709 research outputs found
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 rather than the KPZ exponent 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
- …