A general criterion for the existence of phase separation in driven density-conserving one-dimensional systems is proposed. It is suggested that phase separation is related to the size dependence of the steadystate currents of domains in the system. A quantitative criterion for the existence of phase separation is conjectured using a correspondence made between driven diffusive models and zero-range processes. The criterion is verified in all cases where analytical results are available, and predictions for other models are provided. DOI: 10.1103/PhysRevLett.89.035702 PACS numbers: 64.75. +g, 05.20. -y The existence of phase separation and spontaneous symmetry breaking in low-dimensional systems far from thermal equilibrium has been a subject of recent interest [1,2]. While it is well known that these phenomena do not take place in one dimension in thermal equilibrium, several models of driven one-dimensional systems with local dynamics have recently been demonstrated to exhibit both [3 -5]. Whether or not a given model exhibits phase separation is in many cases not a simple question to answer, and it may depend on numerical evidence which could be rather subtle.For example, in a recent three-species model introduced by Arndt et al. [4] (AHR), it has been suggested that one should expect two distinct phase separated states: one in which the three species are fully separated from each other (related to the phase separation observed by Evans et al.[3] in a related model) and the other is a more subtle mixed state whose existence is supported by extensive numerical simulations of systems of finite length and by a meanfield treatment. Subsequently, an analytical analysis of the model has shown that the mixed state is in fact disordered and that in order to see this in simulations one has to study extremely long systems (of the order of 10 70 ), far beyond existing numerical capabilities [6].In another example introduced by Korniss et al. a twolane extension of a three-species driven system was studied [7]. It has been suggested that while for this model the one-lane system does not exhibit phase separation [8], this phenomenon does exist in the two-lane model. The studies rely on numerical simulations of systems of length up to 10 4 . This result is rather surprising and not well understood. It may very well be the case that as for the AHR model, the two-lane model does not actually exhibit phase separation in the thermodynamic limit and that this could be seen only by studying extremely long systems. It would thus be of great importance to find other criteria, which could distinguish between models supporting phase separation from those which do not.In this Letter we introduce a simple general criterion for the existence of phase separation in density-conserving one-dimensional driven systems. Phase separation is usually accompanied by a coarsening process in which small domains of, say, the high density phase coalesce, eventually leading to macroscopic phase separation. This process takes place as domains exc...

Shear induced alignment of elongated particles is studied experimentally and numerically. We show that shear alignment of ensembles of macroscopic particles is comparable even on a quantitative level to simple molecular systems, despite the completely different types of particle interactions. We demonstrate that for dry elongated grains the preferred orientation forms a small angle with the streamlines, independent of shear rate across three decades. For a given particle shape, this angle decreases with increasing aspect ratio of the particles. The shear-induced alignment results in a considerable reduction of the effective friction of the granular material.

Strain in sheared dense granular material is often localized in a narrow region called the shear band. Recent experiments in a modified Couette cell provided localized shear flow in the bulk away from the confining walls. The nontrivial shape of the shear band was measured as the function of the cell geometry. First, we present a geometric argument for narrow shear bands that connects the function of their surface position with the shape in the bulk. Assuming a simple dissipation mechanism, we show that the principle of minimum dissipation of energy provides a good description of the shape function. Furthermore, we discuss the possibility and behavior of shear bands that are detached from the free surface and are entirely covered in the bulk.

The alignment, ordering, and rotation of elongated granular particles was studied in shear flow. The time evolution of the orientation of a large number of particles was monitored in laboratory experiments by particle tracking using optical imaging and x-ray computed tomography. The experiments were complemented by discrete element simulations. The particles develop an orientational order. In the steady state the time- and ensemble-averaged direction of the main axis of the particles encloses a small angle with the streamlines. This shear alignment angle is independent of the applied shear rate, and it decreases with increasing grain aspect ratio. At the grain level the steady state is characterized by a net rotation of the particles, as dictated by the shear flow. The distribution of particle rotational velocities was measured both in the steady state and also during the initial transients. The average rotation speed of particles with their long axis perpendicular to the shear alignment angle is larger, while shear aligned particles rotate slower. The ratio of this fast/slow rotation increases with particle aspect ratio. During the initial transient starting from an unaligned initial condition, particles having an orientation just beyond the shear alignment angle rotate opposite to the direction dictated by the shear flow.

Information-communication technology promotes collaborative environments like Wikipedia where, however, controversy and conflicts can appear. To describe the rise, persistence, and resolution of such conflicts, we devise an extended opinion dynamics model where agents with different opinions perform a single task to make a consensual product. As a function of the convergence parameter describing the influence of the product on the agents, the model shows spontaneous symmetry breaking of the final consensus opinion represented by the medium. In the case when agents are replaced with new ones at a certain rate, a transition from mainly consensus to a perpetual conflict occurs, which is in qualitative agreement with the scenarios observed in Wikipedia.