arXiv subjects

N. C. Pesheva

Publications and source records attributed to N. C. Pesheva.

7 recordsLinked to original sources

arXiv2022

Generalized TASEP on open chains with a modified injection condition

We report here our preliminary results in the study of a new version of the generalized Totally Asymmetric Simple Exclusion process (gTASEP) on open tracks. In the gTASEP an additional interaction between the particles is considered, besides the hard-core exclusion, which exists in the standard TASEP. It is modeled by the introduction of a second hopping probability $p_m$ for the particles, belonging to the same cluster, in addition to the standard hopping probability p, which now applies only for single particles and the head (rightmost) particle of a cluster. We briefly describe how one can obtain analytically solvable version of gTASEP by modifying the left (injection) boundary condition. A short comparison is made with the previously studied version of gTASEP on open tracks.

cond-mat.stat-mech↗

arXiv2020

gTASEP with attraction interaction on lattices with open boundaries

We study a model of aggregation and fragmentation of clusters of particles on an open segment of a single-lane road. The particles and clusters obey the stochastic discrete-time discrete-space kinetics of the Totally Asymmetric Simple Exclusion Process (TASEP) with backward ordered sequential update (dynamics), endowed with two hopping probabilities, p and pm. The second modified probability, pm, models a special kinematic interaction between the particles belonging to the same cluster. This modification is called generalized TASEP (gTASEP) since it contains as special cases TASEP with parallel update and TASEP with backward ordered sequential update for specific values of the second hopping probability pm. We focus here on exemplifying the effect of the additional attraction interaction on the system properties in the non-equilibrium steady state. We estimate various physical quantities (bulk density, density distribution, and the current) in the system and how they change with the increase of pm (p < pm<1). Within a random walk theory we consider the evolution of the gaps under different boundary conditions and present space-time plots generated by MC simulations, illustrating the applicability of the random walk theory for the study of gTASEP.

cond-mat.stat-mech↗

arXiv2019

One-dimensional discrete aggregation-fragmentation model

We study here one-dimensional model of aggregation and fragmentation of clusters of particles obeying the stochastic discrete-time kinetics of the generalized Totally Asymmetric Simple Exclusion Process (gTASEP) on open chains. Isolated particles and the first particle of a cluster of particles hop one site forward with probability $p$; when the first particle of a cluster hops, the remaining particles of the same cluster may hop with a modified probability $p_m$, modelling a special kinematic interaction between neighboring particles, or remain in place with probability $1-p_m$. The model contains as special cases the TASEP with parallel update ($p_m =0$) and with sequential backward-ordered update ($p_m =p$). These cases have been exactly solved for the stationary states and their properties thoroughly studied. The limiting case of $p_m =1$, which corresponds to irreversible aggregation, has been recently studied too. Its phase diagram in the plane of injection ($α$) and ejection ($β$) probabilities was found to have a different topology. Here we focus on the stationary properties of the gTASEP in the generic case of attraction $p<p_m<1$ when aggregation-fragmentation of clusters occurs. We find that the topology of the phase diagram at $p_m =1$ changes sharply to the one corresponding to $p_m =p$ as soon as $p_m$ becomes less than $1$. Then a maximum current phase appears in the square domain $α_c(p,p_m)\leα\le 1$ and $β_c(p,p_m) \le β\le 1$, where $α_c(p,p_m)= β_c(p,p_m)\equiv σ_c(p,p_m)$ are parameter-dependent injection/ejection critical values. The properties of the phase transitions between the three stationary phases at $p< p_m <1$ are assessed by computer simulations and random walk theory.

