Hydrodynamic equations for attractive particle systems on ?

Andjel, Enrique D.; Vares, Maria Eulália

doi:10.1007/bf01009046

Cited by 52 publications

(44 citation statements)

References 15 publications

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“…The stationary density of the particles in asymmetric exclusion processes, of which TASEP is a special case, is described on suitable macroscopic spatial and temporal scales by the inviscid Burgers’ equation (Andjel and Kipnis 1984, Andjel and Vares 1986, Wick 1985); the latter has shock solutions with a discontinuous jump. One of the main questions was whether the stationary density profile in the stochastic model exhibited the same discontinuity (Ferrari et al 1991, Derrida et al 1993, Derrida et al 1997).…”

Section: Applicationsmentioning

confidence: 99%

A traffic flow model for bio-polymerization processes

et al. 2013

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Bio-polymerization processes like transcription and translation are central to proper function of a cell. The speed at which the bio-polymer grows is affected both by the number of pauses of elongation machinery, as well the number of bio-polymers due to crowding effects. In order to quantify these effects in fast transcribing ribosome genes, we rigorously show that a classical traffic flow model is the limit of a mean occupancy ODE model. We compare the simulation of this model to a stochastic model and evaluate the combined effect of the polymerase density and the existence of pauses on the instantaneous transcription rate of ribosomal genes.

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Section: Applicationsmentioning

confidence: 99%

A traffic flow model for bio-polymerization processes

et al. 2013

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“…This is known as local equilibrium. As it is known, the exact statement involves a space/time change, under Euler scale, and for all these developments we refer to Andjel and Vares (1987), Rezakhanlou (1990), Landim (1992).…”

Section: §1 Introduction and Resultsmentioning

confidence: 99%

The asymmetric simple exclusion model with multiple shocks

Ferrari

Fontes

Vares

2000

Annales De l'Institut Henri Poincare (B) Probability and Statistics

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We consider the one dimensional totally asymmetric simple exclusion process with initial product distribution with densities 0, respectively. The initial distribution has shocks (discontinuities) at ε −1 c k , k = 1, . . . , n and we assume that in the corresponding macroscopic Burgers equation the n shocks meet in r * at time t * . The microscopic position of the shocks is represented by second class particles whose distribution in the scale ε −1/2 is shown to converge to a function of n independent Gaussian random variables representing the fluctuations of these particles "just before the meeting". We show that the density field at time ε −1 t * , in the scale ε −1/2 and as seen from ε −1 r * converges weakly to a random measure with piecewise constant density as ε → 0; the points of discontinuity depend on these limiting Gaussian variables. As a corollary we show that, as ε → 0, the distribution of the process at site ε −1 r * + ε −1/2 a at time ε −1 t * tends to a non trivial convex combination of the product measures with densities ρ k , the weights of the combination being explicitly computable. Keywords Asymmetric simple exclusion process, dynamical phase transition, shock fluctuations AMS subject classification: 60K35, 82C Partially Supported by CNPq and FAPESP and FINEP (PRONEX). (1) IME-USP. Caixa Postal 66.281, São Paulo 05315-970 SP Brasil (2) IMPA. Estrada D. Castorina 110, J. Botânico 22460-320 RJ Brasil 1

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“…Our motivation for [6] was to prove with a constructive method hydrodynamics of one-dimensional attractive dynamics with product invariant measures, but without a concave/convex flux, in view of examples of k-step exclusion processes and misanthropes processes. We initiated for that a "resurrection" of the approach of [4], and we introduced a variational formula for the entropy solution of the hydrodynamic equation in the Riemann case, and an approximation scheme to go from a Riemann to a general initial profile. Our method is based on an interplay of macroscopic properties for the conservation law and analogous microscopic properties for the particle system.…”

Section: Introductionmentioning

confidence: 99%