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At least 145 records · Page 8Linked to original sources
arXiv1999

Cellular Automaton Rule184++C. A Simple Model for the Complex Dynamics of Various Particles Flow

A cellular automaton named Rule 184++C is proposed as a meta-model to investigate the flow of various complex particles. In this model, unlike the granular pipe flow and the traffic flow, not only the free-jam phase transition but also the free-intermediate, the intermediate-jam, and the dilute-dense phase transitions appear. Moreover, the freezing phenomena appear if the system contains two types of different particles.

comp-gas↗
arXiv1996

Lattice Boltzmann Equation: Failure or Success?

The lattice Boltzmann equation (LBE) is a microscopically-inspired method designed to solve macroscopic fluid dynamics problems. As a such, it lives at the interface between the microscopic (molecular) and macroscopic (continuum) worlds, hopefully capturing the best of the two. In this paper we shall discuss whether or not, after almost a decade since its inception, LBE has lived up to the initial expectations. Open problems and future research developments are also briefly outlined.

comp-gas↗
arXiv1997

Perturbation theory predictions and Monte Carlo simulations for the 2-d O(n) non-linear sigma-model

By using the results of a high-statistics (O(10^7) measurements) Monte Carlo simulation we test several predictions of perturbation theory on the O(n) non-linear sigma-model in 2 dimensions. We study the O(3) and O(8) models on large enough lattices to have a good control on finite-size effects. The magnetic susceptibility and three different definitions of the correlation length are measured. We check our results with large-n expansions as well as with standard formulae for asymptotic freedom up to 4 loops in the standard and effective schemes. For this purpose the weak coupling expansions of the energy up to 4 loops for the standard action and up to 3 loops for the Symanzik action are calculated. For the O(3) model we have used two different effective schemes and checked that they lead to compatible results. A great improvement in the results is obtained by using the effective scheme based on the energy at 3 and 4 loops. We find that the O(8) model follows very nicely (within few per mille) the perturbative predictions. For the O(3) model an acceptable agreement (within few per cent) is found.

hep-lat↗
arXiv1993

Numerical Simulations of Particulate Suspensions via a Discretized Boltzmann Equation Part I. Theoretical Foundation

A new and very general technique for simulating solid-fluid suspensions is described; its most important feature is that the computational cost scales linearly with the number of particles. The method combines Newtonian dynamics of the solid particles with a discretized Boltzmann equation for the fluid phase; the many-body hydrodynamic interactions are fully accounted for, both in the creeping-flow regime and at higher Reynolds numbers. Brownian motion of the solid particles arises spontaneously from stochastic fluctuations in the fluid stress tensor, rather than from random forces or displacements applied directly to the particles. In this paper, the theoretical foundations of the technique are laid out, illustrated by simple analytical and numerical examples; in the companion paper, extensive numerical tests of the method, for stationary flows, time-dependent flows, and finite Reynolds number flows, are reported.

comp-gas↗
arXiv1993

Numerical Simulations of Particulate Suspensions via a Discretized Boltzmann Equation Part II. Numerical Results

A new and very general technique for simulating solid-fluid suspensions has been described in a previous paper (Part I); the most important feature of the new method is that the computational cost scales with the number of particles. In this paper (Part II), extensive numerical tests of the method are described; for creeping flows, both with and without Brownian motion, and at finite Reynolds numbers. Hydrodynamic interactions, transport coefficients, and the short-time dynamics of random dispersions of up to 1024 colloidal particles have been simulated.

comp-gas↗
arXiv1997

Majority-Vote Cellular Automata, Ising Dynamics, and P-Completeness

We study cellular automata where the state at each site is decided by a majority vote of the sites in its neighborhood. These are equivalent, for a restricted set of initial conditions, to non-zero probability transitions in single spin-flip dynamics of the Ising model at zero temperature. We show that in three or more dimensions these systems can simulate Boolean circuits of AND and OR gates, and are therefore P-complete. That is, predicting their state t time-steps in the future is at least as hard as any other problem that takes polynomial time on a serial computer. Therefore, unless a widely believed conjecture in computer science is false, it is impossible even with parallel computation to predict majority-vote cellular automata, or zero-temperature single spin-flip Ising dynamics, qualitatively faster than by explicit simulation.

