Simulation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math> dimensional surface growth and lattices gases using GPUs

Schulz, Henrik; Ódor, Géza; Ódor, Gergely; Nagy, M. F.

doi:10.1016/j.cpc.2011.03.016

Cited by 13 publications

(11 citation statements)

References 31 publications

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“…Our model and code proves to be a very efficient tool to study not only the (2 + 1) dimensional KPZ and ASEP models but, more generally it can be used in the research of fundamental nonequilibrium thermodynamical quantities like the large deviation function or entropy production [49,50]. It is also straightforward to extend it to study more complex system exhibiting pattern formation [51,52], the effect of quenched disorder [54], the time-dependent structure factor [53] or to higher dimensions [29].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

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Extremely large-scale simulation of a Kardar-Parisi-Zhang model using graphics cards

Kelling

Ódor

2011

Phys. Rev. E

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The octahedron model introduced recently has been implemented onto graphics cards, which permits extremely large scale simulations via binary lattice gases and bit coded algorithms. We confirm scaling behavior belonging to the two-dimensional Kardar-Parisi-Zhang universality class and find a surface growth exponent: β = 0.2415(15) on 2 17 × 2 17 systems, ruling out β = 1/4 suggested by field theory. The maximum speedup with respect to a single CPU is 240. The steady state has been analyzed by finite size scaling and a growth exponent α = 0.393(4) is found. Correction-to-scaling exponents are computed and the power-spectrum density of the steady state is determined. We calculate the universal scaling functions, cumulants and show that the limit distribution can be obtained by the sizes considered. We provide numerical fitting for the small and large tail behavior of the steady state scaling function of the interface width.

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Section: Conclusion and Discussionmentioning

confidence: 99%

“…It is also straightforward to extend it to study more complex system exhibiting pattern formation [51,52], the effect of quenched disorder [54], the time-dependent structure factor [53] or to higher dimensions [29].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Extremely large-scale simulation of a Kardar-Parisi-Zhang model using graphics cards

Kelling

Ódor

2011

Phys. Rev. E

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“…A more detailed description of our CUDA implementation can be found in [46,47]. For this work we added the capability to perform simulations with arbitrary probabilities p and q. Benchmarks, comparing our GPU implementation on a Tesla C2070 to the optimized sequential CPU implementation running on an Intel Xeon X5650 at 2.67 GHz, have shown a speedup factor of about 230 for the raw simulation.…”

Section: Bit-coded Graphics Processing Unit Algorithmsmentioning

confidence: 99%

Aging of the (2+1)-dimensional Kardar-Parisi-Zhang model

2014

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Extended dynamical simulations have been performed on a (2 + 1)-dimensional driven dimer lattice-gas model to estimate aging properties. The autocorrelation and the autoresponse functions are determined and the corresponding scaling exponents are tabulated. Since this model can be mapped onto the (2 + 1)-dimensional Kardar-Parisi-Zhang surface growth model, our results contribute to the understanding of the universality class of that basic system.

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“…[4,20] (solid lines), using the associated DLG densities referred to in Eq. (8). The mean field description extends as well to (c) T /J = −1, and (d) T /J = −0.1, where however all currents are sector dependent and DLG densities are chosen only as fitting parameters.…”

Section: A Currentsmentioning

confidence: 99%

“…Introduced by Katz, Lebowitz and Spohn [1] in part with the aim of studying the physics of fast ionic conductors [2], it has triggered a great deal of research for almost three decades [3,4]. In the high field limit this system describes an asymmetric simple exclusion process (ASEP) [5,6] which already in one-dimension (1D) under suitable boundary conditions has encountered applications as diverse as protein synthesis [7], inhomogeneous interface growth [8], and vehicular traffic [9]. Notwithstanding the deceptive simplicity of most DLG versions, actually slight modifications of kinetic Ising models [10], the constantly maintained bias results in a net dissipative current (if permitted by boundary conditions), so the emerging steady state (SS) distributions are nonequilibrium ones.…”

Section: Introductionmentioning

confidence: 99%

Simulations of driven and reconstituting lattice gases

Grynberg

2011

Phys. Rev. E

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We discuss stationary aspects of a set of driven lattice gases in which hard-core particles with spatial extent, covering more than one lattice site, diffuse and reconstruct in one dimension under nearest-neighbor interactions. As in the uncoupled case [ M. Barma et al., J. Phys. Condens. Matter 19, 065112 (2007) ], the dynamics of the phase space breaks up into an exponentially large number of mutually disconnected sectors labeled by a non-local construct, the irreducible string. Depending on whether the particle couplings are taken attractive or repulsive, simulations in most of the studied sectors show that both steady state currents and pair correlations behave quite differently at low temperature regimes. For repulsive interactions an order-by-disorder transition is suggested.

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Simulation of 1+1 dimensional surface growth and lattices gases using GPUs

Cited by 13 publications

References 31 publications

Extremely large-scale simulation of a Kardar-Parisi-Zhang model using graphics cards

Extremely large-scale simulation of a Kardar-Parisi-Zhang model using graphics cards

Aging of the (2+1)-dimensional Kardar-Parisi-Zhang model

Simulations of driven and reconstituting lattice gases

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