arXiv subjects

E. Levine

Publications and source records attributed to E. Levine.

At least 19 recordsLinked to original sources

arXiv2007

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.

cond-mat.stat-mech↗

arXiv2006

Dynamical scaling for probe particles in a driven fluid

We investigate two distinct universality classes for probe particles that move stochastically in a one-dimensional driven system. If the random force that drives the probe particles is fully generated by the current fluctuations of the driven fluid, such as when the probe particles are embedded in a ring, they inherit the dynamical exponent of the fluid, which generically is z=3/2. On the other hand, if the random force has a part that is temporally uncorrelated, the resulting motion can be described by a dynamical exponent z=2 as considered in previous work.

cond-mat.stat-mech↗

arXiv2005

Critical phase in non-conserving zero-range processes and equilibrium networks

Zero-range processes, in which particles hop between sites on a lattice, are closely related to equilibrium networks, in which rewiring of links take place. Both systems exhibit a condensation transition for appropriate choices of the dynamical rules. The transition results in a macroscopically occupied site for zero-range processes and a macroscopically connected node for networks. Criticality, characterized by a scale-free distribution, is obtained only at the transition point. This is in contrast with the widespread scale-free real-life networks. Here we propose a generalization of these models whereby criticality is obtained throughout an entire phase, and the scale-free distribution does not depend on any fine-tuned parameter.

cond-mat.stat-mech↗

arXiv2004

Condensation and coexistence in a two-species driven model

Condensation transition in two-species driven systems in a ring geometry is studied in the case where current-density relation of a domain of particles exhibits two degenerate maxima. It is found that the two maximal current phases coexist both in the fluctuating domains of the fluid and in the condensate, when it exists. This has a profound effect on the steady state properties of the model. In particular, phase separation becomes more favorable, as compared with the case of a single maximum in the current-density relation. Moreover, a selection mechanism imposes equal currents flowing out of the condensate, resulting in a neutral fluid even when the total number of particles of the two species are not equal. In this case the particle imbalance shows up only in the condensate.

cond-mat.stat-mech↗

arXiv2004

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 ρ_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.

cond-mat.stat-mech↗

arXiv2004

Long-range attraction between probe particles mediated by a driven fluid

The effective interaction between two probe particles in a one-dimensional driven system is studied. The analysis is carried out using an asymmetric simple exclusion process with nearest-neighbor interactions. It is found that the driven fluid mediates an effective long-range attraction between the two probes, with a force that decays at large distances x as -b/x, where b is a function of the interaction parameters. Depending on the amplitude b the two probes may form one of three states: (a) an unbound state, where the distance grows diffusively with time; (b) a weakly bound state, in which the distance grows sub-diffusively; and (c) a strongly bound state, where the average distance stays finite in the long time limit. Similar results are found for the behavior of any finite number of probes.

cond-mat.stat-mech↗

arXiv2004

Modelling one-dimensional driven diffusive systems by the Zero-Range Process

The recently introduced correspondence between one-dimensional two-species driven models and the Zero-Range Process is extended to study the case where the densities of the two species need not be equal. The correspondence is formulated through the length dependence of the current emitted from a particle domain. A direct numerical method for evaluating this current is introduced, and used to test the assumptions underlying this approach. In addition, a model for isolated domain dynamics is introduced, which provides a simple way to calculate the current also for the non-equal density case. This approach is demonstrated and applied to a particular two-species model, where a phase separation transition line is calculated.

cond-mat.stat-mech↗

arXiv2004

Condensation transition in zero-range processes with diffusion

Recent studies have indicated that the coarse grained dynamics of a large class of traffic models and driven-diffusive systems may be described by urn models. We consider a class of one-dimensional urn models whereby particles hop from an urn to its nearest neighbor by a rate which decays with the occupation number k of the departure site as (1+b/k). In addition a diffusion process takes place, whereby all particles in an urn may hop to an adjacent one with some rate alpha$. Condensation transition which may take place in this model is studied and the (b,alpha) phase diagram is calculated within the mean field approximation and by numerical simulations. A driven-diffusive model whose coarse grained dynamics corresponds to this urn model is considered.

cond-mat.stat-mech↗

arXiv2004

Traffic jams and ordering far from thermal equilibrium

The recently suggested correspondence between domain dynamics of traffic models and the asymmetric chipping model is reviewed. It is observed that in many cases traffic domains perform the two characteristic dynamical processes of the chipping model, namely chipping and diffusion. This correspondence indicates that jamming in traffic models in which all dynamical rates are non-deterministic takes place as a broad crossover phenomenon, rather than a sharp transition. Two traffic models are studied in detail and analyzed within this picture.

cond-mat.stat-mech↗

arXiv2003

Phase Transitions in Traffic Models

It is suggested that the question of existence of a jamming phase transition in a broad class of single-lane cellular-automaton traffic models may be studied using a correspondence to the asymmetric chipping model. In models where such correspondence is applicable, jamming phase transition does not take place. Rather, the system exhibits a smooth crossover between free-flow and jammed states, as the car density is increased.

