A constructive approach to Euler hydrodynamics for attractive processes. Application to k-step exclusion

Bahadoran, Christophe; Guiol, Hervé; Ravishankar, K.; Saada, Ellen

doi:10.1016/s0304-4149(01)00158-2

Cited by 23 publications

(92 citation statements)

References 18 publications

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“…It is worth noting that similar results for density profiles is obtained for an asymmetric exclusion process with another form of cooperative interactions [18,19]. In these works, the same qualitative phase diagram as in Fig.…”

Section: Density Profile Dynamicssupporting

confidence: 72%

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Cooperativity-driven singularities in asymmetric exclusion

Gabel¹,

Redner²

2011

J. Stat. Mech.

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Abstract. We investigate the effect of cooperative interactions on the asymmetric exclusion process, which causes the particle velocity to be an increasing function of the density. Within a hydrodynamic theory, initial density upsteps and downsteps can evolve into: (a) shock waves, (b) continuous compression or rarefaction waves, or (c) a mixture of shocks and continuous waves. These unusual phenomena arise because of an inflection point in the current versus density relation. This anomaly leads to a group velocity that can either be an increasing or a decreasing function of the density on either side of the inflection point, a property that underlies these localized wave singularities.

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Section: Density Profile Dynamicssupporting

confidence: 72%

“…[7], as well as in [18,19]. These latter publications investigated an exclusion model with a somewhat less stringent excludedvolume constraint than in ASEP.…”

Section: Introductionmentioning

confidence: 99%

Cooperativity-driven singularities in asymmetric exclusion

Gabel¹,

Redner²

2011

J. Stat. Mech.

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“…The above model contains in particular the simple exclusion process (where K = 1 and b(n, m) = n(1 − m)) and zero-range process (where K = +∞ and b(n, m) = g(n)). Other examples can be found in [2,6].…”

Section: The Framework and Resultsmentioning

confidence: 99%

Hydrodynamics and Hydrostatics for a Class of Asymmetric Particle Systems with Open Boundaries

Bahadoran

2012

Commun. Math. Phys.

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We consider attractive particle systems in Z d with product invariant measures. We prove that when particles are restricted to a subset of Z d , with birth and death dynamics at the boundaries, the hydrodynamic limit is given by the unique entropy solution of a conservation law, with boundary conditions in the sense of Bardos et al. ([7]). For the hydrostatic limit between parallel hyperplanes, we prove a multidimensional version of the phase diagram conjectured in [38], and show that it is robust with respect to perturbations of the boundaries.AMS 2000 subject classifications. 60K35, 82C22, 82C26; 35L65, 35L67, 35L50.

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“…In this paper we study in full generality the relation between duality and symmetries. 1 We shall give a general scheme to construct a dual stochastic process for continuous time Markov processes whose generator has a symmetry. After the introduction of the general setting we present the main theorems describing the construction of a dual process.…”

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confidence: 99%

“…As for transport of particles, we study exclusion processes. 1 We will restrict to the notion of symmetry groups and all the examples in the present paper are Lie algebras with associated Lie groups. We mention that one could also consider duality relations in the case of a quantum algebra, which a much more richer and complicated structure than a Lie algebra.…”

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confidence: 99%

Duality and Hidden Symmetries in Interacting Particle Systems

Kurchan²,

et al. 2009

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In the context of Markov processes, both in discrete and continuous setting, we show a general relation between duality functions and symmetries of the generator. If the generator can be written in the form of a Hamiltonian of a quantum spin system, then the "hidden" symmetries are easily derived. We illustrate our approach in processes of symmetric exclusion type, in which the symmetry is of SU(2) type, as well as for the KipnisMarchioro-Presutti (KMP) model for which we unveil its SU(1, 1) symmetry. The KMP model is in turn an instantaneous thermalization limit of the energy process associated to a large family of models of interacting diffusions, which we call Brownian energy process (BEP) and which all possess the SU(1, 1) symmetry. We treat in details the case where the system is in contact with reservoirs and the dual process becomes absorbing.

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A constructive approach to Euler hydrodynamics for attractive processes. Application to k-step exclusion

Cited by 23 publications

References 18 publications

Cooperativity-driven singularities in asymmetric exclusion

Cooperativity-driven singularities in asymmetric exclusion

Hydrodynamics and Hydrostatics for a Class of Asymmetric Particle Systems with Open Boundaries

Duality and Hidden Symmetries in Interacting Particle Systems

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