Condensation in randomly perturbed zero-range processes

The zero-range process is a stochastic interacting particle system that exhibits a condensation transition under certain conditions on the dynamics. It has recently been found that a small perturbation of a generic class of jump rates leads to a drastic change of the phase diagram and prevents condensation in an extended parameter range. We complement this study with rigorous results on a finite critical density and quenched free energy in the thermodynamic limit, as well as quantitative heuristic results for small and large noise which are supported by detailed simulation data. While our new results support the initial findings, they also shed new light on the actual (limited) relevance in large finite systems, which we discuss via fundamental diagrams obtained from exact numerics for finite systems.Comment: 18 pages, 6 figure

Network representations of non-equilibrium steady states: Cycle decompositions, symmetries and dominant paths

Non-equilibrium steady states (NESS) of Markov processes give rise to non-trivial cyclic probability fluxes. Cycle decompositions of the steady state offer an effective description of such fluxes. Here, we present an iterative cycle decomposition exhibiting a natural dynamics on the space of cycles that satisfies detailed balance. Expectation values of observables can be expressed as cycle "averages", resembling the cycle representation of expectation values in dynamical systems. We illustrate our approach in terms of an analogy to a simple model of mass transit dynamics. Symmetries are reflected in our approach by a reduction of the minimal number of cycles needed in the decomposition. These features are demonstrated by discussing a variant of an asymmetric exclusion process (TASEP). Intriguingly, a continuous change of dominant flow paths in the network results in a change of the structure of cycles as well as in discontinuous jumps in cycle weights.Comment: 3 figures, 4 table

Nonequilibrium phase transition in a non integrable zero-range process

The present work is an endeavour to determine analytically features of the stationary measure of a non-integrable zero-range process, and to investigate the possible existence of phase transitions for such a nonequilibrium model. The rates defining the model do not satisfy the constraints necessary for the stationary measure to be a product measure. Even in the absence of a drive, detailed balance with respect to this measure is violated. Analytical and numerical investigations on the complete graph demonstrate the existence of a first-order phase transition between a fluid phase and a condensed phase, where a single site has macroscopic occupation. The transition is sudden from an imbalanced fluid where both species have densities larger than the critical density, to a critical neutral fluid and an imbalanced condensate

Zero-range process with open boundaries

We calculate the exact stationary distribution of the one-dimensional zero-range process with open boundaries for arbitrary bulk and boundary hopping rates. When such a distribution exists, the steady state has no correlations between sites and is uniquely characterized by a space-dependent fugacity which is a function of the boundary rates and the hopping asymmetry. For strong boundary drive the system has no stationary distribution. In systems which on a ring geometry allow for a condensation transition, a condensate develops at one or both boundary sites. On all other sites the particle distribution approaches a product measure with the finite critical density \rho_c. In systems which do not support condensation on a ring, strong boundary drive leads to a condensate at the boundary. However, in this case the local particle density in the interior exhibits a complex algebraic growth in time. We calculate the bulk and boundary growth exponents as a function of the system parameters

Condensation Transitions in a One-Dimensional Zero-Range Process with a Single Defect Site

Condensation occurs in nonequilibrium steady states when a finite fraction of particles in the system occupies a single lattice site. We study condensation transitions in a one-dimensional zero-range process with a single defect site. The system is analysed in the grand canonical and canonical ensembles and the two are contrasted. Two distinct condensation mechanisms are found in the grand canonical ensemble. Discrepancies between the infinite and large but finite systems' particle current versus particle density diagrams are investigated and an explanation for how the finite current goes above a maximum value predicted for infinite systems is found in the canonical ensemble.Comment: 18 pages, 4 figures, revtex

Hydrodynamics of the zero-range process in the condensation regime

We argue that the coarse-grained dynamics of the zero-range process in the condensation regime can be described by an extension of the standard hydrodynamic equation obtained from Eulerian scaling even though the system is not locally stationary. Our result is supported by Monte Carlo simulations.Comment: 14 pages, 3 figures. v2: Minor alteration

From urn models to zero-range processes: statics and dynamics

The aim of these lecture notes is a description of the statics and dynamics of zero-range processes and related models. After revisiting some conceptual aspects of the subject, emphasis is then put on the study of the class of zero-range processes for which a condensation transition arises.Comment: Lecture notes for the Luxembourg Summer School 200

Thresholds in layered neural networks with variable activity

The inclusion of a threshold in the dynamics of layered neural networks with variable activity is studied at arbitrary temperature. In particular, the effects on the retrieval quality of a self-controlled threshold obtained by forcing the neural activity to stay equal to the activity of the stored paterns during the whole retrieval process, are compared with those of a threshold chosen externally for every loading and every temperature through optimisation of the mutual information content of the network. Numerical results, mostly concerning low activity networks are discussed.Comment: 15 pages, Latex2e, 6 eps figure

Human Complement Regulators C4b-Binding Protein and C1 Esterase Inhibitor Interact with a Novel Outer Surface Protein of Borrelia recurrentis

The spirochete Borrelia recurrentis is the causal agent of louse-borne relapsing fever and is transmitted to humans by the infected body louse Pediculus humanus. We have recently demonstrated that the B. recurrentis surface receptor, HcpA, specifically binds factor H, the regulator of the alternative pathway of complement activation, thereby inhibiting complement mediated bacteriolysis. Here, we show that B. recurrentis spirochetes express another potential outer membrane lipoprotein, termed CihC, and acquire C4b-binding protein (C4bp) and human C1 esterase inhibitor (C1-Inh), the major inhibitors of the classical and lectin pathway of complement activation. A highly homologous receptor for C4bp was also found in the African tick-borne relapsing fever spirochete B. duttonii. Upon its binding to B. recurrentis or recombinant CihC, C4bp retains its functional potential, i.e. facilitating the factor I-mediated degradation of C4b. The additional finding that ectopic expression of CihC in serum sensitive B. burgdorferi significantly increased spirochetal resistance against human complement suggests this receptor to substantially contribute, together with other known strategies, to immune evasion of B. recurrentis

Dynamics of the condensate in zero-range processes

For stochastic processes leading to condensation, the condensate, once it is formed, performs an ergodic stationary-state motion over the system. We analyse this motion, and especially its characteristic time, for zero-range processes. The characteristic time is found to grow with the system size much faster than the diffusive timescale, but not exponentially fast. This holds both in the mean-field geometry and on finite-dimensional lattices. In the generic situation where the critical mass distribution follows a power law, the characteristic time grows as a power of the system size.Comment: 27 pages, 7 figures. Minor changes and updates performe