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Register a new userShock-dynamics of two-lane driven lattice gases
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Added by
Appert-Rolland Cecile
Publication date
2010
fields
Physics
and research's language is
English
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Driven lattice gases as the ASEP are useful tools for the modeling of various stochastic transport processes carried out by self-driven particles, such as molecular motors or vehicles in road traffic. Often these processes take place in one-dimensional systems offering several tracks to the particles, and in many cases the particles are able to change track with a given rate. In this work we consider the case of strong coupling where the hopping rate along the tracks and the exchange rates are of the same order, and show how a phenomenological approach based on a domain wall theory can describe the dynamics of the system. In particular, the domain walls on the different tracks form pairs, whose dynamics dominate the behavior of the system.
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We consider a large class of two-lane driven diffusive systems in contact with reservoirs at their boundaries and develop a stability analysis as a method to derive the phase diagrams of such systems. We illustrate the method by deriving phase diagrams for the asymmetric exclusion process coupled to various second lanes: a diffusive lane; an asymmetric exclusion process with advection in the same direction as the first lane, and an asymmetric exclusion process with advection in the opposite direction. The competing currents on the two lanes naturally lead to a very rich phenomenology and we find a variety of phase diagrams. It is shown that the stability analysis is equivalent to an `extremal current principle for the total current in the two lanes. We also point to classes of models where both the stability analysis and the extremal current principle fail.
Properties of the one-dimensional totally asymmetric simple exclusion process (TASEP), and their connection with the dynamical scaling of moving interfaces described by a Kardar-Parisi-Zhang (KPZ) equation are investigated. With periodic boundary conditions, scaling of interface widths (the latter defined via a discrete occupation-number-to-height mapping), gives the exponents $alpha=0.500(5)$, $z=1.52(3)$, $beta=0.33(1)$. With open boundaries, results are as follows: (i) in the maximal-current phase, the exponents are the same as for the periodic case, and in agreement with recent Bethe ansatz results; (ii) in the low-density phase, curve collapse can be found to a rather good extent, with $alpha=0.497(3)$, $z=1.20(5)$, $beta=0.41(2)$, which is apparently at variance with the Bethe ansatz prediction $z=0$; (iii) on the coexistence line between low- and high- density phases, $alpha=0.99(1)$, $z=2.10(5)$, $beta=0.47(2)$, in relatively good agreement with the Bethe ansatz prediction $z=2$. From a mean-field continuum formulation, a characteristic relaxation time, related to kinematic-wave propagation and having an effective exponent $z^prime=1$, is shown to be the limiting slow process for the low density phase, which accounts for the above-mentioned discrepancy with Bethe ansatz results. For TASEP with quenched bond disorder, interface width scaling gives $alpha=1.05(5)$, $z=1.7(1)$, $beta=0.62(7)$. From a direct analytic approach to steady-state properties of TASEP with quenched disorder, closed-form expressions for the piecewise shape of averaged density profiles are given, as well as rather restrictive bounds on currents. All these are substantiated in numerical simulations.
We employ Monte Carlo simulations to study the non-equilibrium relaxation of driven Ising lattice gases in two dimensions. Whereas the temporal scaling of the density auto-correlation function in the non-equilibrium steady state does not allow a precise measurement of the critical exponents, these can be accurately determined from the aging scaling of the two-time auto-correlations and the order parameter evolution following a quench to the critical point. We obtain excellent agreement with renormalization group predictions based on the standard Langevin representation of driven Ising lattice gases.
Monte Carlo simulations have been used to study the phase diagrams for square Ising-lattice gas models with two-body and three-body interactions for values of interaction parameters in a range that has not been previously considered. We find unexpected qualitative differences as compared with predictions made on general grounds.
We focus here on the thermodynamic properties of adsorbates formed by two-species $A+B to oslash$ reactions on a one-dimensional infinite lattice with heterogeneous catalytic properties. In our model hard-core $A$ and $B$ particles undergo continuous exchanges with their reservoirs and react when dissimilar species appear at neighboring lattice sites in presence of a catalyst. The latter is modeled by supposing either that randomly chosen bonds in the lattice promote reactions (Model I) or that reactions are activated by randomly chosen lattice sites (Model II). In the case of annealed disorder in spatial distribution of a catalyst we calculate the pressure of the adsorbate by solving three-site (Model I) or four-site (Model II) recursions obeyed by the corresponding averaged grand-canonical partition functions. In the case of quenched disorder, we use two complementary approaches to find $textit{exact}$ expressions for the pressure. The first approach is based on direct combinatorial arguments. In the second approach, we frame the model in terms of random matrices; the pressure is then represented as an averaged logarithm of the trace of a product of random $3 times 3$ matrices -- either uncorrelated (Model I) or sequentially correlated (Model II).
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