Explosive condensation in a mass transport model

We study a far-from-equilibrium system of interacting particles, hopping between sites of a 1d lattice with a rate which increases with the number of particles at interacting sites. We find that clusters of particles, which initially spontaneously form in the system, begin to move at increasing speed as they gain particles. Ultimately, they produce a moving condensate which comprises a finite fraction of the mass in the system. We show that, in contrast with previously studied models of condensation, the relaxation time to steady state decreases as an inverse power of ln L with system size L and that condensation is instantenous for L-->infinity.Comment: 5 pages, 5 figures, minor changes, references adde

Totally asymmetric exclusion process with site-wise dynamic disorder

We propose an extension of the totally asymmetric simple exclusion process (TASEP) in which particles hopping along a lattice can be blocked by obstacles that dynamically attach/detach from lattice sites. The model can be thought as TASEP with site-wise dynamic disorder. We consider two versions of defect dynamics: (i) defects can bind to any site, irrespective of particle occupation, (ii) defects only bind to sites which are not occupied by particles (particle-obstacle exclusion). In case (i) there is a symmetric, parabolic-like relationship between the current and particle density, as in the standard TASEP. Case (ii) leads to a skewed relationship for slow defect dynamics. We also show that the presence of defects induces particle clustering, despite the translation invariance of the system. For open boundaries the same three phases as for the standard TASEP are observed, albeit the position of phase boundaries is affected by the presence of obstacles. We develop a simple mean-field theory that captures the model's quantitative behaviour for periodic and open boundary conditions and yields good estimates for the current-density relationship, mean cluster sizes and phase boundaries. Lastly, we discuss an application of the model to the biological process of gene transcription.Comment: submitted to J. Phys.

Current-density relation in the exclusion process with dynamic obstacles

We investigate the totally asymmetric simple exclusion process (TASEP) in the presence of obstacles that dynamically bind and unbind from the lattice. The model is motivated by biological processes such as transcription in the presence of DNA-binding proteins. Similar models have been studied before using the mean-field approximation, but the exact relation between the particle current and density remains elusive. Here, we first show using extensive Monte Carlo simulations that the current-density relation in this model assumes a quasi-parabolic form similar to that of the ordinary TASEP without obstacles. We then attempt to explain this relation using exact calculations in the limit of low and high density of particles. Our results suggest that the symmetric, quasi-parabolic current-density relation arises through a non-trivial cancellation of higher-order terms, similarly as in the standard TASEP.Comment: 12 pages, 6 figure

A simple non-equilibrium, statistical-physics toy model of thin-film growth

We present a simple non-equilibrium model of mass condensation with Lennard-Jones interactions between particles and the substrate. We show that when some number of particles is deposited onto the surface and the system is left to equilibrate, particles condense into an island if the density of particles becomes higher than some critical density. We illustrate this with numerically obtained phase diagrams for three-dimensional systems. We also solve a two-dimensional counterpart of this model analytically and show that not only the phase diagram but also the shape of the cross-sections of three-dimensional condensates qualitatively matches the two-dimensional predictions. Lastly, we show that when particles are being deposited with a constant rate, the system has two phases: a single condensate for low deposition rates, and multiple condensates for fast deposition. The behaviour of our model is thus similar to that of thin film growth processes, and in particular to Stranski-Krastanov growth.Comment: 26 pages, 16 figure