Exact shock measures and steady-state selection in a driven diffusive system with two conserved densities

We study driven 1d lattice gas models with two types of particles and nearest neighbor hopping. We find the most general case when there is a shock solution with a product measure which has a density-profile of a step function for both densities. The position of the shock performs a biased random walk. We calculate the microscopic hopping rates of the shock. We also construct the hydrodynamic limit of the model and solve the resulting hyperbolic system of conservation laws. In case of open boundaries the selected steady state is given in terms of the boundary densities.Comment: 12 pages, 4 figure

Phase transition in the two-component symmetric exclusion process with open boundaries

We consider single-file diffusion in an open system with two species $A,B$ of particles. At the boundaries we assume different reservoir densities which drive the system into a non-equilibrium steady state. As a model we use an one-dimensional two-component simple symmetric exclusion process with two different hopping rates $D_A,D_B$ and open boundaries. For investigating the dynamics in the hydrodynamic limit we derive a system of coupled non-linear diffusion equations for the coarse-grained particle densities. The relaxation of the initial density profile is analyzed by numerical integration. Exact analytical expressions are obtained for the self-diffusion coefficients, which turns out to be length-dependent, and for the stationary solution. In the steady state we find a discontinuous boundary-induced phase transition as the total exterior density gradient between the system boundaries is varied. At one boundary a boundary layer develops inside which the current flows against the local density gradient. Generically the width of the boundary layer and the bulk density profiles do not depend on the two hopping rates. At the phase transition line, however, the individual density profiles depend strongly on the ratio $D_A/D_B$. Dynamic Monte Carlo simulation confirm our theoretical predictions.Comment: 26 pages, 6 figure

Bethe ansatz and current distribution for the TASEP with particle-dependent hopping rates

Using the Bethe ansatz we obtain in a determinant form the exact solution of the master equation for the conditional probabilities of the totally asymmetric exclusion process with particle-dependent hopping rates on Z. From this we derive a determinant expression for the time-integrated current for a step-function initial state.Comment: 14 page

Phase Coexistence in Driven One Dimensional Transport

We study a one-dimensional totally asymmetric exclusion process with random particle attachments and detachments in the bulk. The resulting dynamics leads to unexpected stationary regimes for large but finite systems. Such regimes are characterized by a phase coexistence of low and high density regions separated by domain walls. We use a mean-field approach to interpret the numerical results obtained by Monte-Carlo simulations and we predict the phase diagram of this non-conserved dynamics in the thermodynamic limit.Comment: 4 pages, 3 figures. Accepted for publication on Phys. Rev. Let

Infinite reflections of shock fronts in driven diffusive systems with two species

Interaction of a domain wall with boundaries of a system is studied for a class of stochastic driven particle models. Reflection maps are introduced for the description of this process. We show that, generically, a domain wall reflects infinitely many times from the boundaries before a stationary state can be reached. This is in an evident contrast with one-species models where the stationary density is attained after just one reflection.Comment: 11 pages, 8 eps figs, to appearin JPhysA 01.200

Bethe ansatz solution of zero-range process with nonuniform stationary state

The eigenfunctions and eigenvalues of the master-equation for zero range process with totally asymmetric dynamics on a ring are found exactly using the Bethe ansatz weighted with the stationary weights of particle configurations. The Bethe ansatz applicability requires the rates of hopping of particles out of a site to be the $q$-numbers $[n]_q$. This is a generalization of the rates of hopping of noninteracting particles equal to the occupation number $n$ of a site of departure. The noninteracting case can be restored in the limit $q\to 1$. The limiting cases of the model for $q=0,\infty$ correspond to the totally asymmetric exclusion process, and the drop-push model respectively. We analyze the partition function of the model and apply the Bethe ansatz to evaluate the generating function of the total distance travelled by particles at large time in the scaling limit. In case of non-zero interaction, $q \ne 1$, the generating function has the universal scaling form specific for the Kardar-Parizi-Zhang universality class.Comment: 7 pages, Revtex4, mistypes correcte

