Tracer dynamics in Dyson's model of interacting Brownian particles

We prove that the mean square displacement of a tracer particle grows as logt for larget. We point out a connection to the low-temperature floating phase of the ANNNI model.     

Memory function approach to the dynamics of interacting Brownian particles

We investigate some of the dynamic properties of diffusing particles described by a many-body Smoluchowski equation. The dynamic structure factor is expressed in terms of a memory function which is evaluated in the cases of i) weak interaction and ii) low particle density, but arbitrary interaction. A one-dimensional system with a hard-core pair potential is treated explicitly. Furthermore, by including a periodic single-particle potential, a model is obtained which has relevance to superionic conductors. For this case we discuss how the frequency-dependent conductivity is affected by the correlated motion of particles.     

Brownian dynamics simulation of linear chain growth

Growth of linear chains is simulated by the technique of Brownian dynamics. The influence of the initial volume fraction of particles on the rate of the process and the structure of the chains is studied. Results show that aggregation is swift at the beginning of the process and very slow at the end. This is due to the decrease of the number of flocs in solution and the decrease in the efficiency of collisions when the degree of aggregation increases. The polydispersity of the system increases during aggregation and reaches a maximum value when the reaction is 96% complete. This increase is greater at higher concentrations. Results indicate that for lower concentrations aggregate growth is principally by reactive collision between aggregates of similar molecular weight, while for higher concentrations there is a relatively high fraction of reactive collisions between aggregates with very different molecular weights. The concentration effect on the structure of the chains is studied, evaluating the fractal dimensions of the chains. When the concentration increases there is a transition from very open structures (fractal dimension 1.76) to very tangled structures, where chains are collapsed (fractal dimension 3).     

Brownian dynamics simulation of polydisperse hard spheres

Standard algorithms used for the numerical integration of the Langevin equation require that interactions should slowly vary during the integration time-step. This in not the case for hard-body systems, where there is no clear-cut between the correlation time of the noise and the time-scale of the interactions. Starting with a short time approximation of the Smoluchowski equation, we introduce an algorithm for the simulation of the over-damped Brownian dynamics of polydisperse hard-spheres in absence of hydrodynamic interactions and briefly discuss the extension to the case of external drifts.     

Brownian dynamics simulation of two confined colloidal particles

The dynamics of two confined colloidal particles is studied by means of Brownian dynamics simulation. The autocorrelation function and cross-correlation function of the two colloidal spheres are computed by utilizing the formulae of hydrodynamic diffusion matrix expanded to different orders, as well as the accurate tensor through numerical algorithm. Furthermore, the numerical results are compared with the experimental results and the theoretical approximation. It is found that the relatively simple theoretical approximation gives good predictions when two spheres are far away from each other, but fails when the two spheres are very close.     

DNA与组蛋白相互作用的布朗动力学研究

在真核生物中,DNA按左手手征性的方式,缠绕在组蛋白八聚体的周围,形成稳定的核小体结构.文章作者运用布朗动力学,数值模拟了DNA与组蛋白相互作用最终形成核小体的动力学过程,揭示了DNA与组蛋白相互作用的详细图景,并提出了组蛋白八聚体旋转模型,以解释这一过程.文章作者还计算了组成核小体的DNA在受到拉伸力时,组蛋白被从核小体中剥离下来的动力学过程,得到了组装和剥离过程的详细图像,给出了与前人单分子实验一致的拉伸力与拉伸长度的关系曲线和拉伸台阶.此外,还通过建立的组蛋白手征性模型,模拟了核小体手征性的形成过程,发现DNA的缠绕方向强烈依赖于组蛋白的手征性,显示出环境温度对核小体手征性有重要影响.     

Brownian motion in gravitationally interacting systems

We derive a model that describes the dynamics of a Brownian particle, such as a massive black hole, in a stellar system dominated by gravitational forces, and examine whether it achieves a state of equipartition of kinetic energy with the stars. This problem has been considered before only for stellar systems with an isothermal Maxwellian distribution of velocities; here we study other examples and confirm our calculations with N-body simulations. We show that in certain cases the black hole's steady state kinetic energy can be very far from equipartition.     

