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Modelling and Simulation of Laser Dynamics with Cellular Automata on Parallel and Distributed Computers



This thesis presents interdisciplinary research carried out in the areas of physics and computer science. We introduce a new model based on cellular automata (CA) to describe laser dynamics, which is an alternative to the standard description based on differential equations. We also study how to take advantage of the intrinsic parallel nature of CA to carry out high perfor- mance computational simulations with that model on parallel and distributed computers. CA are a class of fully discrete, spatially-distributed dynamical systems charac- terized by local interaction and synchronous parallel dynamical evolution. Our CA-based model reproduces the main laser dynamics phenomenology. It reinforces the vision of laser as a complex system, since the macroscopic properties of the laser system emerge with this model as a cooperative phe- nomenon from elementary components that interact locally under simple rules. This model represents a new methodological approach for laser modelling, which can be advantageous in cases in which the differential equations are difficult or impossible to integrate, or not entirely applicable because the usual approximations are not valid. It also opens the door to new more detailed CA-based models that could capture more features of laser behaviour. We investigate how to parallelize the model efficiently. A parallel implementa- tion has been developed using the message passing paradigm. Its performance and scalability have been analysed for the two most usual kinds of platforms for this kind of applications: dedicated clusters, and heterogeneous non-dedicated clusters including a dynamic load balancing strategy. In the latter case a very flexible modular approach has been employed in which the model is executed on top of a dynamic load balancing tool. The results confirm that, in spite of potential difficulties, it is feasible to execute large, fine-grained simulations with CA-based models—including the laser model described—on the most usual types of cluster computing platforms with a good efficiency and scalability.
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... In order to de¯ne a generic CA model [18,32], we must specify the properties of its di®erent components: ...
... Laser dynamics has been traditionally modeled through a macroscopic view based on di®erential equations, the laser rate equations, that describe the global properties of the system [48]. The works [18,22,25] showed that it is possible to model it using a CA model that describe the evolution of the individual components of the system. The interesting point is that with this model the emergent properties of the laser system appear spontaneously as a result of the self-organization of its basic components, thus capturing the essence of the laser behavior as a CS. ...
... Once the model is built and the macroscopic variables are identi¯ed and de¯ned, simulations can be run in order to¯nd emergent behaviors. There are four particular emergent behaviors in laser dynamics that can be reproduced using the CA model [18,22,25]: ...
Cellular automaton models of complex systems (CSs) are gaining greater popularity; simultaneously, they have proven the capability to solve real scientific and engineering applications. To enable everybody a quick penetration into the core of this type of modeling, three real applications of cellular automaton models, including selected open source software codes, are studied: laser dynamics, dynamic recrystallization (DRX) and surface catalytic reactions. The paper is written in a way that it enables any researcher to reach the cutting edge knowledge of the design principles of cellular automata (CA) models of the observed phenomena in any scientific field. The whole sequence of design steps is demonstrated: definition of the model using topology and local (transition) rule of a cellular automaton, achieved results, comparison to real experiments, calibration, pathological observations, flow diagrams, software, and discussions. Additionally, the whole paper demonstrates the extreme expressiveness and flexibility of massively parallel computational approaches compared to other computational approaches. The paper consists of the introductory parts that are explaining CSs, self-organization and emergence, entropy, and CA. This allows readers to realize that there is a large variability in definitions and solutions of this class of models. >>> <<< (Remark: Open-source software included).
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Modelling real systems and processes is a task classically performed through the approach of diferential equation systems, defining the evolution of diferent variables as the diferent components of the system. A bad feature that diferential equations have is that if some new parameter has to be introduced in the system, then often the previous equations are not useful, and the whole system has to be remodeled again. Bioinspired computational models are abstractions of reality into a mathematical system that works with specific semantics and can perform some tasks, such as solving problems or demonstrating the universality of themselves or other models. An interesting application of these models is the modelling of real-life processes, where some of them as the so-called P systems have demonstrated previously that their performance is remarkable. This is not only for the similarity of the results with the experimental ones, but for its adaptability and modularity of the system, that is, if a new component of the real system is taken into account, not the whole system but a small part of it has to be changed in order to simulate the changed scenario. In this work, a first look at the dynamics of a laser physical system is given, reproducing the behavior of a first model with a PDP system.
Technical Report
Abstract A cellular automaton is a decentralized computing model providing an excellent platform for performing complex computation with the help of only local information. Researchers, scientists and practitioners from different fields have exploited the CA paradigm of local information, decentralized control and universal computation for modeling different applications. This article provides a survey of available literature of some of the methodologies employed by researchers to utilize cellular automata for modeling purposes. The survey introduces the different types of cellular automata being used for modeling and the analytical methods used to predict its global behavior from its local configurations. It further gives a detailed sketch of the efforts undertaken to configure the local settings of CA from a given global situation; the problem which has been traditionally termed as the …
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