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arXiv1997

Simulating Ising Spin Glasses on a Quantum Computer

A linear-time algorithm is presented for the construction of the Gibbs distribution of configurations in the Ising model, on a quantum computer. The algorithm is designed so that each run provides one configuration with a quantum probability equal to the corresponding thermodynamic weight. The partition function is thus approximated efficiently. The algorithm neither suffers from critical slowing down, nor gets stuck in local minima. The algorithm can be A linear-time algorithm is presented for the construction of the Gibbs distribution of configurations in the Ising model, on a quantum computer. The algorithm is designed so that each run provides one configuration with a quantum probability equal to the corresponding thermodynamic weight. The partition function is thus approximated efficiently. The algorithm neither suffers from critical slowing down, nor gets stuck in local minima. The algorithm can be applied in any dimension, to a class of spin-glass Ising models with a finite portion of frustrated plaquettes, diluted Ising models, and models with a magnetic field. applied in any dimension, to a class of spin-glass Ising models with a finite portion of frustrated plaquettes, diluted Ising models, and models with a magnetic field.

quant-ph↗

arXiv1997

Jamming transition in a cellular automaton model for traffic flow

The cellular automaton model for traffic flow exhibits a jamming transition from a free-flow phase to a congested phase. In the deterministic case this transition corresponds to a critical point with diverging correlation length. In the presence of noise, however, no consistent picture has emerged up to now. We present data from numerical simulations which suggest the absence of critical behavior. The transition of the deterministic case is smeared out and one only observes the remnants of the critical point.

cond-mat.stat-mech↗

arXiv1998

Lattice Fluid Dynamics from Perfect Discretizations of Continuum Flows

We use renormalization group methods to derive equations of motion for large scale variables in fluid dynamics. The large scale variables are averages of the underlying continuum variables over cubic volumes, and naturally live on a lattice. The resulting lattice dynamics represents a perfect discretization of continuum physics, i.e. grid artifacts are completely eliminated. Perfect equations of motion are derived for static, slow flows of incompressible, viscous fluids. For Hagen-Poiseuille flow in a channel with square cross section the equations reduce to a perfect discretization of the Poisson equation for the velocity field with Dirichlet boundary conditions. The perfect large scale Poisson equation is used in a numerical simulation, and is shown to represent the continuum flow exactly. For non-square cross sections we use a numerical iterative procedure to derive flow equations that are approximately perfect.

comp-gas↗

arXiv1998

Self-Organized States in Cellular Automata: Exact Solution

The spatial structure, fluctuations as well as all state probabilities of self-organized (steady) states of cellular automata can be found (almost) exactly and {\em explicitly} from their Markovian dynamics. The method is shown on an example of a natural sand pile model with a gradient threshold.

cond-mat.stat-mech↗

arXiv1998

Lattice Boltzmann simulations of three-dimensional single droplet deformation and breakup under simple shear flow

We present three-dimensional numerical simulations of the classical Taylor experiment on droplet deformation within a shear flow. We have used the promising Lattice-Boltzmann method numerical scheme to simulate single droplet deformation and breakup under simple shear flow. We first compute the deformation of the droplet and find excellent agreement with the theoretical prediction. We have used the same method to simulate the shear and breakup for larger values of the shear rate. We find that the Lattice Boltzmann method used in conjunction with the interface force model of Shan and Chen results in an excellent treatment of the entire process from small deformation to breakup into multiple droplets. Our results could be extended to study the rheology of dispersed droplets and the dynamics of droplet breakup and coalescence in shear flow.

comp-gas↗

arXiv1998

Maxwell Model of Traffic Flows

We investigate traffic flows using the kinetic Boltzmann equations with a Maxwell collision integral. This approach allows analytical determination of the transient behavior and the size distributions. The relaxation of the car and cluster velocity distributions towards steady state is characterized by a wide range of velocity dependent relaxation scales, $R^{1/2}<τ(v) ^{-4} Ψ(m/< m>^2)$. This distribution is primarily algebraic, $P_m\sim m^{-3/2}$, for $m\ll < m>^2$, and is exponential otherwise.

