A mechanical model of Brownian motion

We consider a dynamical system consisting of one large massive particle and an infinite number of light point particles. We prove that the motion of the massive particle is, in a suitable limit, described by the Ornstein-Uhlenbeck process. This extends to three dimensions previous results by Holley in one dimension.On leave of the Institut für Theoretische Physik I der Universität Münster. Supported by a Nato fellowshipSupported by NSF Grant, No. PHY 78-03816Supported by NSF Grant, Phy 78-15920     

On the kinetic theory of Brownian motion

The influence of fluctuations on the kinetic processes of Brownian motion is investigated. We consider fluctuations for which the correlation time is comparable with the relaxation time of the distribution function. Taking such large scale fluctuations into account is shown to lead to a change of the diffusion coefficient and to the appearance of additional correlations in the motions of Brownian particles. An expression is obtained for the correlation function of a Langevin source in the diffusion equation taking into account the contribution of large scale fluctuations.     

Non-Markovian quantal Brownian motion model

A non-Markovian version of the quantal Brownian motion model is given. The integrodifferential equations of motion are solved, establishing the analytic form of the resolvent poles and analyzing their properties. An explicit investigation of the poles at zero temperature is performed. In this frame a rule can be found that relates the relevant poles of the non-Markovian resolvent to the eigenvalues of the associated Markovian generator of the motion.     

A mechanical model of Brownian motion in half-space

We consider the motion of a heavy mass in an ideal gas in a semi-infinite system, with elastic collisions at the boundary. The motion is determined by elastic collisions. We prove in the Brownian motion limit the convergence of the position and velocity process of the heavy particle to a diffusion process in which velocity and position remain coupled.     

The quasicrystal model of rotational Brownian motion

The quasicrystal model of the rotational Brownian motion in a liquid has been studied. The probability distribution of orientations of a Brownian particle is given in the form of a series of generalized spherical functions.     

Brownian motion in magnetic field: A model for a semi-quantum stochastic process

The Brownian motion of an ensemble of charged particles in a quantizing magnetic field is considered in a simple quasi-classical model. The model describes random jumps between the Landau levels—corresponding to the quantized motion perpendicular to the magnetic field, and markovian fluctuations in momentum space—corresponding to the classical motion parallel to the field. A random walk dynamics is adopted for the former while an Ornstein-Uhlenbeck process is considered for the latter. The resulting Fokker-Planck equations constitute a semi-quantum stochastic process. The equations are solved and several physical aspects of the underlying system are discussed.     

Radiation model for nanoparticle: extension of classical Brownian motion concepts

Emissive power per unit area of a blackbody has been modeled as a function of frequency using quantum electrodynamics, semi-classical and classical approaches in the available literature. Present work extends the classical lumped-parameter systems model of Brownian motion of nanoparticle to abstract an emissive power per unit area model for nanoparticle radiating at temperature greater than absolute zero. The analytical model developed in present work has been based on synergism of local deformation leading to local motion of nanoparticle due to photon impacts. The work suggests the hypothesis of a free parameter f′ characterizing the damping coefficient of resistive forces to local motion of nanoparticle and the manipulation of which is possible to realize desired emissivity from nanoparticles. The model is validated with the well established Planck’s radiation law.     

Brownian motion with inert drift, but without flux: A model

We study the motion of a Brownian particle which interacts with a stationary obstacle in two dimensions. The Brownian particle acquires drift proportionally to the time spent on the boundary of the obstacle. The system approaches equilibrium, and the equilibrium distribution for the location and drift magnitude has the product form. The distribution for the location is uniform, while the drift distribution depends on the shape of the obstacle, resembling a gamma function for the circular or elliptic obstacle.     

A dynamical theory of Brownian motion for the Rayleigh gas

A dynamical theory of the Brownian motion is worked out for the Rayleigh gas and open problems of this theory are surveyed.     

A generalized Faxén theorem for two-dimensional Brownian motion

The induced force method developed by Mazur and Bedeaux is applied here to two-dimensional Brownian motion. We obtain a generalized Faxén theorem which reduces to the Stokes-Basset drag force on a nonuniformly moving cylinder or disk in the special case where the fluid fluctuations are neglected. The resulting modified Langevin equation is solved numerically for the velocity autocorrelation Ø(t) and the expected long time result Ø(t)～1/t is obtained. It is perhaps surprising that the short time behavior of Ø(t) deviates considerably from that predicted on the basis of a modified Langevin equation incorporating the classic Oseen-Lamb drag force on a cylinder.     

A kinetic theory of diffusely reflecting Brownian particles

An analysis is made of the motion of a spherical Brownian particle whose surface can diffusely reflect the molecules of an equilibrium host gas. The analysis is based on Newton's second law and a limiting form of Markov's method. It is shown, both for specular and diffuse reflections, that equipartition of energy is a consequence of the dynamics and randomness of the motion. In addition, it is demonstrated that the diffusion coefficient can depend on the temperature of the particle. The entire analysis is restricted to the case for which the Knudsen number of the particle is large compared to unity.Slinn's work was supported in part by Battelle Memorial Institute and in part by the U.S. Atomic Energy Commission contract AT(45–1)-1830. Shen's work was supported in part by the U.S. Air Force Office of Scientific Research contract 49(638)–1346. Mazo's work was supported in part by the National Science Foundation, NSF Grant GP–8497.     

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     

Model for Brownian motion in soft-jammed systems

Brownian motion in soft-jammed systems (pastes) is directly described by taking into account the specific mechanical characteristics of the material surrounding the moving object. In particular we obtain explicit forms for the fluctuation-dissipation equation and the specific characteristics of diffusion through a soft-jammed system.     

Theory of rotational Brownian motion

The correlation function for the angular velocity of a Brownian particle suspended in a liquid is analyzed with an account of the viscous aftereffect. The main term in the asymptotic exression for this function is equal to the eddy correlation function for the translational velocity of a liquid found from the Navier-Stokes equations.Translated from Izvestiya VUZ. Fizika, No. 10, pp. 13–17, October, 1969.In conclusion the author thanks Professor I. Z. Fisher for guidance and for constant interest in his study.     

Brownian motion with active fluctuations

We study the effect of different types of fluctuation on the motion of self-propelled particles in two spatial dimensions. We distinguish between passive and active fluctuations. Passive fluctuations (e.g., thermal fluctuations) are independent of the orientation of the particle. In contrast, active ones point parallel or perpendicular to the time dependent orientation of the particle. We derive analytical expressions for the speed and velocity probability density for a generic model of active Brownian particles, which yields an increased probability of low speeds in the presence of active fluctuations in comparison to the case of purely passive fluctuations. As a consequence, we predict sharply peaked Cartesian velocity probability densities at the origin. Finally, we show that such a behavior may also occur in non-Gaussian active fluctuations and discuss briefly correlations of the fluctuating stochastic forces.     

Thermodynamic suppression of Brownian motion

We have used helium-3 nuclear reaction analysis to measure the Brownian motion (intradiffusion coefficient) of polystyrene in a partially miscible blend with poly(alpha-methylstyrene). In the one-phase region, when the correlation length is close to the polystyrene chain size, the intradiffusion coefficient falls to half of its thermal value. For larger and smaller values of the correlation length, diffusion is normal. These results show that the correlation length of a polymer blend constrains polymer diffusion, as suggested from previous neutron scattering measurements, and mean-field theory.