cond-mat.stat-mech↗
arXiv1998

Block Spins for Partial Differential Equations

We investigate the use of renormalisation group methods to solve partial differential equations (PDEs) numerically. Our approach focuses on coarse-graining the underlying continuum process as opposed to the conventional numerical analysis method of sampling it. We calculate exactly the coarse-grained or `perfect' Laplacian operator and investigate the numerical effectiveness of the technique on a series of 1+1-dimensional PDEs with varying levels of smoothness in the dynamics: the diffusion equation, the time-dependent Ginzburg-Landau equation, the Swift-Hohenberg equation and the damped Kuramoto-Sivashinsky equation. We find that the renormalisation group is superior to conventional sampling-based discretisations in representing faithfully the dynamics with a large grid spacing, introducing no detectable lattice artifacts as long as there is a natural ultra-violet cut off in the problem. We discuss limitations and open problems of this approach.

cond-mat.stat-mech↗
arXiv1993

The non-linear response of the magnetosphere: 30 October 1978

Previous efforts to find evidence of deterministic nonlinear dynamics in the global geomagnetic system have treated the geomagnetic system as autonomous. However, the geomagnetic system is strongly driven by the stochastic solar wind. We consider the response of the magnetosphere, as given by the AE index, for one day when the IMF had a nearly constant southward value. Using both a series of non-linear statistics and non-linear prediction of the response to the input signal $v B_s$, we find that there is some evidence for deterministic non-linear response of the Earth's magnetosphere on that day.

comp-gas↗
arXiv1993

Prediction of Large Events on a Dynamical Model of a Fault

We present results for long term and intermediate term prediction algorithms applied to a simple mechanical model of a fault. We use long term prediction methods based, for example, on the distribution of repeat times between large events to establish a benchmark for predictability in the model. In comparison, intermediate term prediction techniques, analogous to the pattern recognition algorithms CN and M8 introduced and studied by Keilis-Borok et al., are more effective at predicting coming large events. We consider the implications of several different quality functions Q which can be used to optimize the algorithms with respect to features such as space, time, and magnitude windows, and find that our results are not overly sensitive to variations in these algorithm parameters. We also study the intrinsic uncertainties associated with seismicity catalogs of restricted lengths.

chao-dyn↗
arXiv1999

Coherent Moving States in Highway Traffic (Originally: Moving Like a Solid Block)

Recent advances in multiagent simulations have made possible the study of realistic traffic patterns and allow to test theories based on driver behaviour. Such simulations also display various empirical features of traffic flows, and are used to design traffic controls that maximise the throughput of vehicles in heavily transited highways. In addition to its intrinsic economic value, vehicular traffic is of interest because it may throw light on some social phenomena where diverse individuals competitively try to maximise their own utilities under certain constraints. In this paper, we present simulation results that point to the existence of cooperative, coherent states arising from competitive interactions that lead to a new phenomenon in heterogeneous highway traffic. As the density of vehicles increases, their interactions cause a transition into a highly correlated state in which all vehicles practically move with the same speed, analogous to the motion of a solid block. This state is associated with a reduced lane changing rate and a safe, high and stable flow. It disappears as the vehicle density exceeds a critical value. The effect is observed in recent evaluations of Dutch traffic data.

