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arXiv1995

Plane Waves in a Multispeed Discrete-Velocity Gas

A kinetic flux-splitting procedure used in conjunction with local thermodynamic equilibrium in a finite volume allows us to investigate numerically discrete-velocity gas flows. The procedure, outlined for a general discrete-velocity gas, is used to simulate flows of the nine-velocity gas, a simple two dimensional multiple-speed discrete-velocity gas, wherein a multiplicity of speeds ensures nontrivial thermodynamics. After verifying the linear wave limit and the non-linear steepening of wavefronts, the stability and propagation of planar discontinuities in that model gas is studied. The supersonic-subsonic requirement for the stable propagation of a discontinuity, being kinematic in nature is the same in the model gas, as e.g., in a perfect gas. However, the finiteness of the velocity space in the model gas does not allow a translation of the above kinematic condition to the thermodynamic requirement of increasing entropy across a compressive shock: a case of an entropy decreasing compressive shock in the model gas is presented. Finally, the interaction of various types of waves--shock waves, rarefactions and contact surfaces--in the model gas are shown in a simulation of the shock tube problem.

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arXiv1995

Lattice Boltzmann Model For Magnetic Fluids

A lattice Boltzmann model with interacting particles was developed in order to simulate the magneto-rheological characteristics of magnetic fluids. In the frame of this model, $6\, +\,1$ species of particles are allowed to move across a $2D$ triangular lattice. Among these species, $6$ of them carry an individual magnetic dipole moment and interact themselves not only as a result oflocal collisions, as in current Lattice Boltzmann models, but also as a result of nearest neighbours magnetic dipole-dipole interaction. The relative distribution of the individual magnetic moments is determined by the intensity of an external static magnetic field acting on the whole system. This model exhibits some relevant characteristics of real magnetic fluids, i.e., anisotropic structure formation as a result of magnetic field induced gas-liquid phase transition and magnetic field dependence of the sound velocity and the attenuation coefficient.

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arXiv1995

On reconstruction of chaotic attractor from time series represented as "clusters"

The method of reconstruction of an attractor from a set of short time series ({\it clusters}) is proposed and discussed. This method is most useful for correlation dimension estimation of experimental data.

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arXiv1995

Predicting and characterizing data sequences from structure-variable systems

In principle, all the natural systems such as biological, ecological and economical systems are structure-variable systems (in which some environment parameters are not fixed). In this Letter we show that data sequences from many structure-variable systems are short-term predictable. We also argue how to characterize the data sequences from structure-variable systems.

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arXiv1995

SAMPLING ALMOST PERIODIC FUNCTIONS WITH RANDOM PROBES OF FINITE DENSITY

We consider the problem of reconstructing a function given its values on a set of points with finite density. We prove that with probability one, the values of an almost periodic function on a random array of points (with finite density) completely determine the function. We also give some properties of the associated Blaschke product.

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arXiv1995

Analysis and boundary condition of the lattice Boltzmann BGK model with two velocity components

In this paper, we study the two dimensional lattice Boltzmann BGK model (LBGK) by analytically solving a simple flow in a 2~-D channel. The flow is driven by the movement of upper boundary with vertical injection fluid at the porous boundaries. The velocity profile is shown to satisfy a second-order finite-difference form of the simplified incompressible Navier-Stokes equation. With the analysis, different boundary conditions can be studied theoretically. A momentum exchange principle is also revealed at the boundaries. A general boundary condition for any given velocity boundary is proposed based on the analysis.

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arXiv1995

Estimating Predictability: Redundancy and Surrogate Data Method

A method for estimating theoretical predictability of time series is presented, based on information-theoretic functionals---redundancies and surrogate data technique. The redundancy, designed for a chosen model and a prediction horizon, evaluates amount of information between a model input (e.g., lagged versions of the series) and a model output (i.e., a series lagged by the prediction horizon from the model input) in number of bits. This value, however, is influenced by a method and precision of redundancy estimation and therefore it is a) normalized by maximum possible redundancy (given by the precision used), and b) compared to the redundancies obtained from two types of the surrogate data in order to obtain reliable classification of a series as either unpredictable or predictable. The type of predictability (linear or nonlinear) and its level can be further evaluated. The method is demonstrated using a numerically generated time series as well as high-frequency foreign exchange data and the theoretical predictability is compared to performance of a nonlinear predictor.

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arXiv1995

On pressure and velocity flow boundary conditions for the lattice Boltzmann BGK model

Pressure (density) and velocity boundary conditions inside a flow domain are studied for 2-D and 3-D lattice Boltzmann BGK models (LBGK) and new method to specify these conditions are proposed. These conditions are consistent with the boundary condition we proposed in a previous paper using an idea of bounce-back of non-equilibrium distribution. These conditions give excellent results for the regular LBGK models, and were shown to be second-order accurate by numerical examples. When they are used together with the improved incompressible LBGK model proposed by zou et al. the simulation results recover the analytical solution of the plane Poiseuille flow driven by pressure (density) difference with machine accuracy.

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arXiv1995

CAM-8: A Computer Architecture Based on Cellular Automata

Conventional computers are ill suited to run CA models, and so discourage their development. By creating a hardware platform that makes a broad range of new CA algorithms practical for real applications, we hope to whet the appetite of researchers for the astronomical computing power that can be harnessed in microphysics in a CA format.

