A Fractal Interaction Model for Winding Paths through Complex Distributions: Application to Soil Drainage Networks |
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| Authors: | Miguel Ángel Martín Miguel Reyes |
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| Institution: | (1) Departamento de Matemática Aplicada, Escuela Técnica Superior de Ingenieros Agrónomos, Universidad Politécnica de Madrid, 28040 Madrid, Spain;(2) Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica de Madrid, Campus de Montegancedo, 28660 Boadilla del Monte, Madrid, Spain |
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| Abstract: | Water interacts with soil through pore channels putting mineral constituents and pollutants into solution. The irregularity of pore boundaries and the heterogeneity of distribution of soil minerals and contaminants are, among others, two factors influencing that interaction and, consequently, the leaching of chemicals and the dispersion of solute throughout the soil. This paper deals with the interaction of irregular winding dragging paths through soil complex distributions. A mathematical modelling of the interplay between multifractal distributions of mineral/pollutants in soil and fractal pore networks is presented. A Hölder path is used as a model of soil pore network and a multifractal measure as a model of soil complex distribution, obtaining a mathematical result which shows that the Hölder exponent of the path and the entropy dimension of the distribution may be used to quantify such interplay. Practical interpretation and potential applications of the above result in the context of soil are discussed. Since estimates of the value of both parameters can be obtained from field and laboratory data, hopefully this mathematical modelling might prove useful in the study of solute dispersion processes in soil. |
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| Keywords: | H?lder curves multifractal distributions soil drainage networks |
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