Boundary-driven phase transitions in open two-species driven systems with an umbilic point

Different phases in open driven systems are governed by either shocks or rarefaction waves. A presence of an isolated umbilic point in bidirectional systems of interacting particles stabilizes an unusual large scale excitation, an umbilic shock (U-shock). We show that in open systems the U-shock governs a large portion of phase space, and drives a new discontinuous transition between the two rarefaction-controlled phases. This is in contrast with strictly hyperbolic case where such a transition is always continuous. Also, we describe another robust phase which takes place of the phase governed by the U-shock, if the umbilic point is not isolated.Comment: 17 pages, 6 Figs. arXiv admin note: text overlap with arXiv:1206.1490; small typos in Eq (3),(5) correcte

Transition probabilities and dynamic structure factor in the ASEP conditioned on strong flux

We consider the asymmetric simple exclusion processes (ASEP) on a ring constrained to produce an atypically large flux, or an extreme activity. Using quantum free fermion techniques we find the time-dependent conditional transition probabilities and the exact dynamical structure factor under such conditioned dynamics. In the thermodynamic limit we obtain the explicit scaling form. This gives a direct proof that the dynamical exponent in the extreme current regime is $z=1$ rather than the KPZ exponent $z=3/2$ which characterizes the ASEP in the regime of typical currents. Some of our results extend to the activity in the partially asymmetric simple exclusion process, including the symmetric case.Comment: 16 pages, 2 figure

Two-Channel Totally Asymmetric Simple Exclusion Processes

Totally asymmetric simple exclusion processes, consisting of two coupled parallel lattice chains with particles interacting with hard-core exclusion and moving along the channels and between them, are considered. In the limit of strong coupling between the channels, the particle currents, density profiles and a phase diagram are calculated exactly by mapping the system into an effective one-channel totally asymmetric exclusion model. For intermediate couplings, a simple approximate theory, that describes the particle dynamics in vertical clusters of two corresponding parallel sites exactly and neglects the correlations between different vertical clusters, is developed. It is found that, similarly to the case of one-channel totally asymmetric simple exclusion processes, there are three stationary state phases, although the phase boundaries and stationary properties strongly depend on inter-channel coupling. An extensive computer Monte Carlo simulations fully support the theoretical predictions.Comment: 13 pages, 10 figure

Phase-plane analysis of driven multi-lane exclusion models

We show how a fixed point based boundary-layer analysis technique can be used to obtain the steady-state particle density profiles of driven exclusion processes on two-lane systems with open boundaries. We have considered two distinct two-lane systems. In the first, particles hop on the lanes in one direction obeying exclusion principle and there is no exchange of particles between the lanes. The hopping on one lane is affected by the particle occupancies on the other, which thereby introduces an indirect interaction among the lanes. Through a phase plane analysis of the boundary layer equation, we show why the bulk density undergoes a sharp change as the interaction between the lanes is increased. The second system involves one lane with driven exclusion process and the other with biased diffusion of particles. In contrast to the previous model, here there is a direct interaction between the lanes due to particle exchange between them. In this model, we have looked at two possible scenarios with constant (flat) and non-constant bulk profiles. The fixed point based boundary layer method provides a new perspective on several aspects including those related to maximal/minimal current phases, possibilities of shocks under very restricted boundary conditions for the flat profile but over a wide range of boundary conditions for the non-constant profile.Comment: 13 pages, 17 figure

Boundary-induced phase transitions in traffic flow

Boundary-induced phase transitions are one of the surprising phenomena appearing in nonequilibrium systems. These transitions have been found in driven systems, especially the asymmetric simple exclusion process. However, so far no direct observations of this phenomenon in real systems exists. Here we present evidence for the appearance of such a nonequilibrium phase transition in traffic flow occurring on highways in the vicinity of on- and off-ramps. Measurements on a German motorway close to Cologne show a first-order nonequilibrium phase transition between a free-flow phase and a congested phase. It is induced by the interplay of density waves (caused by an on-ramp) and a shock wave moving on the motorway. The full phase diagram, including the effect of off-ramps, is explored using computer simulations and suggests means to optimize the capacity of a traffic network.Comment: 5 figures, revte

Unusual shock wave in two-species driven systems with an umbilic point

Using dynamical Monte Carlo simulations we observe the occurrence of an unexpected shock wave in driven diffusive systems with two conserved species of particles. This U shock is microscopically sharp, but does not satisfy the usual criteria for the stability of shocks. Exact analysis of the large-scale hydrodynamic equations of motion reveals the presence of an umbilical point which we show to be responsible for this phenomenon. We prove that such an umbilical point is a general feature of multispecies driven diffusive systems with reflection symmetry of the bulk dynamics. We argue that a U shock will occur whenever there are strong interactions between species such that the current-density relation develops a double well and the umbilical point becomes isolated

Large deviation functions in a system of diffusing particles with creation and annihilation

Large deviation functions for an exactly solvable lattice gas model of diffusing particles on a ring, subject to pair annihilation and creation, are obtained analytically using exact free-fermion techniques. Our findings for the large deviation function for the current are compared to recent results of Appert-Rolland et al. [Phys. Rev. E 78, 021122 (2008)] for diffusive systems with conserved particle number. Unlike conservative dynamics, our nonconservative model has no universal finite-size corrections for the cumulants. However, the leading Gaussian part has the same variance as in the conservative case. We also elucidate some properties of the large deviation functions associated with particle creation and annihilation

Commodity and Financial Networks in Regional Economics

The article discusses the relationship between commodity-production and financial network structures in the regional economy as dual conjugate systems. Material flows (raw materials, goods and so on) circulate in the commodity network as shown by Leontiev’s input-output balance model. Nonmaterial flows of property rights, money, and so on circulate in the financial network and reflect the movement of material objects in commodity networks. A network structure comprises closed and open circuits, which have fundamentally different characteristics: locally closed circuits meet local demand by supplying locally produced goods, thus ensuring self-reproduction of the local economy; open (or transit) circuits provide export-import flows. The article describes the mechanism of ‘internal’ money generation in closed circuits of commodity-production networks. The results of the theoretical study are illustrated by the calculations of closed and open circuit flows in the municipal economy model. Mutual settlements between the population and manufacturing enterprises are given in matrix form. It was found that the volume of the turnover in closed circuits of the municipal economic network model is about 28.5 % of the total turnover and can be provided by ‘internal’ non-inflationary money. The remaining 71.5 % of the total turnover correspond to the flows in the network’s open circuits providing export and import. The conclusion is made that in the innovation-driven economy, main attention should be given to the projects oriented towards domestic consumption rather than export supplies. The economy is based on internal production cycles in closed circuits. Thus, it is necessary to find the chains in the inter-industrial and inter-production relations which could become the basis of the production cycle. Money investments will complete such commodity chains and ‘launch’ the production cycle.The work has been prepared with the supprot of the Ural Federal University within the UrFU Program for the winners of the competition “Young Scientists of UrFU” No. 2.1.1.1-14/43

Why spontaneous symmetry breaking disappears in a bridge system with PDE-friendly boundaries

We consider a driven diffusive system with two types of particles, A and B, coupled at the ends to reservoirs with fixed particle densities. To define stochastic dynamics that correspond to boundary reservoirs we introduce projection measures. The stationary state is shown to be approached dynamically through an infinite reflection of shocks from the boundaries. We argue that spontaneous symmetry breaking observed in similar systems is due to placing effective impurities at the boundaries and therefore does not occur in our system. Monte-Carlo simulations confirm our results.Comment: 24 pages, 7 figure