"Non UBC"@en .
"DSpace"@en .
"Voller, Vaughan"@en .
"2019-03-15T05:00:58Z"@en .
"2018-06-21T13:31"@en .
"There has been some recent interest in exploring applications of fractal calculus in transport models. One of the\nmotivations for this is that such models are able to generate anomalous transport signals. For example, when\nfractional calculus is employed to define diffusion transport fluxes (heat, mass etc.) the exponent n in the\nspace-time scaling differs from the classical value of n = \u00C3 \u00CB . In this talk we have two objectives. The first\nobjective is to identify physically realizable systems that exhibit anomalous transport behaviors. The second is to\narrive at suitable fractional governing equations that can model these systems. To these ends we will build direct\nsimulations of the infiltration of moisture into a porous media containing a distribution of flow obstacles. When\nthe obstacles form a repeating pattern, this problem can be viewed as a limit case of the classical one-phase Stefan\nmelting problem and the measure of the advance of the infiltration length changes with the square root of time.\nWhen the obstacles are distributed in a fractal pattern, however, the infiltration shows a sub-diffusive behavior,\nwhere the time exponent is less that the square root. Through considering the time scaling of Brownian motion in a\nfractal obstacle filed we are bale to directly associate this sub-diffusive time exponent to the fractal dimension\nof the obstacle filed. This in turn, allows us to develop fractional calculus based governing equations, with a\nclosed particular solution, for moisture infiltration into a fractal obstacle field. The talk will close with\nconsiderations as to how these findings can be associated with more general Stefan problem that incorporated\nfractional calculus treatments."@en .
"https://circle.library.ubc.ca/rest/handle/2429/68747?expand=metadata"@en .
"23.0"@en .
"video/mp4"@en .
""@en .
"Author affiliation: University of Minnesota"@en .
"Banff (Alta.)"@en .
"10.14288/1.0376914"@en .
"eng"@en .
"Unreviewed"@en .
"Vancouver : University of British Columbia Library"@en .
"Banff International Research Station for Mathematical Innovation and Discovery"@en .
"Attribution-NonCommercial-NoDerivatives 4.0 International"@en .
"http://creativecommons.org/licenses/by-nc-nd/4.0/"@en .
"Faculty"@en .
"BIRS Workshop Lecture Videos (Banff, Alta)"@en .
"Mathematics"@en .
"Partial differential equations"@en .
"Numerical analysis"@en .
"Anomalous Infiltration into Heterogeneous Porous Media: Simulations and Fractional Calculus Models"@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/68747"@en .