Brownian Particles (brownian + particle)

Distribution by Scientific Domains
Mathematics and Statistics50%

Selected Abstracts

Stretching operational life of trickle-bed filters by liquid-induced pulse flow

AICHE JOURNAL, Issue 7 2005
Ion Iliuta
Abstract When dilute liquid suspensions contaminated with fine solids are treated in catalytic trickle-bed reactors, bed plugging develops and increases the resistance to two-phase flow until ultimate unit shutdown for bed substitution with pristine catalyst. The release of deposited fines, or the inhibition of fines deposition over some regions of the collector, is expected to alleviate the plugging if liquid flow shock or periodic operation policies are implemented. Current physical models linking gas,liquid phase flow to space,time evolution of fines deposition and release are unable to depict this new type of filtration in trickle beds. This work attempts to fill in this gap by developing a dynamic multiphase flow deep-bed filtration model. The model incorporates the physical effects of porosity and effective specific surface area changes as a result of fines deposition/release, gas and suspension inertial effects, and coupling effects between the filtration parameters and the interfacial momentum exchange force terms. The release of the fine particles from the collector surface was assumed to be induced by the colloidal forces in the case of Brownian particles or by the hydrodynamic forces in the case of non-Brownian particles. An important finding of the work was that for noncolloidal fines both induced pulsing and liquid flow shock operations conferred substantial improvements (measured in terms of reduction in specific deposit and pressure drop) in the mitigation of plugging in trickle-bed reactors. However, because of the highest critical shear stress for fines in the colloidal range, induced pulsing did not substantiate any practically useful effect. © 2005 American Institute of Chemical Engineers AIChE J, 2005 [source]

Feedback control in flashing ratchets,

ANNALEN DER PHYSIK, Issue 2-3 2008
E.M. Craig
Abstract A flashing ratchet uses a time-dependent, spatially periodic, asymmetric potential to rectify thermal motion of Brownian particles. Here we review approaches to improve the particle flux in this type of Brownian motor by feedback strategies that switch the potential based on the instantaneous particle distribution. We review strategies that are based on the force experienced by the particles, and introduce a new feedback strategy that is based on the expected displacement that can be achieved. Langevin dynamics simulations show that this maximum net displacement strategy performs better than force-based strategies in the limit of very small particle numbers and not too high temperatures. We also review the effects of time delay and noisy channels on feedback control, and perform a feasibility analysis of an experimental system that can realize feedback control using a computer-controlled, scanning-line optical trap and suspended microspheres. [source]

Dyson's nonintersecting Brownian motions with a few outliers

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 3 2009
Mark Adler
Consider n nonintersecting Brownian particles on , (Dyson Brownian motions), all starting from the origin at time t = 0 and forced to return to x = 0 at time t = 1. For large n, the average mean density of particles has its support, for each 0 < t < 1, on the interval ±,2nt(1 , t). The Airy process ,,(,) is defined as the motion of these nonintersecting Brownian motions for large n but viewed from the curve ,, : y = ,2nt(1 , t) with an appropriate space-time rescaling. Assume now a finite number r of these particles are forced to a different target point, say a = ,0,n/2 > 0. Does it affect the Brownian fluctuations along the curve ,, for large n? In this paper, we show that no new process appears as long as one considers points (y, t) , ,, such that 0 < t < (1 + ,),1, which is the t -coordinate of the point of tangency of the tangent to the curve passing through (,0,n/2, 1). At this point the fluctuations obey a new statistics, which we call the Airy process with r outliers ,,(r)(,) (in short, r-Airy process). The log of the probability that at time , the cloud does not exceed x is given by the Fredholm determinant of a new kernel (extending the Airy kernel), and it satisfies a nonlinear PDE in x and ,, from which the asymptotic behavior of the process can be deduced for , , ,,. This kernel is closely related to one found by Baik, Ben Arous, and Péché in the context of multivariate statistics. © 2008 Wiley Periodicals, Inc. [source]

Nonequilibrium statistical mechanics of swarms of driven particles

COMPLEXITY, Issue 4 2003
Werner Ebeling
Abstract As a rough model for the collective motions of cells and organisms we develop here the statistical mechanics of swarms of self-propelled particles. Our approach is closely related to the recently developed theory of active Brownian motion and the theory of canonical-dissipative systems. Free motion and motion of a swarms confined in an external field is studied. Briefly, the case of particles confined on a ring and interacting by repulsive forces is studied. In more detail we investigate self-confinement by Morse-type attracting forces. We begin with pairs N = 2; the attractors and distribution functions are discussed, then the case N > 2 is discussed. Simulations for several dynamical modes of swarms of active Brownian particles interacting by Morse forces are presented. In particular we study rotations, drift, fluctuations of shape, and cluster formation. © 2003 Wiley Periodicals, Inc. [source]