cond-mat.stat-mech↗

arXiv2017

A model of irreversible jam formation in dense traffic

We study an one-dimensional stochastic model of vehicular traffic on open segments of a single-lane road of finite size $L$. The vehicles obey a stochastic discrete-time dynamics which is a limiting case of the generalized Totally Asymmetric Simple Exclusion Process. This dynamics has been previously used by Bunzarova and Pesheva [Phys. Rev. E 95, 052105 (2017)] for an one-dimensional model of irreversible aggregation. The model was shown to have three stationary phases: a many-particle one, MP, a phase with completely filled configuration, CF, and a boundary perturbed MP+CF phase, depending on the values of the particle injection ($α$), ejection ($β$) and hopping ($p$) probabilities. Here we extend the results for the stationary properties of the MP+CF phase, by deriving exact expressions for the local density at the first site of the chain and the probability P(1) of a completely jammed configuration. The unusual phase transition, characterized by jumps in both the bulk density and the current (in the thermodynamic limit), as $α$ crosses the boundary $α=p$ from the MP to the CF phase, is explained by the finite-size behavior of P(1). By using a random walk theory, we find that, when $α$ approaches from below the boundary $α=p$, three different regimes appear, as the size $L\rightarrow \infty$: (i) the lifetime of the gap between the rightmost clusters is of the order $O(L)$ in the MP phase; (ii) small jams, separated by gaps with lifetime $O(1)$, exist in the MP+CF phase close to the left chain boundary; and (iii) when $β=p$, the jams are divided by gaps with lifetime of the order $O(L^{1/2})$. These results are supported by extensive Monte Carlo calculations.

cond-mat.stat-mech↗

arXiv2015

On the appearance of traffic jams in a long chain with a shortcut in the bulk

The appearance of traffic jams on chains with a shunted section between two simple chain segments in the maximum current phase is studied in the framework of the Totally Asymmetric Simple Exclusion Process. The conditions for the occurrence of this phenomenon are investigated both within the effective rates approximation and numerically for arbitrary length of the shortcut. The problem is interesting on its own because the conditions for coexistence of low- and high density phases are essentially different from those for a simple chain between two reservoirs. Our main results are: (1) For any values of the external rates in the domain of the maximum current phase, there exists a position of the shortcut where the shunted segment is in a phase of coexistence with a completely delocalized domain wall; (2) The main features of the coexistence phase and the density profiles in the whole network are well described by the domain wall theory. Apart from the negligible inter-chain correlations, they depend only on the current through the shortcut; (3) The model displays an unexpected feature: the current through the longer shunted segment is larger than the current through the shortcut; (4) From the viewpoint of vehicular traffic, most comfortable conditions for the drivers are provided when the shortcut is shifted downstream from the position of coexistence, when both the shunted segment and the shortcut exhibit low-density lamellar flow. Most unfavorable is the opposite case of upstream shifted shortcut, when both the shunted segment and the shortcut are in a high-density phase describing congested traffic of slowly moving cars. The above results are relevant also to phenomena like crowding of molecular motors moving along twisted protofilaments.

cond-mat.stat-mech↗

arXiv2008

One-Dimensional Traffic Flow Models: Theory and Computer Simulations

Theoretical advances in the study of non-equilibrium phenomena are briefly reviewed with emphasis on steady state properties of one-dimensional driven lattice gases. The presentation is focused on the totally asymmetric simple-exclusion process (TASEP) with open boundary conditions: particles are injected at the left end with rate alpha and removed at the right end with rate beta. Depending on the values of these parameters, the model exhibits three stationary phases, separated by lines of first- and second-order non-equilibrium phase transitions. New simulation results on the power spectrum of the fluctuating total number of particles in the different phases of the system are presented. Our theoretical contribution concerns the approximate evaluation of the power spectrum in the domain-wall picture of the coexisting low- and high-density phases. Finally, we review some of our recent results on the TASEP defined on an open network containing a double-chain section in the middle. With the aid of a simple theory, which neglects correlations at the junctions of the chain segments, the possible phase structures of the model are found. Density profiles and nearest-neighbor correlations in the steady states of the model at representative points of the phase diagram are obtained by means of computer simulations. On the coexistence line cross-correlations are found to exist between equivalent sites in the branches of the middle section.

cond-mat.stat-mech↗

arXiv1995

Layer Features of the Lattice Gas Model for Self-Organized Criticality

A layer-by-layer description of the asymmetric lattice gas model for 1/f-noise suggested by Jensen [Phys. Rev. Lett. 64, 3103 (1990)] is presented. The power spectra of the lattice layers in the direction perpendicular to the particle flux is studied in order to understand how the white noise at the input boundary evolves, on the average, into 1/f-noise for the system. The effects of high boundary drive and uniform driving force on the power spectrum of the total number of diffusing particles are considered. In the case of nearest-neighbor particle interactions, high statistics simulation results show that the power spectra of single lattice layers are characterized by different $β_x$ exponents such that $β_x \to 1.9$ as one approaches the outer boundary.

cond-mat↗