Jan Baetens was born in 1984 and is currently living somewhere between two of Belgium’s major cities, Ghent and Antwerp. In July 2007, he graduated with a master’s in bioscience engineering, with an emphasis on soil and water management, from Ghent University. Two months later he started working at the Reseach Unit Knowledge-Based Systems, Department of Applied Mathematics, Biometrics and Process Control at the Bioscience Engineering Faculty of Ghent University, where he teaches first- and second-year students analytical geometry, calculus, and differential equations. He is also doing research in the field of mathematical soil and water research, for which he would like to involve cellular automata.
“Beatus homo qui invenit sapientiam”
Project: Irregular cellular automata for soil-water flow
The main goal of this NKS project is the construction of a model based on cellular automata (CA) describing soil-water flow in the vadose zone that may be used as an alternative for the classical models based on partial differential equations (PDEs), e.g. the Richards equation (Richards, 1931). As such, computational limitations of the traditional models could be avoided (Mendicino et al., 2006). Recent research in hydrology (e.g. Mendicino et al., 2006; Rinaldi et al., 2007; and Parsons & Fonstad, 2007) offered promising results, encouraging further work and making application in other soil-water research domains attractive.
In order to obtain the project’s goal, several steps must be taken and different approaches explored. First, a framework will be set up enabling simulation of CA across two-dimensional irregular grids, which may be constructed through tessellation (Voronoi). Second, the behavior of these irregular-grid CA will be compared to that of the same CA defined over rectangular, hexagonal, and Penrose grids for different classes of rules. Totalistic rules will be used first because these are most easily implemented when working with irregular CA. Third, there will be focus on simple rules leading to soil-water flow patterns that are in agreement with the ones observed in soils. For that purpose a distinction will be made between irregular grids in which every cell can contain water and grids in which a fraction of the cells are regarded as soil particles incapable of being replaced by soil or water. Water flow through soils with different percentages of voids will be investigated.
Besides the points mentioned above, other interesting topics that may be covered if time permits could be the use of three-dimensional grids, other manners of constructing the grid in which water flow is modeled, and verifying the possibility of applying a geostatistical approach to characterize the spatial variability within the patterns created.
Mendicino, G., Senatore, A., Spezzano, G., and Straface, S. “Three-dimensional unsaturated flow modeling using cellular automata.” Water Resources Research 4 (2006).
Parsons, J. A., and Fonstad, M. A. “A cellular automata model of surface water flow.” Hydrological Processes 21 (2007): 2189-2195.
Richards, L. A. “Capillary conduction of liquids through porous mediums.” Physics 1 (1931): 318-333.
Rinaldi, P. R., Dalponte, D. D., Venere, M. J., and Clausse, A. “Cellular automata for simulations of surface flows in large plains.” Simulation Modelling Practice and Theory 15 (2007): 315-327.
Favorite Radius 3/2 Rule
My favorite k=2, r=3/2 cellular automaton is rule number 50679 because it produces several 3D-like structures during its evolution.