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

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 simula...

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Bibliographic Details
Published in:TEMA (São Carlos) 2017-08, Vol.18 (2), p.305-315
Main Authors: Pereira, Ana Paula De Paiva, Fernandes, João Paulo, Atman, Allbens Picardi Faria, Acebal, José Luiz
Format: Article
Language:English
Subjects:
COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
MATHEMATICS, APPLIED
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Summary: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 andnormal 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.
ISSN:1677-1966
2179-8451
2179-8451
DOI:10.5540/tema.2017.018.02.0305