Geographical Models with Mathematica

Geographical Models with Mathematica

1st Edition - February 1, 2017

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  • Author: Andre Dauphine
  • eBook ISBN: 9780081022306
  • Hardcover ISBN: 9781785482250

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Description

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.

Key Features

  • 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

Readership

Students, teachers and researchers in geography; the user community of Wolfram language and Mathematica students, teachers and researchers in geosciences and social sciences

Table of Contents

  • Introduction

    • I.1 The scientific practice of the geographer
    • I.2 The three forms of geography projects
    • I.3 Plan of the work
    • I.4 How should this work be read?
    • I.5 Appendix 1: a general modeling language Mathematica

    Part 1: Modeling the Relationships between Societies and Nature

    Introduction

    1: The Theoretical Context of Classical Geography

    • Abstract
    • 1.1 Environmentalism – a theory that is still rejected
    • 1.2 The theoretical double paradox of classical geography
    • 1.3 The general theory of systems and the theories derived therefrom
    • 1.4 Conclusion
    • 1.5 Appendix 2: Importing data within Mathematica

    2: Statistical and Probability Models for Given Relationships Between Societies and the Natural Environment

    • Abstract
    • 2.1 Acknowledging the probability model for recorded data
    • 2.2 Modeling the relationships between two or several variables
    • 2.3 Temporalities and time series models
    • 2.4 Conclusion
    • 2.5 Appendix 3: chronological program processing

    3: Models of Ordinary Dynamic Systems

    • Abstract
    • 3.1 Four lines of questioning to understand the behavior of a dynamic system
    • 3.2 Initiation in the modeling of dynamic systems
    • 3.3 Assets and restrictions of ODE models
    • 3.4 More realistic models of geographical systems
    • 3.5 Conclusion
    • 3.6 Appendix 4: crowd behavior in catastrophic situations

    Part 2: Modeling Geographic Locations

    Introduction

    4: Theories of Geographical Locations

    • Abstract
    • 4.1 Introduction to spatial economic theories
    • 4.2 A new urban economy and a new economic geography
    • 4.3 Conclusion

    5: Theoretical Geolocation Models

    • Abstract
    • 5.1 Von Thünen and d’Alonso’s monocentric and polycentric models
    • 5.2 Steiner’s model generalizes Weber’s
    • 5.3 Central place models in the making
    • 5.4 Conclusion

    Part 3: Spatial Structures and Territorial Dynamics

    Introduction

    6: Theories Used to Understand Territorial Structures and Dynamics

    • Abstract
    • 6.1 From terrestrial to geographical space
    • 6.2 Some theories drawn from various fields and used to explain simple territorial forms
    • 6.3 From morphology to morphogenesis
    • 6.4 An overview of morphogenetic theories
    • 6.5 Conclusion
    • 6.6 Appendix 5: globalization at the root of a paradox: homogenization and global fracturing

    7: Models of Basic Structures: Points and Fields

    • Abstract
    • 7.1 Modeling the point structures of a geographical space
    • 7.2 Modeling geographical fields
    • 7.3 Conclusion
    • 7.4 Appendix 6: Introduction to the morphometric analysis of the Grenoble Alps

    8: Models of Basic Structures: Networks

    • Abstract
    • 8.1 The two aspects of a network: graphs and matrices
    • 8.2 Modeling the structure of a spatial network
    • 8.3 Qualitative geographical models and graph theory
    • 8.4 Modeling network dynamics
    • 8.5 Conclusion
    • 8.6 Appendix 7: A geometric approach to the network of French metropolises

    9: Geographical Space as a Mixture of Basic Spatial Structures

    • Abstract
    • 9.1 Testing links between two elementary spatial structures
    • 9.2 Modeling complex spatial structures: machine learning and choremes
    • 9.3 Modeling multiscale spatial structures
    • 9.4 Conclusion

    10: Morphogenetic Macro- and Micro-models

    • Abstract
    • 10.1 Time series typical of morphogenetic theories
    • 10.2 Modeling the dynamics of territorial systems: from ODEs to PDEs
    • 10.3 Cellular automata, Brownian motions and multi-agent systems
    • 10.4 Conclusion
    • 10.5 Appendix 8: simulating urban growth along the French Riviera with a cellular automata model

Product details

  • No. of pages: 314
  • Language: English
  • Copyright: © ISTE Press - Elsevier 2017
  • Published: February 1, 2017
  • Imprint: ISTE Press - Elsevier
  • eBook ISBN: 9780081022306
  • Hardcover ISBN: 9781785482250

About the Author

Andre Dauphine

Andre Dauphine is Honorary Dean of the University of Nice Sophia-Antipolis in France, founder member of the Dupont Group and a recognized expert in theoretical and quantitative geography. He is the author of books on the theories of complexity, fractal geography, risks and disasters.

Affiliations and Expertise

Emeritus Professor, University of Nice Sophia-Antipolis, France

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