Spontaneous pulsing states in an active particle system

Abstract

Abstract.We study a two-lane two-species exclusion process inspired by Lin et al. (C. Lin et al. J. Stat. Mech., 2011), that exhibits a non-equilibrium pulsing phase. Particles move on two parallel one-dimensional tracks, with one open and one reflecting boundary. The particle type defines the hopping direction. When only particles hopping towards the open end are allowed to change lane, the system exhibits a phase transition from a low density phase to a pulsing phase depending on the ratio between particle injection and type-changing rate. This phase transition can be observed in the stochastic model as well as in a mean-field description. In the low density phase, the density profile can be predicted analytically. The pulsing phase is characterised by a fast filling of the system and -once filled -by a slowly backwards moving front separating a decreasing dense region and an expanding low density region. The hopping of the front on the discrete lattice is found to create density oscillations, both, in time and space. By means of a stability analysis we can predict the structure of the dense region during the emptying process, characterised by exponentially damped perturbations, both at the open end and near the moving front.arXiv:1604.08492v1 [cond-mat.stat-mech]

Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension

“…In confined geometries, RTPs and ABPs are known to accumulate near the boundaries of the domain [7]. The steady-state distribution of such active particles in confining potentials are non-Boltzmannian [30,[34][35][36] and can exhibit jammed states [18,37]. More recently there have been a number of studies on computing the steady-state distribution for both RTPs and ABPs in various confined geometries, but using approximate methods in most cases [38][39][40][41].…”

A biologically inspired two-species exclusion model: effects of RNA polymerase motor traffic on simultaneous DNA replication

“…The totally asymmetric simple exclusion process (TASEP) [1][2][3][4] was originally introduced as a simplified model describing the kinetics of protein synthesis [5,6]. Since then it has found many more applications to biological systems, especially to situations [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26], where the kinetics is dominated by the traffic-like collective motion of molecular motors (for reviews, see [27][28][29][30][31]). Genetic message encoded chemically in the sequence of the monomeric subunits of DNA is transcribed into an RNA molecule by a molecular motor called RNA polymerase (RNAP).…”