. The effective equations of motion for the particles are obtained by the Laplace transform method, and, besides recovering all the local dynamical properties for each particle, we end up with an effective interaction potential between them. We explicitly analyze one of its possible forms. 相似文献
16.
Porion P Al-Mukhtar M Faugère AM Meyer S Delville A 《The European physical journal. E, Soft matter》2003,12(Z1):S17-S20
The structure of aqueous dispersion of charged anisotropic nano-composites (synthetic Laponite clays) have been studied by NMR and numerical simulations based on a multi-scale statistical analysis have been used to interpret the mobility of the confined water molecule diffusing within dense Laponite aqueous dispersions (29-52% w/w) prepared by uniaxial compression. Firstly, the lineshape detected by NMR quadrupolar spectroscopy of the counterions ((23)Na or (7)Li) exhibits a large residual splitting Delta nu which is the fingerprint of the macroscopic nematic ordering of the anisotropic particles. Secondly, these results are also confirmed by the anisotropy of the self-diffusion tensor of the water molecule measured by (1)H Pulsed Gradient Spin Echo NMR. This self-diffusion anisotropy increases with the suspension density. Thirdly, the multi-scale statistical analysis of the water mobility bridges the gap between the time-scale (ps) accessible by Molecular Dynamics simulations and the time-scale (micros) accessible by Brownian Dynamics, leading to macroscopic behaviour comparable with PGSE-NMR data measurements. 相似文献
17.
WANG Hai-Yan 《理论物理通讯》2007,48(5):859-863
The transport properties of coupled Brownian motors in rocking ratchet are investigated via solving Langevin equation. By means of velocity, diffusion coefficient, and their ratio (Peclet number), different features from a single particle have been found. In the regime of low-to-moderate D, the average velocity of elastically coupled Brownian motors is larger than that of a single Brownian particles; the Peclet number of elastically coupled Brownian motors is peaked functions of intensity of noise D but the Peclet number of a single Brownian motor decreases monotonously with the increase of a single Brownian motor. The results exhibit an interesting cooperative behavior between coupled particles subjected to a rocking force, which can generate directed transport with low randomness or high transport coherence in symmetrical periodic potential. 相似文献
18.
DING ZeMin CHEN LinGen & SUN FengRui Postgraduate School Naval University of Engineering Wuhan China 《中国科学:物理学 力学 天文学(英文版)》2010,(5)
This paper has studied the thermodynamic performance of a thermal Brownian heat pump,which consists of Brownian particles moving at a periodic sawtooth potential with external forces and contacting with the alternating hot and cold reservoirs along the space coordinate.The heat flows driven by both potential and kinetic energies are taken into account.The analytical expressions for the heating load,coefficient of performance(COP) and power input of the Brownian heat pump are derived and the performance char... 相似文献
19.
Stochastic resonance, reverse-resonance, and resonant activation induced by a multi-state noise 总被引:1,自引:0,他引:1
Jing-hui Li 《Physica A》2010,389(1):7-3266
In this paper, we investigate the periodic response for a linear system driven by a multiplicative multi-state noise (which is composed of the multiplication of two dichotomous noises) to an input temporal oscillatory signal, and the escape of Brownian particles over the fluctuating potential barrier for a system with a piece-wise linear potential and driven by an additive multi-state noise (which is also composed of the multiplication of two dichotomous noises). For the first system, we get the stochastic resonance phenomenon for the amplitude of the periodic response vs. the two dichotomous noise strengths, and the phenomenon of reverse-resonance for the amplitude of the periodic response vs. k, which represents the asymmetry degree of the dichotomous noises. For the second system, we obtain the resonant activation phenomenon, for which the mean first passage time of the Brownian particles over the fluctuating potential barrier shows a minimum as the function of the transition rates of the multi-state noise. 相似文献
20.
We investigate self-diffusion in a classical fluid composed of two species which are distinguished through the color of their particles, either black or white, but are identical as regards their mechanical properties. Disregarding color the fluid is in thermal equilibrium. We show that if a single test particle in the one-component fluid moves asymptotically as Brownian motion, then the color density and current in certain classes of nonequilibrium states are related, on the appropriate macroscopic scale, through Fick's law, and the former is governed by the diffusion equation. If in addition several test particles move asymptotically as independent Brownian motions, then the colored fluid is, on a macroscopic scale, in local equilibrium with parameters governed by the solution of the diffusion equation.Part of this work was done while both authors were at IHES, Bures-sur-Yvette, France.Supported in part by NSF Grant No. PHY 78-15920-02.Supported by a Heisenberg fellowship of the Deutsche Forschungsgemeinschaft. 相似文献