Samira El Yacoubi

Regional Controllability with Cellular Automata Models

In relation with spatio-temporal systems theory some regional analysis aspects were recently developed [6, 24] and well studied in continuous systems described by partial differential equations. The purpose of this paper is to give a comparative study of the regional controllability by means of cellular automata models. We show through various examples how the main features of regional controllability may be simply described and implemented by cellular automata approach. To solve this problem, we propose one of the most efficient evolutionary techniques based on genetic algorithms.

MODELING OF IRRIGATION CHANNELS — A COMPARATIVE STUDY

A free surface Lattice Boltzmann (LB) model – based on a two-fluid system – is considered to simulate the flow of water in an irrigation canal. We compare the behavior of our numerical simulations with simple experiments and theoretical results obtained from the Saint-Venant equation, the partial differential equation commonly used to describe water flow in irrigation canals. The case study we consider are (1) the height of water along the canal in a stationary regime and (2) a draining experiment. The comparisons show that the two-fluid LB approach captures correctly the draining speed and the qualitative water profile.

On the decidability of the evolution of the fuzzy cellular automaton 184

In the previous paper [1] we presented general methods for detecting the evolution and dynamics of any one of the 255 fuzzy cellular automata (FCA) and showed that the method was applicable to all but nine of the 255 FCA. The main result there was that the limiting behavior of these FCA is decidable, except possibly for these nine, for finite initial configurations in a homogeneous background of zeros. Only six of these nine so called exceptional CA namely, FCA 172, 184, 202, 216, 226, and 228, appear to be interesting enough to warrant separate study, the other three, namely FCA 204, 228, and 240 being trivial. In this paper we study the exceptional FCA 184, a cellular automaton that admits a continuum of fixed points, namely the interval [0,1]. This FCA is of interest because the general technique developed in [1] fails for the determination of its asymptotics. We show, in particular, that the asymptotic evolution of FCA 184 from any finite initial including random configuration of non-zero cells is decidable.

A bi-fluid lattice boltzmann model for water flow in an irrigation channel

This paper is devoted to modelling of water flow dynamics in open-channels for the goal of controlling irrigation systems We expose and validate a methodology based on Lattice Boltzmann models as an alternative to the commonly used Saint-Venant equations We adapt a bi-fluid model to the case of a free surface water flow A gravity force is applied to the heaviest fluid as to maintain it at the bottom The considered boundary conditions take into account the control actions provided by the two underflow gates located at the left and right ends of the reach Numerical results for density profiles are given to validate our approach.

Vulnerability and Protector Control: Cellular Automata Approach

In this work we consider the protector control problem using cellular automata approach. We give some definitions and characterizations of vulnerable zones and protector control for a cellular automaton model. We illustrate this notion through a fire forest example using a developed application with JAVA environment.

Synchronization and control of cellular automata

We study the problem of targeted synchronization of stable chaotic extended systems, i.e., systems which are not chaotic in the usual sense, but are unpredictable for finite perturbations. Examples are cellular automata, which are completely discrete dynamical systems. We show that the usual approach may lead to counter intuitive results, but that it is possible to exploit the characteristics of the system in order to reduce the distance between two replicas with less control.

Spreadable probabilistic cellular automata models: an application in epidemiology

Many important physical processes reveal spreadable phenomena which describe the expansion with time of a given spatial property The general spreadability concept have been studied using models based on partial differential equations (PDEs) These spreadable dynamics are generally non linear and then difficult to simulate particularly in 2 dimensions A cellular automata approach have been used as an alternative modelling tool to model and simulate spreadable systems in the deterministic case. We propose in this paper a probabilistic cellular automaton model that exhibits the growth with time of a spatial property The obtained local dynamics are directly implemented and the numerical results are performed to illustrate spreadable phenomena An example to epidemic propagation is given to illustrate the considered phenomena.

The spatial reproduction number in a cellular automaton model for vector-borne diseases applied to the transmission of Chagas disease

This work aims at developing a general methodology to determine the spatial changes in the basic reproduction number for vector-borne diseases. This requires a spatially explicit modeling system which will be based on a cellular automata (CA) approach and applied to the Chagas disease for both homogeneous and heterogeneous landscapes. Using an extension of the so-called next-generation matrix, we obtained an expression for the basic reproduction number R 0 that characterizes the spatial heterogeneity of the risk of emergence of an outbreak. The performed simulation with the built CA model shows the effect of local vector dispersal in a heterogeneous landscape for Chagas disease transmission.

A cellular automata model for adaptive sympatric speciation

The emergence of new species is one of the trickiest issues of evolutionary biology We propose a cellular automata model to investigate the possibility that speciation proceeds in sympatry, focusing on the importance of the structure of the landscape on the likelihood of speciation The conditions for speciation are shown to be limited whatever the landscape being considered, although habitat structure best favours the emergence of new species.

Regional Control of Probabilistic Cellular Automata

Probabilistic Cellular Automata are extended stochastic systems, widely used for modelling phenomena in many disciplines. The possibility of controlling their behaviour is therefore an important topic. We shall present here an approach to the problem of controlling such systems by acting only on the boundary of a target region.