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arXiv2010

Communication and trust in the bounded confidence model

The communication process in a situation of emergency is discussed within the Scheff theory of shame and pride. The communication involves messages from media and from other persons. Three strategies are considered: selfish (to contact friends), collective (to join other people) and passive (to do nothing). We show that the pure selfish strategy cannot be evolutionarily stable. The main result is that the community structure is statistically meaningful only if the interpersonal communication is weak.

physics.soc-ph↗

arXiv2020

Orbits of Bernoulli Measures in Cellular Automata

We discuss how to construct shift-invariant probability measures over the space of bisequences of symbols, and how to describe such measures in terms of block probabilities. We then define cellular automata as maps in the space of measures and discuss orbits of shift-invariant probability measures under these maps. Subsequently, the local structure approximation is discussed as a method to approximate orbits of Bernoulli measures under the action of cellular automata. The final sections presents some known examples of cellular automata, both deterministic and probabilistic, for which elements of the orbit of the Bernoulli measure (probabilities of short blocks) can be determined exactly.

nlin.CG↗

arXiv2013

A framework for the local information dynamics of distributed computation in complex systems

The nature of distributed computation has often been described in terms of the component operations of universal computation: information storage, transfer and modification. We review the first complete framework that quantifies each of these individual information dynamics on a local scale within a system, and describes the manner in which they interact to create non-trivial computation where "the whole is greater than the sum of the parts". We describe the application of the framework to cellular automata, a simple yet powerful model of distributed computation. This is an important application, because the framework is the first to provide quantitative evidence for several important conjectures about distributed computation in cellular automata: that blinkers embody information storage, particles are information transfer agents, and particle collisions are information modification events. The framework is also shown to contrast the computations conducted by several well-known cellular automata, highlighting the importance of information coherence in complex computation. The results reviewed here provide important quantitative insights into the fundamental nature of distributed computation and the dynamics of complex systems, as well as impetus for the framework to be applied to the analysis and design of other systems.

nlin.CG↗

arXiv2014

Neighborhood Selection and Rules Identification for Cellular Automata: A Rough Sets Approach

In this paper a method is proposed which uses data mining techniques based on rough sets theory to select neighborhood and determine update rule for cellular automata (CA). According to the proposed approach, neighborhood is detected by reducts calculations and a rule-learning algorithm is applied to induce a set of decision rules that define the evolution of CA. Experiments were performed with use of synthetic as well as real-world data sets. The results show that the introduced method allows identification of both deterministic and probabilistic CA-based models of real-world phenomena.

cs.AI↗

arXiv2015

The ideal energy of classical lattice dynamics

We define, as local quantities, the least energy and momentum allowed by quantum mechanics and special relativity for physical realizations of some classical lattice dynamics. These definitions depend on local rates of finite-state change. In two example dynamics, we see that these rates evolve like classical mechanical energy and momentum.

nlin.CG↗

arXiv2018

Simple networks on complex cellular automata: From de Bruijn diagrams to jump-graphs

We overview networks which characterise dynamics in cellular automata. These networks are derived from one-dimensional cellular automaton rules and global states of the automaton evolution: de Bruijn diagrams, subsystem diagrams, basins of attraction, and jump-graphs. These networks are used to understand properties of spatially-extended dynamical systems: emergence of non-trivial patterns, self-organisation, reversibility and chaos. Particular attention is paid to networks determined by travelling self-localisations, or gliders.

nlin.CG↗

arXiv2013

Pedestrians moving in dark: Balancing measures and playing games on lattices

We present two conceptually new modeling approaches aimed at describing the motion of pedestrians in obscured corridors: * a Becker-Döring-type dynamics * a probabilistic cellular automaton model. In both models the group formation is affected by a threshold. The pedestrians are supposed to have very limited knowledge about their current position and their neighborhood; they can form groups up to a certain size and they can leave them. Their main goal is to find the exit of the corridor. Although being of mathematically different character, the discussion of both models shows that it seems to be a disadvantage for the individual to adhere to larger groups. We illustrate this effect numerically by solving both model systems. Finally we list some of our main open questions and conjectures.

