Brownian motion of suspended particles in an anisotropic medium

Some experimental results in the case of anisotropic media are at variance with the Einstein-Stokes formula of Brownian motion and the Singwi-Sjölander model. The disagreement comes from the anchor effect. The concept of “pseudoparticle” is introduced in order to retain the Singwi-Sjölander formalism. Mössbauer spectroscopy can be used to estimate the thickness of the anchored liquid-crystalline molecular textures forming on the surface of Brownian particles.     

Collective motion of active Brownian particles in one dimension

We analyze a model of active Brownian particles with non-linear friction and velocity coupling in one spatial dimension. The model exhibits two modes of motion observed in biological swarms: A disordered phase with vanishing mean velocity and an ordered phase with finite mean velocity. Starting from the microscopic Langevin equations, we derive mean-field equations of the collective dynamics. We identify the fixed points of the mean-field equations corresponding to the two modes and analyze their stability with respect to the model parameters. Finally, we compare our analytical findings with numerical simulations of the microscopic model.     

Cooling kinetics of a granular gas of viscoelastic particles

The evolution of a granular gas of viscoelastic particles in the homogeneous cooling state is studied. The velocity distribution function of granular particles and the time dependence of the mean kinetic energy of particles (granular temperature) are found. The noticeable deviation of the distribution function from the Maxwell distribution and its non-monotonous evolution are established. The perturbation theory with respect to the small dispersion parameter is elaborated and the analytical expressions for the asymptotic time dependence of the velocity distribution function and the granular gas temperature are derived.     

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     

Simultaneous Brownian motion of N particles in a temperature gradient

A system of N Brownian particles suspended in a nonuniform heat bath is treated as a thermodynamic system with internal degrees of freedom, in this case their velocities and coordinates. Applying the scheme of nonequilibrium thermodynamics, one then easily obtains the Fokker-Planck equation for simultaneous Brownian motion of N particles in a temperature gradient. This equation accounts for couplings in the motion as a result of hydrodynamic interactions between particles.     

Spectral-correlation characteristics of the Brownian motion of inertial particles

An analytical-numerical approach is used for studying the correlation function and spectrum of one-dimensional Brownian motion of real (inertial) particles in the symmetric monomodal potential profile. The method of analysis is based on cumulantless expansions of the moment functions. The obtained results can also be interpreted as the spectral-correlation characteristics of a nonlinear oscillator affected by intense wideband noise. The dependence of the spectral-correlation characteristics of the Brownian motion on the noise intensity, nonlinear rigidity, and viscosity of the medium is obtained. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 1, pp. 82–89, January 2008.     

On the theory of Brownian motion. I. Interaction between Brownian particles

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.     

Brownian motion of particles embedded in a solution of giant micelles

We have measured the mean-square displacement of colloidal particles embedded in a semi-dilute solution of worm-like micelles, using diffusing wave spectroscopy. This allowed us to describe their rheological properties over a very wide time range. At very short times, the particles diffuse freely in the solvent, and then, they experience the characteristic relaxation times of the living chains. We deduced directly, from the mean-square displacement of the particles, the mechanical properties of the micellar solution, not only in the high-frequency regime, but also in the low-frequency range, in which we compared our results with direct mechanical measurements, and found good agreement. Received 22 March 2002 and Received in final form 5 June 2002     

Self-diffusion in granular gases

The coefficient of self-diffusion for a homogeneously cooling granular gas changes significantly if the impact-velocity dependence of the restitution coefficient epsilon is taken into account. For the case of a constant epsilon the particles spread logarithmically slowly with time, whereas a velocity-dependent coefficient yields a power law time dependence. The impact of the difference in these time dependences on the properties of a freely cooling granular gas is discussed.     

Phase separation dynamics in binary systems containing mobile particles with variable Brownian motion

In this paper, we consider a particular form of coupling, namely \(B=\sigma (\dot{\rho _m}-\dot{\rho _\phi })\) in spatially flat (\(k=0\)) Friedmann–Lemaitre–Robertson–Walker (FLRW) space–time. We perform phase-space analysis for this interacting quintessence (dark energy) and dark matter model for different numerical values of parameters. We also show the phase-space analysis for the ‘best-fit Universe’ or concordance model. In our analysis, we observe the existence of late-time scaling attractors.     