cond-mat.stat-mech↗
arXiv1993

Don't bleach chaotic data

A common first step in time series signal analysis involves digitally filtering the data to remove linear correlations. The residual data is spectrally white (it is ``bleached''), but in principle retains the nonlinear structure of the original time series. It is well known that simple linear autocorrelation can give rise to spurious results in algorithms for estimating nonlinear invariants, such as fractal dimension and Lyapunov exponents. In theory, bleached data avoids these pitfalls. But in practice, bleaching obscures the underlying deterministic structure of a low-dimensional chaotic process. This appears to be a property of the chaos itself, since nonchaotic data are not similarly affected. The adverse effects of bleaching are demonstrated in a series of numerical experiments on known chaotic data. Some theoretical aspects are also discussed.

comp-gas↗
arXiv1996

Stabilizing the Richardson Algorithm by Controlling Chaos

By viewing the operations of the Richardson purification algorithm as a discrete time dynamical process, we propose a method to overcome the instability of the algorithm by controlling chaos. We present theoretical analysis and numerical results on the behavior and performance of the stabilized algorithm.

cmp-lg↗
arXiv1997

Object orientation and visualization of physics in two dimensions

We present a generalized framework for cellular/lattice based visualizations in two dimensions based on state of the art computing abstractions. Our implementation takes the form of a library of reusable functions written in C++ which hides complex graphical programming issues from the user and mimics the algebraic structure of physics at the Hamiltonian level. Our toolkit is not just a graphics library but an object analysis of physical systems which disentangles separate concepts in a faithful analytical way. It could be rewritten in other languages such as Java and extended to three dimensional systems straightforwardly. We illustrate the usefulness of our analysis with implementations of spin-films (the two-dimensional XY model with and without an external magnetic field) and a model for diffusion through a triangular lattice.

cond-mat↗
arXiv1993

A Lattice Boltzmann Model for Multi-phase Fluid Flows

We develop a lattice Boltzmann equation method for simulating multi-phase immiscible fluid flows with variation of density and viscosity, based on the model proposed by Gunstensen {\em et al} for two-component immiscible fluids. The numerical measurements of surface tension and viscosity agree well with theoretical predictions. Several basic numerical tests, including spinodal decomposition, two-phase fluid flows in two-dimensional channels and two-phase viscous fingering, are shown in agreement of experiments and analytical solutions.

comp-gas↗
arXiv1993

Comparison of Spectral Method and Lattice Boltzmann Simulations of Two-Dimensional Hydrodynamics

We present numerical solutions of the two-dimensional Navier-Stokes equations by two methods; spectral and the novel Lattice Boltzmann Equation (LBE) scheme. Very good agreement is found for global quantities as well as energy spectra. The LBE scheme is, indeed, providing reasonably accurate solutions of the Navier-Stokes equations with an isothermal equation of state, in the nearly incompressible limit. Relaxation to a previously reported ``sinh-Poisson'' state is also observed for both runs.

comp-gas↗
arXiv1994

Eddy diffusivities in scalar transport

Standard and anomalous transport in incompressible flow is investigated using multiscale techniques. Eddy-diffusivities emerge from the multiscale analysis through the solution of an auxiliary equation. From the latter it is derived an upper bound to eddy-diffusivities, valid for both static and time-dependent flow. The auxiliary problem is solved by a perturbative expansion in powers of the Péclet number resummed by Padé approximants and by a conjugate gradient method. The results are compared to numerical simulations of tracers dispersion for three flows having different properties of Lagrangian chaos. It is shown on a concrete example how the presence of anomalous diffusion can be revealed from the singular behaviour of the eddy-diffusivity at very small molecular diffusivities.

cond-mat↗
arXiv1995

A non-slip boundary condition for lattice Boltzmann simulations

A non-slip boundary condition at a wall for the lattice Boltzmann method is presented. In the present method unknown distribution functions at the wall are assumed to be an equilibrium distribution function with a counter slip velocity which is determined so that fluid velocity at the wall is equal to the wall velocity. Poiseuille flow and Couette flow are calculated with the nine-velocity model to demonstrate the accuracy of the present boundary condition.

comp-gas↗