Equilibrium fluctuations for interacting Brownian particles

We consider an infinitely extended system of Brownian particles interacting by a pair force-gradV. Their initial distribution is stationary and given by the Gibbs measure associated with the potentialV with fugacityz. We assume thatV is symmetric, finite range, three times continuously differentiable, superstable, and positive and that the fugacity is small in the sense that 0z0.28/edq(1-e ^–V(q)). In addition a certain essential self-adjointness property is assumed. We prove then that the time-dependent fluctuations in the density on a spatial scale of order ^–1 and on a time scale of order ^–2 converge as 0 to a Gaussian field with covariance dqg(q)(e ^(/2)|t| f)(q) withp the density and the compressibility.     

Coupling effect of Brownian motion and laminar shear flow on colloid coagulation:a Brownian dynamics simulation study

Simultaneous orthokinetic and perikinetic coagulations(SOPCs) are studied for small and large Peclet numbers(P e) using Brownian dynamics simulation.The results demonstrate that the contributions of the Brownian motion and the shear flow to the overall coagulation rate are basically not additive.At the early stages of coagulation with small Peclet numbers,the ratio of overall coagulation rate to the rate of pure perikinetic coagulation is proportional to P 1/2 e,while with high Peclet numbers,the ratio of overall coagulation rate to the rate of pure orthokinetic coagulation is proportional to P 1/2 e.Moreover,our results show that the aggregation rate generally changes with time for the SOPC,which is different from that for pure perikinetic and pure orthokinetic coagulations.By comparing the SOPC with pure perikinetic and pure orthokinetic coagulations,we show that the redistribution of particles due to Brownian motion can play a very important role in the SOPC.In addition,the effects of redistribution in the directions perpendicular and parallel to the shear flow direction are different.This perspective explains the behavior of coagulation due to the joint effects of the Brownian motion(perikinetic) and the fluid motion(orthokinetic).     

On the transport coefficients of interacting Brownian particles

A macroscopic argument shows that the ratios between the coefficients of particle transport are given by the equation of state of the diffusing substance, which may interact both by classical and by quantum mechanical effects. This fact is compared with the results of two microscopic treatments: first it agrees with the diffusion equation for interacting particles, and — on a less coarse-grained level — it can also be inferred from Boltzmann's transport equation.Work supported by the Swiss National Science Foundation     

Algorithms for Brownian dynamics

We derive a class of efficient and stable algorithms of Brownian dynamics using a formula, derived by Suzuki, to express time-ordered operators. These algorithms are simpler than those derived by Helfand from Runge-Kutta algorithms and, like Helfand algorithms, can be combined with SHAKE to describe the Brownian dynamics of constrained systems.     

Brownian dynamics simulation of gelation in soft sphere systems with irreversible bond formation

Brownian dynamics simulation is used to study the structure and small-deformation shear rheology of three-dimensional particle gels formed from a model of soft spherical particles incorporating a combination of flexible, irreversible bond formation and non-bonded interparticle interactions. An essential feature of the model is the restriction of angular reorganization of cross-linked aggregates during and after gelation. Numerical data relating to the fractal structure and porosity of the gels are compared with those from some related particle gel simulation models in two and three dimensions. Stress relaxation and frequency dependent rheological properties are determined as a function of the strength and nature of the interparticle interactions, and the results are discussed in relation to structural properties. A linear relationship is demonstrated between the high-frequency modulus and the number of bonds in the gel network.     

Brownian dynamics with constraints

Systems possessing degrees of freedom operating on widely separated timescales, where the effects of those operating on the smaller timescales are relatively unimportant, may be modelled by the use of the Langevin equation. In order to study such systems containing complex polyatomic particles, holonomic constraints may be used. Though there is no lack of published algorithms for the numerical solution of the Langevin equation, few of them have been developed with sufficient rigour to ensure their precision, nor to demonstrate their compatibility with constraints. This study recapitulates an approach based upon Runge-Kutta equations which has the advantage of being perfectible to any desired order in the time-step, and shows how it may be combined with the SHAKE method in order to perform constrained Brownian dynamics simulations. Results are presented for some simple systems with a third order algorithm, and it is found that the correct dynamic and statistical behaviour is recovered.     

Brownian dynamics of a microswimmer

We report on dynamic properties of a simple model microswimmer composed of three spheres and propelling itself in a viscous fluid by spinning motion of the spheres under zero net torque constraint. At a fixed temperature and increasing the spinning frequency, the swimmer demonstrates a transition from dissipation-dominated to a pumping-dominated motion regime characterized by negative effective friction coefficient. In the limit of high frequencies, the diffusion of the swimmer can be described by a model of an active particle with constant velocity.     

