Cet ouvrage est le résultat de plusieurs années de travail dans le domaine de la modélisation géographique. Il est structuré en trois parties. La première partie pose les fondements de la modélisation géographique, à travers les concepts les plus généraux de structure, organisation, système, géométries, topologies, métriques, matière, objet. Enfin le concept de temps permet d'aborder les notions de processus et d'interaction spatiale, fondamentales en géographie. La deuxième partie aborde l'étude des outils informatiques de modélisation des dynamiques que sont les automates cellulaires géographiques (ACG) et expose plusieurs modèles appliqués à des thématiques variées comme la croissance urbaine, les risques naturels par la simulation d'inondations, ou des thématiques plus politiques comme les fonds européens ou l'évolution des votes en France. La troisième partie de l'ouvrage présente un modèle général de système à agents géographiques (SAG) pouvant servir de base à la construction d'une plateforme de modélisation de modèles dynamiques spatiaux

This book provides a comprehensive view of the field of geographical modeling by dividing the topic into three parts. The first part of the work establishes the foundations of geographical modeling through the use of more general concepts, including: structure, organization, system, geometries, topologies, metrics, material, and object. Finally, introduction of the concept of time leads to the theories of process and spatial interaction, which are fundamental in geography. The second part of the book tackles the use of computer tools for dynamic model building, which are the geographic cellular automata (GCA), and presents several models applied to various themes, such as urban growth, natural risks by flood simulations, as well as more political themes, such as the use of European funds, or the development of voting patterns in France. Finally, a general model of the geographic agents system (GAS) which can be used as a basis for the construction of a model-building platform for dynamic spatial models is presented.

Geographical Models with Mathematica provides a fairly comprehensive overview of the types of models necessary for the development of new geographical knowledge, including stochastic models, models for data analysis, for geostatistics, for networks, for dynamic systems, for cellular automata and for multi-agent systems, all discussed in their theoretical context. The author then provides over 65 programs, written in the Mathematica language, that formalize these models. Case studies are provided to help the reader apply these programs to their own studies. - Provides theoretical, stochastic and dynamic system models - Covers data science, both in a spatial and spatio-temporal analysis - Presents a microstructural understanding of the mechanical behavior of granular materials

This monograph presents urban simulation methods that help in better understanding urban dynamics. Over historical times, cities have progressively absorbed a larger part of human population and will concentrate three quarters of humankind before the end of the century. This “urban transition” that has totally transformed the way we inhabit the planet is globally understood in its socio-economic rationales but is less frequently questioned as a spatio-temporal process. However, the cities, because they are intrinsically linked in a game of competition for resources and development, self organize in “systems of cities” where their future becomes more and more interdependent. The high frequency and intensity of interactions between cities explain that urban systems all over the world exhibit large similarities in their hierarchical and functional structure and rather regular dynamics. They are complex systems whose emergence, structure and further evolution are widely governed by the multiple kinds of interaction that link the various actors and institutions investing in cities their efforts, capital, knowledge and intelligence. Simulation models that reconstruct this dynamics may help in better understanding it and exploring future plausible evolutions of urban systems. This would provide better insight about how societies can manage the ecological transition at local, regional and global scales. The author has developed a series of instruments that greatly improve the techniques of validation for such models of social sciences that can be submitted to many applications in a variety of geographical situations. Examples are given for several BRICS countries, Europe and United States. The target audience primarily comprises research experts in the field of urban dynamics, but the book may also be beneficial for graduate students.

Ce travail d'HDR retrace le parcours scientifique de l'auteur et contextualise son investissement actuel dans l'interdisciplinarité et les sciences de la complexité. Géographe de formation, l'auteur s'est intéressé très tôt aux rapports structures/processus dans l'évolution des systèmes spatiaux et ses investigations l'ont amené à travailler sur les mobilités spatiales et certains de leurs risques ou externalités négatives associés (accidents, pollution, bruit, épidémies, congestion) dans une perspective associant étroitement la modélisation et la simulation, au service d'une démarche délibérément exploratoire. Ce positionnement a amené très tôt l'auteur à s'investir dans l'interdisciplinarité et dans la direction de collectifs interdisciplinaires, à l'image du GDR-E S4, de l'Institut des Systèmes Complexes de Paris-Ile-de-France ou de l'UMR Géographie-cités (CNRS-Paris1-Paris7).