cond-mat.stat-mech↗

arXiv1999

Synchronization and Maximum Lyapunov Exponents of Cellular Automata

We study the synchronization of totalistic one dimensional cellular automata (CA). The CA with a non zero synchronization threshold exhibit complex non periodic space time patterns and conversely. This synchronization transition is related to directed percolation. We study also the maximum Lyapunov exponent for CA, defined in analogy with continuous dynamical systems as the exponential rate of expansion of the linear map induced by the evolution rule of CA, constructed with the aid of the Boolean derivatives. The synchronization threshold is strongly correlated to the maximum Lyapunov exponent and we propose approximate relations between these quantities. The value of this threshold can be used to parametrize the space time complexity of CA.

cond-mat.stat-mech↗

arXiv1999

Self-organization of traffic jams in cities: effects of stochastic dynamics and signal periods

We propose a cellular automata model for vehicular traffic in cities by combining (and appropriately modifying) ideas borrowed from the Biham-Middleton-Levine (BML) model of city traffic and the Nagel-Schreckenberg (NS) model of highway traffic. We demonstrate a phase transition from the "free-flowing" dynamical phase to the completely "jammed" phase at a vehicle density which depends on the time periods of the synchronized signals and the separation between them. The intrinsic stochasticity of the dynamics, which triggers the onset of jamming, is similar to that in the NS model, while the phenomenon of complete jamming through self-organization as well as the final jammed configurations are similar to those in the BML model. Using our new model, we have made an investigation of the time-dependence of the average speeds of the cars in the "free-flowing" phase as well as the dependence of flux and jamming on the time period of the signals.

cond-mat.stat-mech↗

arXiv1999

Cellular Automata Simulating Experimental Properties of Traffic Flows

A model for 1D traffic flow is developed, which is discrete in space and time. Like the cellular automaton model by Nagel and Schreckenberg [J. Phys. I France 2, 2221 (1992)], it is simple, fast, and can describe stop-and-go traffic. Due to its relation to the optimal velocity model by Bando et al. [Phys. Rev. E 51, 1035 (1995)], its instability mechanism is of deterministic nature. The model can be easily calibrated to empirical data and displays the experimental features of traffic data recently reported by Kerner and Rehborn [Phys. Rev. E 53, R1297 (1996)].

cond-mat.stat-mech↗

arXiv1999

Exact results for deterministic cellular automata traffic models

We present a rigorous derivation of the flow at arbitrary time in a deterministic cellular automaton model of traffic flow. The derivation employs regularities in preimages of blocks of zeros, reducing the problem of preimage enumeration to a well known lattice path counting problem. Assuming infinite lattice size and random initial configuration, the flow can be expressed in terms of generalized hypergeometric function. We show that the steady state limit agrees with previously published results.

comp-gas↗

arXiv1998

A thermodynamically reversible generalization of Diffusion Limited Aggregation

We introduce a lattice gas model of cluster growth via the diffusive aggregation of particles in a closed system obeying a local, deterministic, microscopically reversible dynamics. This model roughly corresponds to placing the irreversible Diffusion Limited Aggregation model (DLA) in contact with a heat bath. Particles release latent heat when aggregating, while singly connected cluster members can absorb heat and evaporate. The heat bath is initially empty, hence we observe the flow of entropy from the aggregating gas of particles into the heat bath, which is being populated by diffusing heat tokens. Before the population of the heat bath stabilizes, the cluster morphology (quantified by the fractal dimension) is similar to a standard DLA cluster. The cluster then gradually anneals, becoming more tenuous, until reaching configurational equilibrium when the cluster morphology resembles a quenched branched random polymer. As the microscopic dynamics is invertible, we can reverse the evolution, observe the inverse flow of heat and entropy, and recover the initial condition. This simple system provides an explicit example of how macroscopic dissipation and self-organization can result from an underlying microscopically reversible dynamics.

