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Discrete spatio-temporal modelling paradigms for environmental processes: SWOT analysis, application portfolio and Lyapunovian stability analysis

Jan Baetens (UGent)
(2012)
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(UGent)
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Abstract
The power of mathematics in describing the processes that govern the dynamics of planet Earth has long been acknowledged as simulations that are built upon such mathematical descriptions (i.e. mathematical models) often give rise to results that are highly comparable with the mimicked process. For instance, the propagation of forest fires and tsunami waves can be described mathematically, while also biological processes, such as species competition, can be mimicked by means of a mathematical model. Clearly, a trustworthy description of such processes can only be achieved if their dynamics is tracked through both space and time by means of a spatio-temporal model. Although partial differential equations are dominating the field of mathematical modelling, the awareness of their shortcomings is growing and other modelling paradigms are increasingly explored. In this dissertation, several aspects of spatio-temporal modelling paradigms with a discrete slant are investigated in order to consolidate their use as a full-fledged alternative to the fully continuous differential equations. More precisely, in the first part of this dissertation, the strengths, weaknesses, opportunities and merits of discrete modelling paradigms are reviewed, after which discrete models are developed for mimicking various processes, such as molecular diffusion, disease and forest fire propagation, fish migration, and finally, the gasification of calcium carbonate. In the third and last part of this dissertation, the stability of utter discrete mathematical models, i.e. cellular automata, is investigated.
Keywords
stability, cellular automata, discrete, spatio-temporal, coupled-map lattice, individual-based model, modelling, diffusion, forest fire, epidemics

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Please use this url to cite or link to this publication:

Chicago
Baetens, Jan. 2012. “Discrete Spatio-temporal Modelling Paradigms for Environmental Processes: SWOT Analysis, Application Portfolio and Lyapunovian Stability Analysis”. Ghent, Belgium: Ghent University. Faculty of Bioscience Engineering.
APA
Baetens, Jan. (2012). Discrete spatio-temporal modelling paradigms for environmental processes: SWOT analysis, application portfolio and Lyapunovian stability analysis. Ghent University. Faculty of Bioscience Engineering, Ghent, Belgium.
Vancouver
1.
Baetens J. Discrete spatio-temporal modelling paradigms for environmental processes: SWOT analysis, application portfolio and Lyapunovian stability analysis. [Ghent, Belgium]: Ghent University. Faculty of Bioscience Engineering; 2012.
MLA
Baetens, Jan. “Discrete Spatio-temporal Modelling Paradigms for Environmental Processes: SWOT Analysis, Application Portfolio and Lyapunovian Stability Analysis.” 2012 : n. pag. Print.
@phdthesis{2077731,
  abstract     = {The power of mathematics in describing the processes that govern the dynamics of planet Earth has long been acknowledged as simulations that are built upon such mathematical descriptions (i.e. mathematical models) often give rise to results that are highly comparable with the mimicked process. For instance, the propagation of forest fires and tsunami waves can be described mathematically, while also biological processes, such as species competition, can be mimicked by means of a mathematical model. Clearly, a trustworthy description of such processes can only be achieved if their dynamics is tracked through both space and time by means of a spatio-temporal model. Although partial differential equations are dominating the field of mathematical modelling, the awareness of their shortcomings is growing and other modelling paradigms are increasingly explored. In this dissertation, several aspects of spatio-temporal modelling paradigms with a discrete slant are investigated in order to consolidate their use as a full-fledged alternative to the fully continuous differential equations. More precisely, in the first part of this dissertation, the strengths, weaknesses, opportunities and merits of discrete modelling paradigms are reviewed, after which discrete models are developed for mimicking various processes, such as molecular diffusion, disease and forest fire propagation, fish migration, and finally, the gasification of calcium carbonate. In the third and last part of this dissertation, the stability of utter discrete mathematical models, i.e. cellular automata, is investigated.},
  author       = {Baetens, Jan},
  isbn         = {9789059895102},
  keyword      = {stability,cellular automata,discrete,spatio-temporal,coupled-map lattice,individual-based model,modelling,diffusion,forest fire,epidemics},
  language     = {eng},
  pages        = {XL, 397},
  publisher    = {Ghent University. Faculty of Bioscience Engineering},
  school       = {Ghent University},
  title        = {Discrete spatio-temporal modelling paradigms for environmental processes: SWOT analysis, application portfolio and Lyapunovian stability analysis},
  year         = {2012},
}