Strategies for optimize off-lattice aggregate simulations

Alves, Sidiney G.; Ferreira, Silvio C.; Martins, Marcelo L.

doi:10.1590/s0103-97332008000100016

Cited by 17 publications

(13 citation statements)

References 35 publications

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“…In the case of overlap, simulation proceeds to the next step. The time is increased by ∆t = 1/N , where N is the number of particles of the cluster at time t. Optimization strategies described in reference [32] were used to speed up the simulation. A cluster of diameter 8000 takes typically 8 min of simulation in a CPU Intel Xeon 3.2 GHz, whereas if no optimization is used the same simulation takes several hours of computation.…”

Section: Isotropic Radial Growthmentioning

confidence: 99%

Non-universal parameters, corrections and universality in Kardar–Parisi–Zhang growth

Alves¹,

Ferreira²

2013

J. Stat. Mech.

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We present a comprehensive numerical investigation of non-universal parameters and corrections related to interface fluctuations of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class, in d = 1 + 1, for both flat and curved geometries. We analyzed two classes of models. In the isotropic models the non-universal parameters are uniform along the surface, whereas in the anisotropic growth they vary. In the latter case, that produces curved surfaces, the statistics must be computed independently along fixed directions.where χ is a Tracy-Widom (geometry-dependent) distribution and η is a timeindependent correction, is probed.Our numerical analysis shows that the nonuniversal parameter Γ determined through the first cumulant leads to a very good accordance with the extended KPZ ansatz for all investigated models in contrast with the estimates of Γ obtained from higher order cumulants that indicate a violation of the generalized ansatz for some of the studied models. We associate the discrepancies to corrections of unknown nature, which hampers an accurate estimation of Γ at finite times. The discrepancies in Γ via different approaches are relatively small but sufficient to modify the scaling law t −1/3 that characterize the finite-time corrections due to η. Among the investigated models, we have revisited an off-lattice Eden model that supposedly disobeyed the shift in the mean scaling as t −1/3 and showed that there is a crossover to the expected regime. We have found model-dependent (non-universal) corrections for cumulants of order n ≥ 2. All investigated models are consistent with a further term of order t −1/3 in the KPZ ansatz.

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Section: Isotropic Radial Growthmentioning

confidence: 99%

Non-universal parameters, corrections and universality in Kardar–Parisi–Zhang growth

Alves¹,

Ferreira²

2013

J. Stat. Mech.

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“…The previously introduced variables r l and r k must be as large as possible, but computational limitations restrict their values. For the DLA simulations, ∆ can be a few particle diameters [27]. However, for the BA limit, ∆ cannot be small due to distortions caused by shadow instabilities [28,29].…”

Section: Modelmentioning

confidence: 99%

“…Cluster growth optimizations were implemented using steps of size 16a in the large empty regions nearby the cluster and three step sizes (16a, 100a and 200a) were used far from the cluster. More details about long step and off-lattice optimizations are available elsewhere [27].…”

Section: Modelmentioning

confidence: 99%

Scaling laws in the diffusion limited aggregation of persistent random walkers

Nogueira

Alves

Ferreira

2011

Physica A: Statistical Mechanics and its Applications

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We investigate the diffusion limited aggregation of particles executing persistent random walks. The scaling properties of both random walks and large aggregates are presented. The aggregates exhibit a crossover between ballistic and diffusion limited aggregation models. A non-trivial scaling relation ξ ∼ 1.25 between the characteristic size ξ, in which the cluster undergoes a morphological transition, and the persistence length , between ballistic and diffusive regimes of the random walk, is observed.

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“…If the growth starts with a single particle, the model yields asymptotically spherical clusters with a self-affine surface exhibiting the scaling exponents of the KPZ universality class [21]. We simulated off-lattice clusters in twodimensions with the usual algorithm [21,22]: a particle in the active (growing) zone 1 is selected at random and a new particle is added in a random position chosen in the empty neighbourhood of the selected particle. The procedure is repeated while the cluster does not reach N particles.…”

mentioning

confidence: 99%

Universal fluctuations in radial growth models belonging to the KPZ universality class

Alves¹,

Ferreira²

2011

EPL

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PACS 81.15.Aa -Theory and models of film growth PACS 05.40.-a -Fluctuation phenomena, random processes, noise, and Brownian motion PACS 89.75.Da -Systems obeying scaling laws Abstract. -We investigate the radius distributions (RD) of surfaces obtained with large-scale simulations of radial clusters that belong to the KPZ universality class. For all investigated models, the RDs are given by the Tracy-Widom distribution of the Gaussian unitary ensemble, in agreement with the conjecture of the KPZ universality class for curved surfaces. The quantitative agreement was also confirmed by two-point correlation functions asymptotically given by the covariance of the Airy2 process. Our simulation results fill the last lacking gap of the conjecture that had been recently verified analytically and experimentally.

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Strategies for optimize off-lattice aggregate simulations

Cited by 17 publications

References 35 publications

Non-universal parameters, corrections and universality in Kardar–Parisi–Zhang growth

Non-universal parameters, corrections and universality in Kardar–Parisi–Zhang growth

Scaling laws in the diffusion limited aggregation of persistent random walkers

Universal fluctuations in radial growth models belonging to the KPZ universality class

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