Cooperative Transport of Brownian Particles

We consider the collective motion of finite-sized, overdamped Brownian particles (e.g., motor proteins) in a periodic potential. Simulations of our model have revealed a number of novel cooperative transport phenomena, including (i) the reversal of direction of the net current as the particle density is increased and (ii) a very strong and complex dependence of the average velocity on both the size and the average distance of the particles.Comment: 4 pages, 5 figure

Anomalous fluctuations of active polar filaments

Using a simple model, we study the fluctuating dynamics of inextensible, semiflexible polar filaments interacting with active and directed force generating centres such as molecular motors. Taking into account the fact that the activity occurs on time-scales comparable to the filament relaxation time, we obtain some unexpected differences between both the steady-state and dynamical behaviour of active as compared to passive filaments. For the statics, the filaments have a {novel} length-scale dependent rigidity. Dynamically, we find strongly enhanced anomalous diffusion.Comment: 5 pages, 3 figure

Feynman's ratchet and pawl: an exactly solvable model

We introduce a simple, discrete model of Feynman's ratchet and pawl, operating between two heat reservoirs. We solve exactly for the steady-state directed motion and heat flows produced, first in the absence and then in the presence of an external load. We show that the model can act both as a heat engine and as a refrigerator. We finally investigate the behavior of the system near equilibrium, and use our model to confirm general predictions based on linear response theory.Comment: 19 pages + 10 figures; somewhat tighter presentatio

Force Dependence of the Michaelis Constant in a Two-State Ratchet Model for Molecular Motors

We present a quantitative analysis of recent data on the kinetics of ATP hydrolysis, which has presented a puzzle regarding the load dependence of the Michaelis constant. Within the framework of coarse grained two-state ratchet models, our analysis not only explains the puzzling data, but provides a modified Michaelis law, which could be useful as a guide for future experiments.Comment: 4 pages, 3 eps figures, accepted for publication on Physical Review Letter

Superconducting Fluxon Pumps and Lenses

We study stochastic transport of fluxons in superconductors by alternating current (AC) rectification. Our simulated system provides a fluxon pump, "lens", or fluxon "rectifier" because the applied electrical AC is transformed into a net DC motion of fluxons. Thermal fluctuations and the asymmetry of the ratchet channel walls induce this "diode" effect, which can have important applications in devices, like SQUID magnetometers, and for fluxon optics, including convex and concave fluxon lenses. Certain features are unique to this novel two-dimensional (2D) geometric pump, and different from the previously studied 1D ratchets.Comment: Phys. Rev. Lett. 83, in press (1999); 4 pages, 5 .gif figures; figures also available at http://www-personal.engin.umich.edu/~nori/ratche

Deppining of a Superfluid Vortex Inside a Circular Defect

In this work we study the process of depinning of a quantum of circulation trapped inside a disk by an applied two dimensional superflow. We use the Gross-Pitaevskii model to describe the neutral superfluid. The collective coordinate dynamics is derived directly from the condensate equation of motion, the nonlinear Schroedinger equation, and it is used to obtain an expression for the critical velocity as a function of the defect radius. This expression is compared with a numerical result obtained from the time independent nonlinear Schroedinger equation. Below the critical velocity, we obtain the dependence of the semiclassical nucleation rate with the flow velocity at infinity. Above the critical velocity, the classical vortex depinning is illustrated with a numerical simulation of the time dependent nonlinear Schroedinger equation.Comment: 8 pages, 5 figures, uses revtex and epsf.st

Molecular motor that never steps backwards

We investigate the dynamics of a classical particle in a one-dimensional two-wave potential composed of two periodic potentials, that are time-independent and of the same amplitude and periodicity. One of the periodic potentials is externally driven and performs a translational motion with respect to the other. It is shown that if one of the potentials is of the ratchet type, translation of the potential in a given direction leads to motion of the particle in the same direction, whereas translation in the opposite direction leaves the particle localized at its original location. Moreover, even if the translation is random, but still has a finite velocity, an efficient directed transport of the particle occurs.Comment: 4 pages, 5 figures, Phys. Rev. Lett. (in print

Polydispersity and ordered phases in solutions of rodlike macromolecules

We apply density functional theory to study the influence of polydispersity on the stability of columnar, smectic and solid ordering in the solutions of rodlike macromolecules. For sufficiently large length polydispersity (standard deviation $\sigma>0.25$) a direct first-order nematic-columnar transition is found, while for smaller $\sigma$ there is a continuous nematic-smectic and first-order smectic-columnar transition. For increasing polydispersity the columnar structure is stabilized with respect to solid perturbations. The length distribution of macromolecules changes neither at the nematic-smectic nor at the nematic-columnar transition, but it does change at the smectic-columnar phase transition. We also study the phase behaviour of binary mixtures, in which the nematic-smectic transition is again found to be continuous. Demixing according to rod length in the smectic phase is always preempted by transitions to solid or columnar ordering.Comment: 13 pages (TeX), 2 Postscript figures uuencode