physics.soc-ph↗

arXiv2004

Perturbing the topology of the Game of Life increases its robustness to asynchrony

An experimental analysis of the asynchronous version of the "Game of Life" is performed to estimate how topology perturbations modify its evolution. We focus on the study of a phase transition from an "inactive-sparse phase" to a "labyrinth phase" and produce experimental data to quantify these changes as a function of the density of the initial configuration, the value of the synchrony rate, and the topology missing-link rate. An interpretation of the experimental results is given using the hypothesis that initial "germs" colonize the whole lattice and the validity of this hypothesis is tested.

nlin.CG↗

arXiv1996

Estimating the Fractal Dimension, K_2-entropy, and the Predictability of the Atmosphere

The series of mean daily temperature of air recorded over a period of 215 years is used for analysing the dimensionality and the predictability of the atmospheric system. The total number of data points of the series is 78527. Other 37 versions of the original series are generated, including ``seasonally adjusted'' data, a smoothed series, series without annual course, etc. Modified methods of Grassberger and Procaccia are applied. A procedure for selection of the ``meaningful'' scaling region is proposed. Several scaling regions are revealed in the ln C(r) versus ln r diagram. The first one in the range of larger ln r has a gradual slope and the second one in the range of intermediate ln r has a fast slope. Other two regions are settled in the range of small ln r. The results lead us to claim that the series arises from the activity of at least two subsystems. The first subsystem is low-dimensional (d_f=1.6) and it possesses the potential predictability of several weeks. We suggest that this subsystem is connected with seasonal variability of weather. The second subsystem is high-dimensional (d_f>17) and its error-doubling time is about 4-7 days. It is found that the predictability differs in dependence on season. The predictability time for summer, winter and the entire year (T_2 approx. 4.7 days) is longer than for transition-seasons (T_2 approx. 4.0 days for spring, T_2 approx. 3.6 days for autumn). The role of random noise and the number of data points are discussed. It is shown that a 15-year-long daily temperature series is not sufficient for reliable estimations based on Grassberger and Procaccia algorithms.

comp-gas↗

arXiv1994

Heat Transfer in Lattice BGK Modeled Fluid

The thermal lattice BGK model is a recently suggested numerical tool which aims to simulate thermohydrodynamic problems. We investigate the quality of the lattice BGK simulation by calculating the temperature profiles in the Couette flow under different Eckert and Mach numbers. A revised lower order model is proposed and the higher order model is proved once again to be advantageous.

comp-gas↗

arXiv1995

Simulating Three-Dimensional Hydrodynamics on a Cellular-Automata Machine

We demonstrate how three-dimensional fluid flow simulations can be carried out on the Cellular Automata Machine 8 (CAM-8), a special-purpose computer for cellular-automata computations. The principal algorithmic innovation is the use of a lattice-gas model with a 16-bit collision operator that is specially adapted to the machine architecture. It is shown how the collision rules can be optimized to obtain a low viscosity of the fluid. Predictions of the viscosity based on a Boltzmann approximation agree well with measurements of the viscosity made on CAM-8. Several test simulations of flows in simple geometries -- channels, pipes, and a cubic array of spheres -- are carried out. Measurements of average flux in these geometries compare well with theoretical predictions.

chao-dyn↗

arXiv1995

An Euler Solver Based on Locally Adaptive Discrete Velocities

A new discrete-velocity model is presented to solve the three-dimensional Euler equations. The velocities in the model are of an adaptive nature---both the origin of the discrete-velocity space and the magnitudes of the discrete-velocities are dependent on the local flow--- and are used in a finite volume context. The numerical implementation of the model follows the near-equilibrium flow method of Nadiga and Pullin [1] and results in a scheme which is second order in space (in the smooth regions and between first and second order at discontinuities) and second order in time. (The three-dimensional code is included.) For one choice of the scaling between the magnitude of the discrete-velocities and the local internal energy of the flow, the method reduces to a flux-splitting scheme based on characteristics. As a preliminary exercise, the result of the Sod shock-tube simulation is compared to the exact solution.

