[Show abstract][Hide abstract] ABSTRACT: We carry out a detailed study of the motion of particles driven by a constant external force over a landscape consisting of a periodic potential corrugated by a small amount of spatial disorder. We observe anomalous behavior in the form of subdiffusion and superdiffusion and even subtransport over very long time scales. Recent studies of transport over slightly random landscapes have focused only on parameters leading to normal behavior, and while enhanced diffusion has been identified when the external force approaches the critical value associated with the transition from locked to running solutions, the regime of anomalous behavior had not been recognized. We provide a qualitative explanation for the origin of these anomalies, and make connections with a continuous time random walk approach.
[Show abstract][Hide abstract] ABSTRACT: Transport and diffusion of particles on modulated surfaces is a nonequilibrium problem which is receiving a great deal of attention due to its technological applications, but analytical calculations are scarce. In earlier work, we developed a perturbative approach to begin to provide an analytic platform for predictions about particle trajectories over such surfaces. In some temperature and forcing regimes, we successfully reproduced results for average particle velocities obtained from numerical simulations. In this paper, we extend the perturbation theory to the calculation of higher moments, in particular the diffusion tensor and the skewness. Numerical simulations are used to check the domain of validity of the perturbative approach.
[Show abstract][Hide abstract] ABSTRACT: Sorting of colloidal particles of different sizes is of importance in the transport and delivery of such particles in biological, materials science, and other technological contexts. A successful methodology involves the flow of a mixture of particles over designer surfaces presenting a periodic array of traps (optical tweezers) or microfabricated obstacles. The trajectories of the particles over these surfaces deviate from the direction of flow as the particles are attracted (traps) or repelled (obstacles) by the features of the landscape. The deviation of the particles from that of the flow depends on particle size (or on some other particle characteristic) and hence the particles can be sorted according to trajectory direction. On the basis of extensive numerical simulations, we present a unified view of these methodologies and discuss the effects of system parameters such as the magnitude and direction of the flow on the sorting efficacy.
Modern Physics Letters B 01/2006; 20:1427-1442. · 0.48 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Particles moving on perfect periodic surfaces under the influence of external forces may move along directions that deviate from that of the force. We briefly recall previous results for transport of particles on surfaces with periodic traps or periodic obstacles driven by a constant external force, and present new results for particles moving in a harmonic periodic potential. The sorting properties are explored as a function of a number of control parameters, specifically the friction, force amplitude and direction, temperature, and lattice constants.