Constructive Euler Hydrodynamics for One-Dimensional Attractive Particle Systems

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

doi:10.1007/978-981-15-0302-3_3

Cited by 8 publications

(8 citation statements)

References 47 publications

(198 reference statements)

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“…This has been proved rigorously for attractive processes which preserve stochastic order in time using coupling techniques (see e.g. [38,39] and references therein). Models of the form (1) are attractive if and only if u is a non-decreasing and v is a non-increasing function of the number of particles.…”

Section: Phase Separated Profiles For Current Large Deviationsmentioning

confidence: 99%

Current large deviations for partially asymmetric particle systems on a ring

Chleboun

Großkinsky

Pizzoferrato

2018

J. Phys. A: Math. Theor.

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We study large deviations for the current of one-dimensional stochastic particle systems with periodic boundary conditions. Following a recent approach based on an earlier result by Jensen and Varadhan, we compare several candidates for atypical currents to travelling wave density profiles, which correspond to non-entropic weak solutions of the hyperbolic scaling limit of the process. We generalize previous results to partially asymmetric systems and systems with convex as well as concave current-density relations, including zero-range and inclusion processes. We provide predictions for the large deviation rate function covering the full range of current fluctuations using heuristic arguments, and support them by simulation results using cloning algorithms wherever they are computationally accessible. For partially asymmetric zero-range processes we identify an interesting dynamic phase transition between different strategies for atypical currents, which is of a generic nature and expected to apply to a large class of particle systems on a ring. arXiv:1804.07844v1 [cond-mat.stat-mech]

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Section: Phase Separated Profiles For Current Large Deviationsmentioning

confidence: 99%

Current large deviations for partially asymmetric particle systems on a ring

Chleboun

Großkinsky

Pizzoferrato

2018

J. Phys. A: Math. Theor.

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“…Also, when the interactions are asymmetric and finite-range, for systems, such as 'simple exclusion' and 'zero-range', as well as other processes, hydrodynamics has been proved (cf. [2], [3], [4], [13], [15], [16], Chapter 8 in [19], [23], and reference therein).…”

Section: Introductionmentioning

confidence: 99%

“…The α ≥ 1 hydrodynamic equation may be understood in terms of results say in [4], [23], for finite-range asymmetric systems. When α > 1, the mean of the jump probability p(·) is bounded.…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamic limits for long-range asymmetric interacting particle systems

Sethuraman¹,

Shahar²

2018

Electron. J. Probab.

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We consider the hydrodynamic scaling behavior of the mass density with respect to a general class of mass conservative interacting particle systems on Z n , where the jump rates are asymmetric and long-range of order x −(n+α) for a particle displacement of order x . Two types of evolution equations are identified depending on the strength of the long-range asymmetry. When 0 < α < 1, we find a new integro-partial differential hydrodynamic equation, in an anomalous space-time scale. On the other hand, when α ≥ 1, we derive a Burgers hydrodynamic equation, as in the finite-range setting, in Euler scale.2010 Mathematics Subject Classification. 60K35.

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“…Under the more general Assumptions 1-2, the flux function depends on the pair (Q 0 , c) defined in ( 11)-( 13). In the latter case, the inequality in (11) can be strict, so c should be regarded as an additional parameter not contained in Q 0 , whereas in the ergodic case, equality always holds in (11). A simple non-ergodic example is given in Subsection 5.3 below.…”

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confidence: 99%

Zero-range process in random environment

Bahadoran,

Mountford,

Ravishankar

et al. 2020

Preprint

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We survey our recent articles dealing with one dimensional attractive zero range processes moving under site disorder. We suppose that the underlying random walks are biased to the right and so hyperbolic scaling is expected. Under the conditions of our model the process admits a maximal invariant measure. The initial focus of the project was to find conditions on the initial law to entail convergence in distribution to this maximal distribution, when it has a finite density. Somewhat surprisingly, necessary and sufficient conditions were found. In this part hydrodynamic results were employed chiefly as a tool to show distributional convergence but subsequently we developed a theory for hydrodynamic limits treating profiles possessing densities that did not admit corresponding equilibria. Finally we derived strong local equilibrium results.

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Constructive Euler Hydrodynamics for One-Dimensional Attractive Particle Systems

Abstract: We review a (constructive) approach first introduced in [6] and further developed in [7,8,38,9] for hydrodynamic limits of asymmetric attractive particle systems, in a weak or in a strong (that is, almost sure) sense, in an homogeneous or in a quenched disordered setting.

Cited by 8 publications

References 47 publications

Current large deviations for partially asymmetric particle systems on a ring

Current large deviations for partially asymmetric particle systems on a ring

Hydrodynamic limits for long-range asymmetric interacting particle systems

Zero-range process in random environment

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