Long-range correlations for conservative dynamics

Garrido, P. L.; Lebowitz, Joel L.; Maes, Christian; Spohn, Herbert

doi:10.1103/physreva.42.1954

Cited by 192 publications

(171 citation statements)

References 22 publications

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“…4). Figure 5 shows that a long-range correlation, predicted by [12,17,29], is observed in the AERW, SPDE, and AERW/SPDE solvers and the three simulations are in good agreement with each other. This figure also shows that the AR hybrid using a deterministic PDE solver erroneously enhances this correlation; Fig.…”

Section: Rarefaction Steady Statesupporting

confidence: 65%

Algorithm refinement for the stochastic Burgers’ equation

Bell

Foo

Garcia

2007

Journal of Computational Physics

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In this paper, we develop an algorithm refinement (AR) scheme for an excluded random walk model whose mean field behavior is given by the viscous Burgers' equation. AR hybrids use the adaptive mesh refinement framework to model a system using a molecular algorithm where desired while allowing a computationally faster continuum representation to be used in the remainder of the domain. The focus in this paper is the role of fluctuations in the dynamics. In particular, we demonstrate that it is necessary to include a stochastic forcing term in Burgers' equation to accurately capture the correct behavior of the system. The conclusion we draw from this study is that the fidelity of multiscale methods that couple disparate algorithms depends on the consistent modeling of fluctuations in each algorithm and on a coupling, such as algorithm refinement, that preserves this consistency.

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Section: Rarefaction Steady Statesupporting

confidence: 65%

Algorithm refinement for the stochastic Burgers’ equation

Bell

Foo

Garcia

2007

Journal of Computational Physics

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“…It is shown that the Langevin equation (and therefore the critical behavior) of the anisotropic diffusive system coincides with that of the randomly driven lattice gas system as well. Other systems in this universality class are the two-temperature model (Garrido et al, 1990), the ALGA model (Binder, 1981) and the infinitely fast driven lattice gas model (Achahbar et al, 2001). In the randomly driven lattice gas model particle current does not occur but an anisotropy can be found, therefore it was argued (Achahbar et al, 2001) that the particle current is not a relevant feature for this class.…”

Section: Competing Dynamics Added To Spin-exchangementioning

confidence: 99%

Universality classes in nonequilibrium lattice systems

2004

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This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second section I briefly address the question of scaling behavior at first order phase transitions. In section three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and the percolation behavior. The main body of this work is given in section four where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. In section five I continue overviewing such nonequilibrium classes but in coupled, multi-component systems. Most of the known nonequilibrium transition classes are explored in low dimensions between active and absorbing states of reaction-diffusion type of systems. However by mapping they can be related to universal behavior of interface growth models, which I overview in section six. Finally in section seven I summarize families of absorbing state system classes, mean-field classes and give an outlook for further directions of research.

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“…Strikingly, although density and temperature profiles, as well as pressures, all depend strongly on N , see Figs macroscopically and thus obeys locally the thermodynamic EoS, and the boundary layers near the thermal walls, which sum up all sorts of artificial finite-size and boundary corrections to renormalize the effective boundary conditions on the remaining bulk. This remarkable bulk-boundary decoupling phenomenon, instrumental in the recent discovery of novel scaling laws in nonequilibrium fluids [46,47], is even more surprising at the light of the long range correlations present in nonequilibrium fluids [4,17,18], offering a tantalizing method to obtain macroscopic properties of nonequilibrium fluids without resorting to unreliable finite-size scaling extrapolations [47]. For comparison, we include in Fig.…”

Section: Macroscopic Local Equilibriummentioning

confidence: 99%

“…Such nonlocality emerges from tiny, O(N −1 ) corrections to LTE which spread over macroscopic regions of size O(N ), with N the number of particles in the system of interest [16]. This shows that LTE is a subtle property: while corrections to LTE vanish locally in the N → ∞ limit, they have a fundamental impact on nonequilibrium LDFs in the form of nonlocality, which in turn gives rise to the ubiquitous longrange correlations which characterize nonequilibrium fluids [4,17,18]. These fundamental insights about LTE and its role out of equilibrium are coming forth from the study of a few oversimplified stochastic models of transport [4][5][6][7]16].…”

Section: Introductionmentioning

confidence: 99%

Probing local equilibrium in nonequilibrium fluids

2015

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We use extensive computer simulations to probe local thermodynamic equilibrium (LTE) in a quintessential model fluid, the two-dimensional hard-disks system. We show that macroscopic LTE is a property much stronger than previously anticipated, even in the presence of important finite size effects, revealing a remarkable bulk-boundary decoupling phenomenon in fluids out of equilibrium. This allows us to measure the fluid's equation of state in simulations far from equilibrium, with an excellent accuracy comparable to the best equilibrium simulations. Subtle corrections to LTE are found in the fluctuations of the total energy which strongly point out to the nonlocality of the nonequilibrium potential governing the fluid's macroscopic behavior out of equilibrium.

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Long-range correlations for conservative dynamics

Cited by 192 publications

References 22 publications

Algorithm refinement for the stochastic Burgers’ equation

Algorithm refinement for the stochastic Burgers’ equation

Universality classes in nonequilibrium lattice systems

Probing local equilibrium in nonequilibrium fluids

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