Simulation and Calibration Between Parameters of Continuous Time Random Walks and Subdifusive Model

Ana Paula de Paiva Pereira, João Paulo Fernandes, Allbens Picardi Faria Atman, José Luiz Acebal

Abstract


We address the problem of subdiusion or normal diusion to perform a calibration between the parameters used in simulation and the parameters of a subdifusive model. The theoretical model is written as a generalized diusion equation with fractional derivatives in time. The data is generated by simulations consisting of continuous-time random walks with controlled mean waiting time and jump length variance to provide a full range of cases between subdiusion and
normal diusion. From the simulations, we compare the accuracy of two methods to obtain the diusion constant, the order of fractional derivatives: the analysis of the dispersion of the variance in time and the optimization tting of theoretical model solutions to histogram of positions. We highlight the connection between the parameters of the simulations the parameters of the theoretical models.


Keywords


Anomalous diffusion; fractional diffusion equation; calibration

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DOI: http://dx.doi.org/10.5540/tema.2017.018.02.0305

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TEMA - Trends in Applied and Computational Mathematics

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