Factorised steady states for multi-species mass transfer models

A general class of mass transport models with Q species of conserved mass is considered. The models are defined on a lattice with parallel discrete time update rules. For one-dimensional, totally asymmetric dynamics we derive necessary and sufficient conditions on the mass transfer dynamics under which the steady state factorises. We generalise the model to mass transfer on arbitrary lattices and present sufficient conditions for factorisation. In both cases, explicit results for random sequential update and continuous time limits are given.Comment: 11 page

Criticality and Condensation in a Non-Conserving Zero Range Process

The Zero-Range Process, in which particles hop between sites on a lattice under conserving dynamics, is a prototypical model for studying real-space condensation. Within this model the system is critical only at the transition point. Here we consider a non-conserving Zero-Range Process which is shown to exhibit generic critical phases which exist in a range of creation and annihilation parameters. The model also exhibits phases characterised by mesocondensates each of which contains a subextensive number of particles. A detailed phase diagram, delineating the various phases, is derived.Comment: 15 pages, 4 figure, published versi

Phase Transitions in one-dimensional nonequilibrium systems

The phenomenon of phase transitions in one-dimensional systems is discussed. Equilibrium systems are reviewed and some properties of an energy function which may allow phase transitions and phase ordering in one dimension are identified. We then give an overview of the one-dimensional phase transitions which we have been studied in nonequilibrium systems. A particularly simple model, the zero-range process, for which the steady state is know exactly as a product measure, is discussed in some detail. Generalisations of the model, for which a product measure still holds, are also discussed. We analyse in detail a condensation phase transition in the model and show how conditions under which it may occur may be related to the existence of an effective long-range energy function. Although the zero-range process is not well known within the physics community, several nonequilibrium models have been proposed that are examples of a zero-range process, or closely related to it, and we review these applications here.Comment: latex, 28 pages, review article; references update

Construction of the factorized steady state distribution in models of mass transport

For a class of one-dimensional mass transport models we present a simple and direct test on the chipping functions, which define the probabilities for mass to be transferred to neighbouring sites, to determine whether the stationary distribution is factorized. In cases where the answer is affirmative, we provide an explicit method for constructing the single-site weight function. As an illustration of the power of this approach, previously known results on the Zero-range process and Asymmetric random average process are recovered in a few lines. We also construct new models, namely a generalized Zero-range process and a binomial chipping model, which have factorized steady states.Comment: 6 pages, no figure

Bose-Einstein Condensation In Disordered Exclusion Models and Relation to Traffic Flow

A disordered version of the one dimensional asymmetric exclusion model where the particle hopping rates are quenched random variables is studied. The steady state is solved exactly by use of a matrix product. It is shown how the phenomenon of Bose condensation whereby a finite fraction of the empty sites are condensed in front of the slowest particle may occur. Above a critical density of particles a phase transition occurs out of the low density phase (Bose condensate) to a high density phase. An exponent describing the decrease of the steady state velocity as the density of particles goes above the critical value is calculated analytically and shown to depend on the distribution of hopping rates. The relation to traffic flow models is discussed.Comment: 7 pages, Late

Condensation Transitions in Nonequilibrium systems

Systems driven out of equilibrium can often exhibit behaviour not seen in systems in thermal equilibrium- for example phase transitions in one-dimensional systems. In this talk I will review several `condensation' transitions that occur when a conserved quantity is driven through the system. Although the condensation is spatial, i.e. a finite fraction of the conserved quantity condenses into a small spatial region, useful comparison can be made with usual Bose-Einstein condensation. Amongst some one-dimensional examples I will discuss the `Bus Route Model' where the condensation corresponds to the clustering together of buses moving along a bus-route.Comment: 10 pages. Lecture from TH-2002, Pari

Flocking Regimes in a Simple Lattice Model

We study a one-dimensional lattice flocking model incorporating all three of the flocking criteria proposed by Reynolds [Computer Graphics vol.21 4 (1987)]: alignment, centring and separation. The model generalises that introduced by O. J. O' Loan and M. R. Evans [J. Phys. A. vol. 32 L99 (1999)]. We motivate the dynamical rules by microscopic sampling considerations. The model exhibits various flocking regimes: the alternating flock, the homogeneous flock and dipole structures. We investigate these regimes numerically and within a continuum mean-field theory.Comment: 24 pages 7 figure

Conserved mass models with stickiness and chipping

We study a chipping model in one dimensional periodic lattice with continuous mass, where a fixed fraction of the mass is chipped off from a site and distributed randomly among the departure site and its neighbours; the remaining mass sticks to the site. In the asymmetric version, the chipped off mass is distributed among the site and the right neighbour, whereas in the symmetric version the redistribution occurs among the two neighbours. The steady state mass distribution of the model is obtained using a perturbation method for both parallel and random sequential updates. In most cases, this perturbation theory provides a steady state distribution with reasonable accuracy.Comment: 17 pages, 4 eps figure

Phase Diagrams for Deformable Toroidal and Spherical Surfaces with Intrinsic Orientational Order

A theoretical study of toroidal membranes with various degrees of intrinsic orientational order is presented at mean-field level. The study uses a simple Ginzburg-Landau style free energy functional, which gives rise to a rich variety of physics and reveals some unusual ordered states. The system is found to exhibit many different phases with continuous and first order phase transitions, and phenomena including spontaneous symmetry breaking, ground states with nodes and the formation of vortex-antivortex quartets. Transitions between toroidal phases with different configurations of the order parameter and different aspect ratios are plotted as functions of the thermodynamic parameters. Regions of the phase diagrams in which spherical vesicles form are also shown.Comment: 40, revtex (with epsf), M/C.TH.94/2