The contribution of Brownian motion to the viscosity of suspensions of spherical particles

We study the contribution of Brownian motion to the viscosity of a suspension of spherical particles immersed in an incompressible fluid. We evaluate expressions derived from linear response theory applied to the generalized Smoluchowski equation and from a cluster expansion of the response. This leads to results obtained earlier by Batchelor for hard spheres and by Russel for more general pair interactions.     

颗粒气体的团簇行为

颗粒体系由于粒子间非弹性碰撞和摩擦等内秉的能量耗散特性,由宏观粒子形成的颗粒气体体系经常会有局部凝聚现象,这是颗粒气体体系与分子气体体系的最大区别之一。理解和预测这一现象的发生将有助于人们对远离平衡态体系的复杂现象(如有序结构、斑图和团簇形成)的认知。这种局部凝聚现象可以类比于分子气体中亚稳分解形成的液滴,将气液相分离用于解释和寻求局部凝聚现象的模型得到了分子动力学模拟的校验。但是实验的校验却由于宏观粒子运动受重力作用的影响难以在实验室中实现。实践十号卫星为我们提供了长时稳定微重力条件,使得实验观察成为可能,有望获得团簇形成及颗粒冷却行为等颗粒动力学重要实验结果。     

Nearly smooth granular gases

Hydrodynamic equations for nearly smooth granular gases are derived from the pertinent Boltzmann equation. The angular velocity distribution field needs to be included in the set of hydrodynamic fields. The angular velocity distribution is strongly non-Maxwellian for the homogeneous cooling state and any homogeneous steady state. In the case of steady wall-bounded shear flows the average spin (created at the boundaries) has a finite penetration length into the bulk.     

Hydrodynamics of Brownian particles

When considering the hydrodynamics of Brownian particles, one is confronted to a difficult closure problem. One possibility to close the hierarchy of hydrodynamic equations is to consider a strong friction limit. This leads to the Smoluchowski equation that reduces to the ordinary diffusion equation in the absence of external forces. Unfortunately, this equation has infinite propagation speed leading to some difficulties. Another possibility is to make a Local Thermodynamic Equilibrium (L.T.E) assumption. This leads to the damped Euler equation with an isothermal equation of state. However, this approach is purely phenomenological. In this paper, we provide a preliminary discussion of the validity of the L.T.E assumption. To that purpose, we consider the case of free Brownian particles and harmonically bound Brownian particles for which exact analytical results can be obtained [S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943)]. For these systems, we find that the L.T.E. assumption is not unreasonable and that it can be improved by introducing a time dependent kinetic temperature T_kin(t)=γ(t)T instead of the bath temperature T. We also compare hydrodynamic equations and generalized diffusion equations with time dependent diffusion coefficients.     

Measurement of the translational and rotational Brownian motion of individual particles in a rarefied gas

We measured the free Brownian motion of individual spherical and the Brownian rotation of individual nonspherical micrometer-sized particles in rarefied gas. Measurements were done with high spatial and temporal resolution under microgravity conditions in the Bremen drop tower so that the transition from diffusive to ballistic motion could be resolved. We find that the translational and rotational diffusion can be described by the relation given by Uhlenbeck and Ornstein [Phys. Rev. 36, 823 (1930)]. Measurements of rotational Brownian motion can be used for the determination of the moments of inertia of small particles.     

Velocity distributions in dissipative granular gases

Motivated by recent experiments reporting non-Gaussian velocity distributions in driven dilute granular materials, we study by numerical simulation the properties of 2D inelastic gases. We find theoretically that the form of the observed velocity distribution is governed primarily by the coefficient of restitution eta and q=N(H)/N(C), the ratio between the average number of heatings and the average number of collisions in the gas. The differences in distributions we find between uniform and boundary heating can then be understood as different limits of q, for q>1 and q less, similar 1, respectively.