Parallel Coupling of Symmetric and Asymmetric Exclusion Processes

A system consisting of two parallel coupled channels where particles in one of them follow the rules of totally asymmetric exclusion processes (TASEP) and in another one move as in symmetric simple exclusion processes (SSEP) is investigated theoretically. Particles interact with each other via hard-core exclusion potential, and in the asymmetric channel they can only hop in one direction, while on the symmetric lattice particles jump in both directions with equal probabilities. Inter-channel transitions are also allowed at every site of both lattices. Stationary state properties of the system are solved exactly in the limit of strong couplings between the channels. It is shown that strong symmetric couplings between totally asymmetric and symmetric channels lead to an effective partially asymmetric simple exclusion process (PASEP) and properties of both channels become almost identical. However, strong asymmetric couplings between symmetric and asymmetric channels yield an effective TASEP with nonzero particle flux in the asymmetric channel and zero flux on the symmetric lattice. For intermediate strength of couplings between the lattices a vertical cluster mean-field method is developed. This approximate approach treats exactly particle dynamics during the vertical transitions between the channels and it neglects the correlations along the channels. Our calculations show that in all cases there are three stationary phases defined by particle dynamics at entrances, at exits or in the bulk of the system, while phase boundaries depend on the strength and symmetry of couplings between the channels. Extensive Monte Carlo computer simulations strongly support our theoretical predictions.Comment: 16 page

Inhomogeneous Coupling in Two-Channel Asymmetric Simple Exclusion Processes

Asymmetric exclusion processes for particles moving on parallel channels with inhomogeneous coupling are investigated theoretically. Particles interact with hard-core exclusion and move in the same direction on both lattices, while transitions between the channels is allowed at one specific location in the bulk of the system. An approximate theoretical approach that describes the dynamics in the vertical link and horizontal lattice segments exactly but neglects the correlation between the horizontal and vertical transport is developed. It allows us to calculate stationary phase diagrams, particle currents and densities for symmetric and asymmetric transitions between the channels. It is shown that in the case of the symmetric coupling there are three stationary phases, similarly to the case of single-channel totally asymmetric exclusion processes with local inhomogeneity. However, the asymmetric coupling between the lattices lead to a very complex phase diagram with ten stationary-state regimes. Extensive Monte Carlo computer simulations generally support theoretical predictions, although simulated stationary-state properties slightly deviate from calculated in the mean-field approximation, suggesting the importance of correlations in the system. Dynamic properties and phase diagrams are discussed by analyzing constraints on the particle currents across the channels

Dynamics at barriers in bidirectional two-lane exclusion processes

A two-lane exclusion process is studied where particles move in the two lanes in opposite directions and are able to change lanes. The focus is on the steady state behavior in situations where a positive current is constrained to an extended subsystem (either by appropriate boundary conditions or by the embedding environment) where, in the absence of the constraint, the current would be negative. We have found two qualitatively different types of steady states and formulated the conditions of them in terms of the transition rates. In the first type of steady state, a localized cluster of particles forms with an anti-shock located in the subsystem and the current vanishes exponentially with the extension of the subsystem. This behavior is analogous to that of the one-lane partially asymmetric simple exclusion process, and can be realized e.g. when the local drive is induced by making the jump rates in two lanes unequal. In the second type of steady state, which is realized e.g. if the local drive is induced purely by the bias in the lane change rates, and which has thus no counterpart in the one-lane model, a delocalized cluster of particles forms which performs a diffusive motion as a whole and, as a consequence, the current vanishes inversely proportionally to the extension of the subsystem. The model is also studied in the presence of quenched disordered, where, in case of delocalization, phenomenological considerations predict anomalously slow, logarithmic decay of the current with the system size in contrast with the usual power-law.Comment: 24 pages, 13 figure

Perception of Relative Depth Interval: Systematic Biases in Perceived Depth

Given an estimate of the binocular disparity between a pair of points and an estimate of the viewing distance, or knowledge of eye position, it should be possible to obtain an estimate of their depth separation. Here we show that, when points are arranged in different vertical geometric configurations across two intervals, many observers find this task difficult. Those who can do the task tend to perceive the depth interval in one configuration as very different from depth in the other configuration. We explore two plausible explanations for this effect. The first is the tilt of the empirical vertical horopter: Points perceived along an apparently vertical line correspond to a physical line of points tilted backwards in space. Second, the eyes can rotate in response to a particular stimulus. Without compensation for this rotation, biases in depth perception would result. We measured cyclovergence indirectly, using a standard psychophysical task, while observers viewed our depth configuration. Biases predicted from error due either to cyclovergence or to the tilted vertical horopter were not consistent with the depth configuration results. Our data suggest that, even for the simplest scenes, we do not have ready access to metric depth from binocular disparity.</jats:p

Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport

Unlike equilibrium statistical mechanics, with its well-established foundations, a similar widely-accepted framework for non-equilibrium statistical mechanics (NESM) remains elusive. Here, we review some of the many recent activities on NESM, focusing on some of the fundamental issues and general aspects. Using the language of stochastic Markov processes, we emphasize general properties of the evolution of configurational probabilities, as described by master equations. Of particular interest are systems in which the dynamics violate detailed balance, since such systems serve to model a wide variety of phenomena in nature. We next review two distinct approaches for investigating such problems. One approach focuses on models sufficiently simple to allow us to find exact, analytic, non-trivial results. We provide detailed mathematical analyses of a one-dimensional continuous-time lattice gas, the totally asymmetric exclusion process (TASEP). It is regarded as a paradigmatic model for NESM, much like the role the Ising model played for equilibrium statistical mechanics. It is also the starting point for the second approach, which attempts to include more realistic ingredients in order to be more applicable to systems in nature. Restricting ourselves to the area of biophysics and cellular biology, we review a number of models that are relevant for transport phenomena. Successes and limitations of these simple models are also highlighted.Comment: 72 pages, 18 figures, Accepted to: Reports on Progress in Physic