Brownian dynamics simulation of the cross-talking effect among modified histones on conformations of nucleosomes

Using Brownian dynamics simulation,we studied the effect of histone modifications on conformations of an array of nucleosomes in a segment of chromatin.The simulation demonstrated that the segment of chromatin shows the dynamic behaviour that its conformation can switch between a state with nearly all of the histones being wrapped by DNA and a state with nearly all of the histones being unwrapped by DNA,thus involving the "cross-talking" interactions among the histones.Each state can stay for a sufficiently long time.These conformational states are essential for gene expression or gene silence.The simulation also shows that these conformational states can be inherited by the daughter DNAs during DNA replication,giving a theoretical explanation of the epigenetic phenomenon.     

Conductivity of interacting Brownian particles in a periodic medium

Thed c-conductivity of interacting Brownian particles diffusing in a periodic potential is investigated. An approximate method is used which relates the conductivity to the spatial variation of the particle density. Numerical results are given for arbitrary temperatures, moderate densities and various forms of the pair potential.     

More efficient Brownian dynamics algorithms

We examine the relative efficiencies of three- algorithms for performing Brownian Dynamics simulations without many-body hydrodynamics. We compare the conventional Brownian Dynamics algorithm of Ermak (CBD), Smart Monte Carlo (SMC) which incorporates Boltzmann sampling into essentially a CBD procedure, and the Stochastic Runge Kutta (SRK) method. We show, using the repulsive potential φ(r) = ε(σ/r) ⁿ , where n = 36 and 72, that the SRK algorithm gives the most accurate short-time dynamics for the mean-square displacements. The SRK algorithm static and dynamical properties converge better with a reducing time step to the exact values, than those generated by the CBD algorithm; giving efficiency gains typically of a factor of 3–4. Both CBD and SMC have the incorrect sign for the first correction term to the mean square displacement in a time step, whereas the SRK algorithm gives essentially the exact solution to order Δt ², where Δt is the simulation time step. In fact, these correction terms are almost equal and opposite in sign. Expressions for these terms were derived in terms of the average interaction energy per particle. The force, shear and bulk stress autocorrelation functions were calculated. The average energy per particle and time correlation functions at short time have values in excess of the exact values, while the corresponding quantities for SRK are below this. This difference in behaviour can be traced back to the extent of compliance of the particle trajectories with the exact expansion of the Smoluchowski equation. The accuracy, at a given value of the time step, of the stochastic algorithms can significantly depend on the form of the interaction potential between particles. It is also demonstrated that the long time limits of various correlation functions are fairly insensitive to a particular scheme (SRK or CBD) used in the simulations. All the correlation functions have a stretched exponential region at intermediate to long times, and the values of the exponents on density and force law steepness have been determined.     

Brownian motion in inhomogeneous media and with interacting particles

Brownian motion in media with a space-dependent temperature and density is described by Langevin equations in phase space. Elimination of the velocity shows that diffusion inx-space cannot in general be characterized by a single diffusion parameter, nor can space-dependence always be accounted for by mere assignment of some sense of stochastic integration to the Langevin equation which has been reduced as in the homogeneous case. Steady solutions of the resulting equations agree with thermodynamics. Interactions between Brownian particles (giving rise to nonlinear Fokker-Planck equations) lead to a generalization of Einstein's relation.Work supported by the Swiss National Science Foundation     

Diffusion of interacting Brownian particles on non-regularly spaced stepped structures

In this paper, we investigate the diffusion process of interacting Brownian particles on stepped surfaces through a Langevin dynamic simulation method. Our primary interest is the investigation of the dynamics properties by calculating the collective diffusion coefficient for non-regularly spaced stepped structures using the Frenkel–Kontorova repulsive interactions. In particular, we have studied the effects of the Ehrlich–Schwoebel barrier $E_{S}$ and the additional binding energy $E_{B}$ on the diffusion process. Overall, our simulation results show that the value of the diffusion coefficient $D$ is reduced with increasing $E_{S}$ and $E_{B}$ . This reduction is also observed when decreasing the size of terraces. This diminution is well interpreted by calculating the effective potential which includes the effect of both potentials of Frenkel–Kontorova and the substrate.