1,798 research outputs found
Quantum algebra symmetry of the ASEP with second-class particles
We consider a two-component asymmetric simple exclusion process (ASEP) on a
finite lattice with reflecting boundary conditions. For this process, which is
equivalent to the ASEP with second-class particles, we construct the
representation matrices of the quantum algebra that
commute with the generator. As a byproduct we prove reversibility and obtain in
explicit form the reversible measure. A review of the algebraic techniques used
in the proofs is given.Comment: 23 pages, presented at conference Particle systems and PDE's - III,
17-19 Dec 2014, Braga, Portuga
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
RNA polymerase interactions and elongation rate
We show that non-steric molecular interactions between RNA polymerase (RNAP)
motors that move simultaneously on the same DNA track determine strongly the
kinetics of transcription elongation. With a focus on the role of collisions
and cooperation, we introduce a stochastic model that allows for the exact
analytical computation of the stationary properties of transcription elongation
as a function of RNAP density, their interaction strength, nucleoside
triphosphate concentration, and rate of pyrophosphate release. Cooperative
pushing, i.e., an enhancement of the average RNAP velocity and elongation rate,
arises due to stochastic pushing. This cooperative effect cannot be explained
by steric hindrance alone but requires a sufficiently strong molecular
repulsion. It disappears beyond a critical RNAP density, above which jamming
due to collisions takes over. For strong stochastic blocking the cooperative
pushing is suppressed at low RNAP densities, but a reappears at higher
densities.Comment: 26 pages, 6 figure
Microscopic structure of shocks and antishocks in the ASEP conditioned on low current
We study the time evolution of the ASEP on a one-dimensional torus with
sites, conditioned on an atypically low current up to a finite time . For a
certain one-parameter family of initial measures with a shock we prove that the
shock position performs a biased random walk on the torus and that the measure
seen from the shock position remains invariant. We compute explicitly the
transition rates of the random walk. For the large scale behaviour this result
suggests that there is an atypically low current such that the optimal density
profile that realizes this current is a hyperbolic tangent with a travelling
shock discontinuity. For an atypically low local current across a single bond
of the torus we prove that a product measure with a shock at an arbitrary
position and an antishock at the conditioned bond remains a convex combination
of such measures at all times which implies that the antishock remains
microscopically stable under the locally conditioned dynamics. We compute the
coefficients of the convex combinations.Comment: 20 papes, 4 figure
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
Self-Duality for the Two-Component Asymmetric Simple Exclusion Process
We study a two-component asymmetric simple exclusion process (ASEP) that is
equivalent to the ASEP with second-class particles. We prove self-duality with
respect to a family of duality functions which are shown to arise from the
reversible measures of the process and the symmetry of the generator under the
quantum algebra . We construct all invariant measures in
explicit form and discuss some of their properties. We also prove a sum rule
for the duality functions.Comment: 27 page
Green functions for the TASEP with sublattice parallel update
We consider the totally asymmetric simple exclusion process (TASEP) in
discrete time with the sublattice parallel dynamics describing particles moving
to the right on the one-dimensional infinite chain with equal hoping
probabilities. Using sequentially two mappings, we show that the model is
equivalent to the TASEP with the backward-ordered sequential update in the case
when particles start and finish their motion not simultaneously. The Green
functions are obtained exactly in a determinant form for different initial and
final conditions.Comment: 11 pages, 4 figure
Cross border Classical Swine Fever control: Improving Dutch and German crisis management systems by an integrated public-private approach
The objective of this research approach is to analyse in which ways crisis management measures against Classical Swine Fever (CSF) can be improved by a public private cross border model. A core activity contains the analysis of information and communication systems: In a case study it has been empirically analysed if a sufficient supply of public and private information enables crisis managers at both sides of the Dutch-German border area to take decisions about CSF control more efficient. At the end of this approach a new crisis management model had been developed. One of the most important aspects thereby is the assessment of data: (1) within private quality management systems in normal times according to the benefit for public management tasks in times of crisis and (2) within public crisis management systems according to the benefit for cross-border CSF-control activities. To this effect two different methodological approaches have been combined within the model: (1) a method to identify and illustrate public actors and their options in crisis management decision making and (2) a system of communication and information exchange between public and private as well as Dutch and German actors (engage& exchange model) which permit to collect and to evaluate data in addition for a predefined time period are activated
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
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