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HomeDefect and Diffusion ForumDefect and Diffusion Forum Vol. 399Direct and Inverse Problems for a Fourth Order...

Direct and Inverse Problems for a Fourth Order Anomalous Diffusion Model

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Abstract:

The second order equation (also known as Fick’s equation) is derived from a classical well-known theory, but it is not enough to model all applications of interest. Recently, fractional equations and higher order equations began to receive more attention, demanding increased research efforts. They are used to simulate the diffusion process in many important applications in sciences, such as chemistry, heat and mass transfer, biology and ecology. In this work, the sensitivity analysis is performed for a recently developed anomalous diffusion model in order to evaluate the possibility of estimating a set of parameters that are part of the fourth order equation model, including the parameters representing the variation of the fraction of particles that are allowed to diffuse using a sigmoid function. Finally, after the sensitivity analysis the Inverse Problem approach is used to estimate viable parameters that are necessary for simulation in the cases considered. The differential equation was approximated using the Finite Difference Method, and that solution was implemented in the RStudio platform. The Sensitivity Matrix was calculated and the Inverse Problem was solved using the same RStudio platform, and the Simulated Annealing Method.

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Transfer Phenomena in Fluid and Heat Flows XI

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Periodical:

Defect and Diffusion Forum (Volume 399)

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55-64

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https://doi.org/10.4028/www.scientific.net/DDF.399.55

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Online since:

February 2020

Authors:

Jader Lugon Junior*, Luiz Bevilacqua, Antônio José da Silva Neto

Keywords:

Anomalous Diffusion, Bi-Flux Diffusion, Differential Equations, Mean Square Displacement

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© 2020 Trans Tech Publications Ltd. All Rights Reserved

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