148 research outputs found
Extremely large scale simulation of a Kardar-Parisi-Zhang model using graphics cards
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 behaviour belonging to the 2d
Kardar-Parisi-Zhang universality class and find a surface growth exponent:
beta=0.2415(15) on 2^17 x 2^17 systems, ruling out beta=1/4 suggested by field
theory. The maximum speed-up with respect to a single CPU is 240. The steady
state has been analysed by finite size scaling and a growth exponent
alpha=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 behaviour of the steady state scaling function of the interface
width.Comment: 7 pages, 8 figures, slightly modified, accepted version for PR
Mapping of 2+1-dimensional Kardar-Parisi-Zhang growth onto a driven lattice gas model of dimer
We show that a 2+1 dimensional discrete surface growth model exhibiting
Kardar-Parisi-Zhang (KPZ) class scaling can be mapped onto a two dimensional
conserved lattice gas model of directed dimers. In case of KPZ height
anisotropy the dimers follow driven diffusive motion. We confirm by numerical
simulations that the scaling exponents of the dimer model are in agreement with
those of the 2+1 dimensional KPZ class. This opens up the possibility of
analyzing growth models via reaction-diffusion models, which allow much more
efficient computer simulations.Comment: 5 pages, 4 figures, final form to appear in PR
One-dimensional spin-anisotropic kinetic Ising model subject to quenched disorder
Large-scale Monte Carlo simulations are used to explore the effect of
quenched disorder on one dimensional, non-equilibrium kinetic Ising models with
locally broken spin symmetry, at zero temperature (the symmetry is broken
through spin-flip rates that differ for '+' and '-' spins). The model is found
to exhibit a continuous phase transition to an absorbing state. The associated
critical behavior is studied at zero branching rate of kinks, through analysis
spreading of '+' and '-' spins and, of the kink density. Impurities exert a
strong effect on the critical behavior only for a particular choice of
parameters, corresponding to the strongly spin-anisotropic kinetic Ising model
introduced by Majumdar et al. Typically, disorder effects become evident for
impurity strengths such that diffusion is nearly blocked. In this regime, the
critical behavior is similar to that arising, for example, in the
one-dimensional diluted contact process, with Griffiths-like behavior for the
kink density. We find variable cluster exponents, which obey a hyperscaling
relation, and are similar to those reported by Cafiero et al. We also show that
the isotropic two-component AB -> 0 model is insensitive to reaction-disorder,
and that only logarithmic corrections arise, induced by strong disorder in the
diffusion rate.Comment: 10 pages, 13 figures. Final, accepted form in PRE, including a new
table summarizing the molde
Single-site approximation for reaction-diffusion processes
We consider the branching and annihilating random walk and with reaction rates and , respectively, and hopping rate
, and study the phase diagram in the plane. According
to standard mean-field theory, this system is in an active state for all
, and perturbative renormalization suggests that this mean-field
result is valid for ; however, nonperturbative renormalization predicts
that for all there is a phase transition line to an absorbing state in the
plane. We show here that a simple single-site
approximation reproduces with minimal effort the nonperturbative phase diagram
both qualitatively and quantitatively for all dimensions . We expect the
approach to be useful for other reaction-diffusion processes involving
absorbing state transitions.Comment: 15 pages, 2 figures, published versio
Probability distribution of the order parameter in the directed percolation universality class
The probability distributions of the order parameter for two models in the
directed percolation universality class were evaluated. Monte Carlo simulations
have been performed for the one-dimensional generalized contact process and the
Domany-Kinzel cellular automaton. In both cases, the density of active sites
was chosen as the order parameter. The criticality of those models was obtained
by solely using the corresponding probability distribution function. It has
been shown that the present method, which has been successfully employed in
treating equilibrium systems, is indeed also useful in the study of
nonequilibrium phase transitions.Comment: 6 pages, 4 figure
Multicomponent binary spreading process
I investigate numerically the phase transitions of two-component
generalizations of binary spreading processes in one dimension. In these models
pair annihilation: AA->0, BB->0, explicit particle diffusion and binary pair
production processes compete with each other. Several versions with spatially
different productions have been explored and shown that for the cases: 2A->3A,
2B->3B and 2A->2AB, 2B->2BA a phase transition occurs at zero production rate
(), that belongs to the class of N-component, asymmetric branching
and annihilating random walks, characterized by the order parameter exponent
. In the model with particle production: AB->ABA, BA-> BAB a phase
transition point can be located at that belongs to the class
of the one-component binary spreading processes.Comment: 5 pages, 5 figure
The universal behavior of one-dimensional, multi-species branching and annihilating random walks with exclusion
A directed percolation process with two symmetric particle species exhibiting
exclusion in one dimension is investigated numerically. It is shown that if the
species are coupled by branching (, ) a continuous phase
transition will appear at zero branching rate limit belonging to the same
universality class as that of the dynamical two-offspring (2-BARW2) model. This
class persists even if the branching is biased towards one of the species. If
the two systems are not coupled by branching but hard-core interaction is
allowed only the transition will occur at finite branching rate belonging to
the usual 1+1 dimensional directed percolation class.Comment: 3 pages, 3 figures include
Aging of the (2+1)-dimensional Kardar-Parisi-Zhang model
Extended dynamical simulations have been performed on a 2+1 dimensional
driven dimer lattice gas model to estimate ageing properties. The
auto-correlation and the auto-response 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.Comment: 6 pages, 5 figs, 1 table, accepted version in PR
Comparison of Different Parallel Implementations of the 2+1-Dimensional KPZ Model and the 3-Dimensional KMC Model
We show that efficient simulations of the Kardar-Parisi-Zhang interface
growth in 2 + 1 dimensions and of the 3-dimensional Kinetic Monte Carlo of
thermally activated diffusion can be realized both on GPUs and modern CPUs. In
this article we present results of different implementations on GPUs using CUDA
and OpenCL and also on CPUs using OpenCL and MPI. We investigate the runtime
and scaling behavior on different architectures to find optimal solutions for
solving current simulation problems in the field of statistical physics and
materials science.Comment: 14 pages, 8 figures, to be published in a forthcoming EPJST special
issue on "Computer simulations on GPU
Slow, bursty dynamics as a consequence of quenched network topologies
Bursty dynamics of agents is shown to appear at criticality or in extended GrifïŹths phases, even in case of
Poisson processes. I provide numerical evidence for a power-law type of intercommunication time distributions
by simulating the contact process and the susceptible-infected-susceptible model. This observation suggests that
in the case of nonstationary bursty systems, the observed non-Poissonian behavior can emerge as a consequence
of an underlying hidden Poissonian network process, which is either critical or exhibits strong rare-region effects.
On the contrary, in time-varying networks, rare-region effects do not cause deviation from the mean-ïŹeld behavior,
and heterogeneity-induced burstyness is absent
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