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arXiv1995

Detecting Nonlinearity in Pressure Data Inside the Draft Tube of a Real Francis Turbine

A general method for testing nonlinearity in time series is described and applied to measurements of different pressure data inside the draft tube surge of a real Francis turbine. Comparing the current original time series to an ensemble of surrogates time series, suitably constructed to mimic the linear properties of the original one, we was able to distinguish a linear stochastic from a nonlinear deterministic behaviour and, moreover, to quantify the degree of nonlinearity present in the related dynamics. The problem of detecting nonlinear structure in real data is quite complicated by the influence of various contaminations, like broadband noise and/or long coherence times. These difficulties have been overcame using the combination of a suitable nonlinear filtering technique and a qualitative redundancy statistic analysis. The above investigations allow a quantitative characterization of different dynamical regimes of motion of gas cavities inside real turbines and, moreover, allow to support the reliability of some related mathematical modelizations.

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arXiv1995

On Surrogate Data Testing for Linearity based on the Periodogram

The method of surrogate data is a tool to test whether data were generated by some class of model. Tests based on the periodogram have been proposed to decide if linear systems driven by Gaussian noise could have generated a sample time series. We show that this procedure based on the periodogram, in general, misspecifies the test statistic. Based on the theory of linear systems we suggest an alternative procedure to obtain the correct distribution of the test statistic and discuss problems of this approach.

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arXiv1995

The developing structure of dynamical systems

In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced and discussed. The boundary crises and the period-doubling bifurcations are found suppressed and scaling properties for these phenomena are exploited. Due to this suppression, the period-doubling bifurcations seem no longer continuous. We further discuss the possible applications of these models.

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arXiv1995

Parallel Algorithms on the ASTRA SIMD Machine

In view of the tremendous computing power jump of modern RISC processors the interest in parallel computing seems to be thinning out. Why use a complicated system of parallel processors, if the problem can be solved by a single powerful micro-chip? It is a general law, however, that exponential growth will always end by some kind of a saturation, and then parallelism will again become a hot topic. We try to prepare ourselves for this eventuality. The MPPC project started in 1990 in the heydeys of parallelism and produced four ASTRA machines (presented at CHEP'92) with 4k processors (which are expandable to 16k) based on `yesterday's chip-technology' (chip presented at CHEP'91). These machines now provide excellent test-beds for algorithmic developments in a complete, real environment. We are developing for example fast-pattern recognition algorithms which could be used in high-energy physics experiments at the LHC (planned to be operational after 2004 at CERN) for triggering and data reduction. The basic feature of our ASP (Associative String Processor) approach is to use extremely simple (thus very cheap) processor elements but in huge quantities (up to millions of processors) connected together by a very simple string-like communication chain. In this paper we present powerful algorithms based on this architecture indicating the performance perspectives if the hardware (i.e. chip fabrication) quality reaches `present or even future technology levels'.

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arXiv1995

Mutual Information as a Bayesian Measure of Independence

The problem of hypothesis testing is examined from both the historical and Bayesian points of view in the case that sampling is from an underlying joint probability distribution and the hypotheses tested for are those of independence and dependence of the underlying distribution. Exact results for the Bayesian method are provided. Asymptotic Bayesian results and historical method test quantities are compared, and historical method quantities are interpreted in terms of clearly defined Bayesian quantities. The asymptotic Bayesian test relies upon a statistic that is primarily mutual information.

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arXiv1995

Investigations of a Two-Phase Fluid Model

We study an interface-capturing two-phase fluid model in which the interfacial tension is modelled as a volumetric stress. Since these stresses are obtainable from a Van der Waals-Cahn-Hilliard free energy, the model is, to a certain degree, thermodynamically realistic. Thermal fluctuations are not considered presently for reasons of simplicity. The utility of the model lies in its momentum-conservative representation of surface tension and the simplicity of its numerical implementation resulting from the volumetric modelling of the interfacial dynamics. After validation of the model in two spatial dimensions, two prototypical applications---instability of an initially high-Reynolds-number liquid jet in the gaseous phase and spinodal decomposition in a liquid-gas system--- are presented.

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arXiv1996

Generating high-dimensional chaotic signals by the sum

The method of generating of high-dimensional oscillations on the basis of summing of low-dimensional chaotic signals of noncoupled dynamical systems is investigated. It is shown that the correlation dimension of attractor reconstructed from such oscillations is equal to the sum of dimensions of the original signals. The possibilities for obtaining of homogeneous high-dimensional chaotic attractor are numerically demonstrated with the original signals of R{ö}ssler system.

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arXiv1996

Two-Dimensional Navier-Stokes Simulation of Breaking Waves

Numerical simulations describing plunging breakers including the splash-up phenomenon are presented. The motion is governed by the classical, incompressible, two-dimensional Navier-Stokes equation. The numerical modelling of this two-phase flow is based on a piecewise linear version of the volume of fluid method. Preliminary results concerning the time evolution of the liquid-gas interface and the vorticity field are given for short waves, showing how an initial steep wave undergoes breaking and successive splash-up cycles.

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arXiv1996

Lattice kinetic theory for numerical combustion

A simple extension of the Lattice Boltzmann equation is proposed, which permits to handle reactive flow dynamics in the limit of fast chemistry at virtually no extra-cost with respect to the purely hydrodynamic scheme.

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