Driven Diffusive Systems: An Introduction and Recent Developments

Nonequilibrium steady states in driven diffusive systems exhibit many features which are surprising or counterintuitive, given our experience with equilibrium systems. We introduce the prototype model and review its unusual behavior in different temperature regimes, from both a simulational and analytic view point. We then present some recent work, focusing on the phase diagrams of driven bi-layer systems and two-species lattice gases. Several unresolved puzzles are posed.Comment: 25 pages, 5 figures, to appear in Physics Reports vol. 299, June 199

Generic flow profiles induced by a beating cilium

We describe a multipole expansion for the low Reynolds number fluid flows generated by a localized source embedded in a plane with a no-slip boundary condition. It contains 3 independent terms that fall quadratically with the distance and 6 terms that fall with the third power. Within this framework we discuss the flows induced by a beating cilium described in different ways: a small particle circling on an elliptical trajectory, a thin rod and a general ciliary beating pattern. We identify the flow modes present based on the symmetry properties of the ciliary beat.Comment: 12 pages, 6 figures, to appear in EPJ

Novel Phases and Finite-Size Scaling in Two-Species Asymmetric Diffusive Processes

We study a stochastic lattice gas of particles undergoing asymmetric diffusion in two dimensions. Transitions between a low-density uniform phase and high-density non-uniform phases characterized by localized or extended structure are found. We develop a mean-field theory which relates coarse-grained parameters to microscopic ones. Detailed predictions for finite-size ($L$) scaling and density profiles agree excellently with simulations. Unusual large-$L$ behavior of the transition point parallel to that of self-organized sandpile models is found.Comment: 7 pages, plus 6 figures uuencoded, compressed and appended after source code, LATeX, to be published as a Phys. Rev. Let

Long Range Correlations in the Disordered Phase of a Simple Three State Lattice Gas

We investigate the dynamics of a three-state stochastic lattice gas, consisting of holes and two oppositely "charged" species of particles, under the influence of an "electric" field, at zero total charge. Interacting only through an excluded volume constraint, particles can hop to nearest neighbour empty sites. With increasing density and drive, the system orders into a charge-segregated state. Using a combination of Langevin equations and Monte Carlo simulations, we study the steady-state structure factors in the disordered phase where homogeneous configurations are stable against small harmonic perturbations. They show a discontinuity singularity at the origin which in real space leads to an intricate crossover between power laws of different kinds.Comment: 7 RevTeX pages, 1 postscript figure include

Reconstructed Rough Growing Interfaces; Ridgeline Trapping of Domain Walls

We investigate whether surface reconstruction order exists in stationary growing states, at all length scales or only below a crossover length, $l_{\rm rec}$. The later would be similar to surface roughness in growing crystal surfaces; below the equilibrium roughening temperature they evolve in a layer-by-layer mode within a crossover length scale $l_{\rm R}$, but are always rough at large length scales. We investigate this issue in the context of KPZ type dynamics and a checker board type reconstruction, using the restricted solid-on-solid model with negative mono-atomic step energies. This is a topology where surface reconstruction order is compatible with surface roughness and where a so-called reconstructed rough phase exists in equilibrium. We find that during growth, reconstruction order is absent in the thermodynamic limit, but exists below a crossover length $l_{\rm rec}>l_{\rm R}$, and that this local order fluctuates critically. Domain walls become trapped at the ridge lines of the rough surface, and thus the reconstruction order fluctuations are slaved to the KPZ dynamics

An interacting spin flip model for one-dimensional proton conduction

A discrete asymmetric exclusion process (ASEP) is developed to model proton conduction along one-dimensional water wires. Each lattice site represents a water molecule that can be in only one of three states; protonated, left-pointing, and right-pointing. Only a right(left)-pointing water can accept a proton from its left(right). Results of asymptotic mean field analysis and Monte-Carlo simulations for the three-species, open boundary exclusion model are presented and compared. The mean field results for the steady-state proton current suggest a number of regimes analogous to the low and maximal current phases found in the single species ASEP [B. Derrida, Physics Reports, {\bf 301}, 65-83, (1998)]. We find that the mean field results are accurate (compared with lattice Monte-Carlo simulations) only in the certain regimes. Refinements and extensions including more elaborate forces and pore defects are also discussed.Comment: 13pp, 6 fig

Tug-of-war in motility assay experiments

The dynamics of two groups of molecular motors pulling in opposite directions on a rigid filament is studied theoretically. To this end we first consider the behavior of one set of motors pulling in a single direction against an external force using a new mean-field approach. Based on these results we analyze a similar setup with two sets of motors pulling in opposite directions in a tug-of-war in the presence of an external force. In both cases we find that the interplay of fluid friction and protein friction leads to a complex phase diagram where the force-velocity relations can exhibit regions of bistability and spontaneous symmetry breaking. Finally, motivated by recent work, we turn to the case of motility assay experiments where motors bound to a surface push on a bundle of filaments. We find that, depending on the absence or the presence of a bistability in the force-velocity curve at zero force, the bundle exhibits anomalous or biased diffusion on long-time and large-length scales

Phase Transition in the ABC Model

Recent studies have shown that one-dimensional driven systems can exhibit phase separation even if the dynamics is governed by local rules. The ABC model, which comprises three particle species that diffuse asymmetrically around a ring, shows anomalous coarsening into a phase separated steady state. In the limiting case in which the dynamics is symmetric and the parameter $q$ describing the asymmetry tends to one, no phase separation occurs and the steady state of the system is disordered. In the present work we consider the weak asymmetry regime $q=\exp{(-\beta/N)}$ where $N$ is the system size and study how the disordered state is approached. In the case of equal densities, we find that the system exhibits a second order phase transition at some nonzero $\beta_c$. The value of $\beta_c = 2 \pi \sqrt{3}$ and the optimal profiles can be obtained by writing the exact large deviation functional. For nonequal densities, we write down mean field equations and analyze some of their predictions.Comment: 18 pages, 3 figure

Effects of differential mobility on biased diffusion of two species

Using simulations and a simple mean-field theory, we investigate jamming transitions in a two-species lattice gas under non-equilibrium steady-state conditions. The two types of particles diffuse with different mobilities on a square lattice, subject to an excluded volume constraint and biased in opposite directions. Varying filling fraction, differential mobility, and drive, we map out the phase diagram, identifying first order and continuous transitions between a free-flowing disordered and a spatially inhomogeneous jammed phase. Ordered structures are observed to drift, with a characteristic velocity, in the direction of the more mobile species.Comment: 15 pages, 4 figure

Synchronization of active mechanical oscillators by an inertial load

Motivated by the operation of myogenic (self-oscillatory) insect flight muscle, we study a model consisting of a large number of identical oscillatory contractile elements joined in a chain, whose end is attached to a damped mass-spring oscillator. When the inertial load is small, the serial coupling favors an antisynchronous state in which the extension of one oscillator is compensated by the contraction of another, in order to preserve the total length. However, a sufficiently massive load can sychronize the oscillators and can even induce oscillation in situations where isolated elements would be stable. The system has a complex phase diagram displaying quiescent, synchronous and antisynchrononous phases, as well as an unsual asynchronous phase in which the total length of the chain oscillates at a different frequency from the individual active elements.Comment: 5 pages, 4 figures, To appear in Phys. Rev. Let