cond-mat.stat-mech↗

arXiv2003

Spontaneous Symmetry Breaking in a Non-Conserving Two-Species Driven Model

A two species particle model on an open chain with dynamics which is non-conserving in the bulk is introduced. The dynamical rules which define the model obey a symmetry between the two species. The model exhibits a rich behavior which includes spontaneous symmetry breaking and localized shocks. The phase diagram in several regions of parameter space is calculated within mean-field approximation, and compared with Monte-Carlo simulations. In the limit where fluctuations in the number of particles in the system are taken to zero, an exact solution is obtained. We present and analyze a physical picture which serves to explain the different phases of the model.

cond-mat.stat-mech↗

arXiv2002

Novel phase-separation transition in one-dimensional driven models

A class of models of driven diffusive systems which is shown to exhibit phase separation in $d=1$ dimensions is introduced. Unlike all previously studied models exhibiting similar phenomena, here the phase separated state is fluctuating in the bulk of the macroscopic domains. The nature of the phase transition from the homogeneous to the phase separated state is discussed in view of a recently introduced criterion for phase separation in one-dimensional driven systems.

cond-mat.stat-mech↗

arXiv2002

Criterion for phase separation in one-dimensional driven systems

A general criterion for the existence of phase separation in driven one-dimensional systems is proposed. It is suggested that phase separation is related to the size dependence of the steady-state 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. Several driven diffusive models are discussed in light of the conjecture.

cond-mat.stat-mech↗

arXiv2002

Sharp crossover and anomalously large correlation length in driven systems

Models of one-dimensional driven diffusive systems sometimes exhibit an abrupt increase of the correlation length to an anomalously large but finite value as the parameters of the model are varied. This behavior may be misinterpreted as a genuine phase transition. A simple mechanism for this sharp increase is presented. The mechanism is introduced within the framework of a recently suggested correspondence between driven diffusive systems and zero-range processes. It is shown that when the dynamics of the model is such that small domains are suppressed in the steady-state distribution, anomalously large correlation length may build up. The mechanism is examined in detail in two models.

cond-mat.stat-mech↗

arXiv2002

Phase transition in a non-conserving driven diffusive system

An asymmetric exclusion process comprising positive particles, negative particles and vacancies is introduced. The model is defined on a ring and the dynamics does not conserve the number of particles. We solve the steady state exactly and show that it can exhibit a continuous phase transition in which the density of vacancies decreases to zero. The model has no absorbing state and furnishes an example of a one-dimensional phase transition in a homogeneous non-conserving system which does not belong to the absorbing state universality classes.

cond-mat.stat-mech↗

arXiv2001

Ordering dynamics of the driven lattice gas model

The evolution of a two-dimensional driven lattice-gas model is studied on an L_x X L_y lattice. Scaling arguments and extensive numerical simulations are used to show that starting from random initial configuration the model evolves via two stages: (a) an early stage in which alternating stripes of particles and vacancies are formed along the direction y of the driving field, and (b) a stripe coarsening stage, in which the number of stripes is reduced and their average width increases. The number of stripes formed at the end of the first stage is shown to be a function of L_x/L_y^ϕ, with ϕ~ 0.2. Thus, depending on this parameter, the resulting state could be either single or multi striped. In the second, stripe coarsening stage, the coarsening time is found to be proportional to L_y, becoming infinitely long in the thermodynamic limit. This implies that the multi striped state is thermodynamically stable. The results put previous studies of the model in a more general framework.

cond-mat.stat-mech↗

arXiv2000

Coarsening of a Class of Driven Striped Structures

The coarsening process in a class of driven systems exhibiting striped structures is studied. The dynamics is governed by the motion of the driven interfaces between the stripes. When two interfaces meet they coalesce thus giving rise to a coarsening process in which l(t), the average width of a stripe, grows with time. This is a generalization of the reaction-diffusion process A + A -> A to the case of extended coalescing objects, namely, the interfaces. Scaling arguments which relate the coarsening process to the evolution of a single driven interface are given, yielding growth laws for l(t), for both short and long time. We introduce a simple microscopic model for this process. Numerical simulations of the model confirm the scaling picture and growth laws. The results are compared to the case where the stripes are not driven and different growth laws arise.

cond-mat.stat-mech↗

arXiv2000

Coupled Two-Way Clustering Analysis of Gene Microarray Data

We present a novel coupled two-way clustering approach to gene microarray data analysis. The main idea is to identify subsets of the genes and samples, such that when one of these is used to cluster the other, stable and significant partitions emerge. The search for such subsets is a computationally complex task: we present an algorithm, based on iterative clustering, which performs such a search. This analysis is especially suitable for gene microarray data, where the contributions of a variety of biological mechanisms to the gene expression levels are entangled in a large body of experimental data. The method was applied to two gene microarray data sets, on colon cancer and leukemia. By identifying relevant subsets of the data and focusing on them we were able to discover partitions and correlations that were masked and hidden when the full dataset was used in the analysis. Some of these partitions have clear biological interpretation; others can serve to identify possible directions for future research.

physics.bio-ph↗