cond-mat.stat-mech↗

arXiv1999

Spinodal decomposition of off-critical quenches with a viscous phase using dissipative particle dynamics in two and three spatial dimensions

We investigate the domain growth and phase separation of hydrodynamically-correct binary immiscible fluids of differing viscosity as a function of minority phase concentration in both two and three spatial dimensions using dissipative particle dynamics. We also examine the behavior of equal-viscosity fluids and compare our results to similar lattice-gas simulations in two dimensions.

cond-mat.soft↗

arXiv1993

Explicit Lie-Poisson integration and the Euler equations

We give a wide class of Lie-Poisson systems for which explicit, Lie-Poisson integrators, preserving all Casimirs, can be constructed. The integrators are extremely simple. Examples are the rigid body, a moment truncation, and a new, fast algorithm for the sine-bracket truncation of the 2D Euler equations.

chao-dyn↗

arXiv1993

Domain Growth, Wetting and Scaling in Porous Media

The lattice Boltzmann (LB) method is used to study the kinetics of domain growth of a binary fluid in a number of geometries modeling porous media. Unlike the traditional methods which solve the Cahn-Hilliard equation, the LB method correctly simulates fluid properties, phase segregation, interface dynamics and wetting. Our results, based on lattice sizes of up to $4096\times 4096$, do not show evidence to indicate the breakdown of late stage dynamical scaling, and suggest that confinement of the fluid is the key to the slow kinetics observed. Randomness of the pore structure appears unnecessary.

comp-gas↗

arXiv1994

Generating surrogate data for time series with several simultaneously measured variables

We propose an extension to multivariate time series of the phase-randomized Fourier-transform algorithm for generating surrogate data. Such surrogate data sets must mimic not only the autocorrelations of each of the variables in the original data set, they must mimic the cross-correlations {\em between} all the variables as well. The method is applied both to a simulated example (the three components of the Lorenz equations) and to data from a multichannel electroencephalogram.

comp-gas↗

arXiv1995

Monte Carlo with Absorbing Markov Chains: Fast Local Algorithms for Slow Dynamics

A class of Monte Carlo algorithms which incorporate absorbing Markov chains is presented. In a particular limit, the lowest-order of these algorithms reduces to the $n$-fold way algorithm. These algorithms are applied to study the escape from the metastable state in the two-dimensional square-lattice nearest-neighbor Ising ferromagnet in an unfavorable applied field, and the agreement with theoretical predictions is very good. It is demonstrated that the higher-order algorithms can be many orders of magnitude faster than either the traditional Monte Carlo or $n$-fold way algorithms.

cond-mat↗

arXiv1994

A Class of Fast Methods for Processing Irregularly Sampled or Otherwise Inhomogeneous One-Dimensional Data

With the ansatz that a data set's correlation matrix has a certain parametrized form (one general enough, however, to allow the arbitrary specification of a slowly-varying decorrelation distance and population variance) the general machinery of Wiener or optimal filtering can be reduced from $O(n^3)$ to $O(n)$ operations, where $n$ is the size of the data set. The implied vast increases in computational speed can allow many common sub-optimal or heuristic data analysis methods to be replaced by fast, relatively sophisticated, statistical algorithms. Three examples are given: data rectification, high- or low- pass filtering, and linear least squares fitting to a model with unaligned data points.

comp-gas↗

arXiv1995

Mean Field Theory for Lyapunov Exponents and KS Entropy in Lorentz Lattice Gases

Cellular automata lattice gases are useful systems for systematically exploring the connections between non-equilibrium statisitcal mechanics and dynamical systems theory. Here the chaotic properties of a Lorentz lattice gas are studied analytically and by computer simulations. The escape-rates, Lyapunov exponents, and KS entropies are estimated for a one-dimensional example using a mean-field theory, and the results are compared with simulations for a range of densities and scattering parameters of the lattice gas. The computer results show a distribution of values for the dynamical quantities with average values that are in good agreement with the mean field theory, and consistent with the escape-rate formalism for the coefficient of diffusion.

chao-dyn↗