comp-gas↗

arXiv1995

Cellular automaton model of precipitation/dissolution coupled with solute transport

Precipitation/dissolution reactions coupled with solute transport are modelled as a cellular automaton in which solute molecules perform a random walk on a regular lattice and react according to a local probabilistic rule. Stationary solid particles dissolve with a certain probability and, provided solid is already present or the solution is saturated, solute particles have a probability to precipitate. In our simulation of the dissolution of a solid block inside uniformly flowing water we obtain solid precipitation downstream from the original solid edge, in contrast to the standard reaction-transport equations. The observed effect is the result of fluctuations in solute density and diminishes when we average over a larger ensemble. The additional precipitation of solid is accompanied by a substantial reduction in the relatively small solute concentration. The model is appropriate for the study of the rôle of intrinsic fluctuations in the presence of reaction thresholds and can be employed to investigate porosity changes associated with the carbonation of cement.

comp-gas↗

arXiv1994

Growth Kinetics in Multicomponent Fluids

The hydrodynamic effects on the late stage kinetics in spinodal decomposition of multicomponent fluids are examined using a lattice Boltzmann scheme with stochastic fluctuations in the fluid and at the interface. In two dimensions, the three and four component immiscible fluid mixture (with a $1024^2$ lattice) behaves like an off-critical binary fluid with an estimated domain growth of $t^{0.4\pm.03}$ rather than $t^{1/3}$ as previously predicted, showing the significant influence of hydrodynamics. In three dimensions (with a $256^3$ lattice), we estimate the growth as $t^{0.96\pm0.05}$ for both critical and off-critical quenching, in agreement with phenomenological theory.

comp-gas↗

arXiv1995

Renormalized Equilibria of a Schloegl Model Lattice Gas

A lattice gas model for Schloegl's second chemical reaction is described and analyzed. Because the lattice gas does not obey a semi-detailed-balance condition, the equilibria are non-Gibbsian. In spite of this, a self-consistent set of equations for the exact homogeneous equilibria are described, using a generalized cluster-expansion scheme. These equations are solved in the two-particle BBGKY approximation, and the results are compared to numerical experiment. It is found that this approximation describes the equilibria far more accurately than the Boltzmann approximation. It is also found, however, that spurious solutions to the equilibrium equations appear which can only be removed by including effects due to three-particle correlations.

comp-gas↗

arXiv1995

Analytical solutions of the lattice Boltzmann BGK model

Analytical solutions of the two dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plain Poiseuille flow and the plain Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time $τ$ and the lattice spacing. The analytic solutions are the exact representation of these two flows without any approximation.

comp-gas↗

arXiv1995

Lattice gas with ``interaction potential''

We present an extension of a simple automaton model to incorporate non-local interactions extending over a spatial range in lattice gases. {}From the viewpoint of Statistical Mechanics, the lattice gas with interaction range may serve as a prototype for non-ideal gas behavior. {}From the density fluctuations correlation function, we obtain a quantity which is identified as a potential of mean force. Equilibrium and transport properties are computed theoretically and by numerical simulations to establish the validity of the model at macroscopic scale.

comp-gas↗

arXiv1995

Multi-component lattice-Boltzmann model with interparticle interaction

A previously proposed [X. Shan and H. Chen, Phys. Rev. E {\bf 47}, 1815, (1993)] lattice Boltzmann model for simulating fluids with multiple components and interparticle forces is described in detail. Macroscopic equations governing the motion of each component are derived by using Chapman-Enskog method. The mutual diffusivity in a binary mixture is calculated analytically and confirmed by numerical simulation. The diffusivity is generally a function of the concentrations of the two components but independent of the fluid velocity so that the diffusion is Galilean invariant. The analytically calculated shear kinematic viscosity of this model is also confirmed numerically.

comp-gas↗