Der Einfluss von Blütenduftstoffen auf die Oviposition der Rosskastanienminiermotte Cameraria ohridella

The larval stages of Cameraria ohridella develop mining in leaves of the horse chestnut tree Aesculus hippocastanum. The insect establishes three generations in Central Europe. During the appearance of the first generation the horse chestnut trees bloom. Further on, parallel to the flying time of all generations other plant species bloom. The olfactory detection of flower odour compounds and the influence on oviposition of C. ohridella were examined using trace analytical and electrophysiological methods as well as bioassays.Die Larven von Cameraria ohridella (Lepidoptera, Gracillariidae) entwickeln sich als Minierer in den Blättern der gemeinen Rosskastanie, Aesculus hippocastanum. In Mitteleuropa können drei Faltergenerationen ausgebildet werden, wobei die erste während der Blütezeit der Wirtspflanze A. hippocastanum fliegt. Der Schmetterlingsstrauch Buddleja davidii blüht von Sommer bis Herbst während der Flugzeit der zweiten und dritten Generation. Die großen Blütenstände locken zahlreiche Insekten an, die den Nektar als Nahrung nutzen. Mit Hilfe von Spurenanalytischen und elektrophysiologischen Methoden (GC-MS, EAG) sowie Verhaltensversuchen wurde der Einfluss von Blütendüften auf die Oviposition der Rosskastanienminiermotte untersucht. Der Blütenduft von A. hippocastanum und B. davidii unterschied sich in der Komposition emittierter Komponenten. C. ohridella war in der Lage, Blütendüfte zu detektieren. Die untersuchten Blütenduftstoffkomponenten beeinflussten die Oviposition der Miniermotten. Benzaldehyd, Linalool und (E)-β-Caryophyllen wurden von Rosskastanienblüten emittiert und steigerten die Oviposition auf den Blättern. Benzylalkohol wurde nicht von der Rosskastanie abgegeben und reduzierte im Gegensatz zu den anderen Duftstoffkomponenten die Eiablage. Der Blütenduft der Rosskastanie kann Faltern der ersten Generation bei der Wirtspflanzensuche helfen. In Zweifachwahltests mit getopften Rosskastaniensämlingen und blühendem Sommerflieder wurden die Blätter der Wirtspflanze bei der Eiablage bevorzugt. Aber auch auf den Blättern des Sommerflieders konnten abgelegte Eier gezählt werden. Bei alleinigem Angebot (Einfachwahltest) stieg die Anzahl der abgelegten Eier auf dem blühenden Sommerflieder. Falter der dritten Generation, die im Herbst auf eine starke Blattverbräunung der Wirtspflanze A. hippocastanum durch Minierfraß treffen und dort keine grünen Blattbereiche mehr finden, suchen auf anderen Wirtspflanzen einen geeigneten Eiablageplatz. Dabei können Blütenduftstoffkomponenten die Oviposition der Motten beeinflussen

Hydrodynamics of the zero-range process in the condensation regime

We argue that the coarse-grained dynamics of the zero-range process in the condensation regime can be described by an extension of the standard hydrodynamic equation obtained from Eulerian scaling even though the system is not locally stationary. Our result is supported by Monte Carlo simulations.Comment: 14 pages, 3 figures. v2: Minor alteration

Shocks in asymmetric simple exclusion processes of interacting particles

In this paper, we study shocks and related transitions in asymmetric simple exclusion processes of particles with nearest neighbor interactions. We consider two kinds of inter-particle interactions. In one case, the particle-hole symmetry is broken due to the interaction. In the other case, particles have an effective repulsion due to which the particle-current-density drops down near the half filling. These interacting particles move on a one dimensional lattice which is open at both the ends with injection of particles at one end and withdrawal of particles at the other. In addition to this, there are possibilities of attachments or detachments of particles to or from the lattice with certain rates. The hydrodynamic equation that involves the exact particle current-density of the particle conserving system and additional terms taking care of the attachment-detachment kinetics is studied using the techniques of boundary layer analysis.Comment: 10 pages, 8 figure