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

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

ABSTRACT We address the problem of subdiffusion or normal diffusion to perform a calibration between simulations parameters and those from a subdiffusive model. The theoretical model consists to a generalized diffusion equation with fractional derivatives in time. The data generated by simulations represents continuous-time random walks with controlled mean waiting time and jump length variance to provide a full range of cases between subdiffusion and normal diffusion. From simulations, we compare the accuracy of two methods to obtain the diffusion constant and the order of fractional derivatives: the analysis of the dispersion of the variance in time and an optimized fitting of the histograms of positions with theoretical model solutions. We highlight the connection between the parameters of the simulations those of theoretical models.

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Main Authors: PEREIRA,A.P.P., FERNANDES,J.P., ATMAN,A.P.F., ACEBAL,J.L.
Format: Digital revista
Language:English
Published: Sociedade Brasileira de Matemática Aplicada e Computacional 2017
Online Access:http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512017000200305
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spelling oai:scielo:S2179-845120170002003052017-09-14Simulation and Calibration Between Parameters of Continuous Time Random Walks and Subdifusive ModelPEREIRA,A.P.P.FERNANDES,J.P.ATMAN,A.P.F.ACEBAL,J.L. anomalous diffusion fractional diffusion equation calibration ABSTRACT We address the problem of subdiffusion or normal diffusion to perform a calibration between simulations parameters and those from a subdiffusive model. The theoretical model consists to a generalized diffusion equation with fractional derivatives in time. The data generated by simulations represents continuous-time random walks with controlled mean waiting time and jump length variance to provide a full range of cases between subdiffusion and normal diffusion. From simulations, we compare the accuracy of two methods to obtain the diffusion constant and the order of fractional derivatives: the analysis of the dispersion of the variance in time and an optimized fitting of the histograms of positions with theoretical model solutions. We highlight the connection between the parameters of the simulations those of theoretical models.info:eu-repo/semantics/openAccessSociedade Brasileira de Matemática Aplicada e ComputacionalTEMA (São Carlos) v.18 n.2 20172017-08-01info:eu-repo/semantics/articletext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512017000200305en10.5540/tema.2017.018.02.0305
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country Brasil
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libraryname SciELO
language English
format Digital
author PEREIRA,A.P.P.
FERNANDES,J.P.
ATMAN,A.P.F.
ACEBAL,J.L.
spellingShingle PEREIRA,A.P.P.
FERNANDES,J.P.
ATMAN,A.P.F.
ACEBAL,J.L.
Simulation and Calibration Between Parameters of Continuous Time Random Walks and Subdifusive Model
author_facet PEREIRA,A.P.P.
FERNANDES,J.P.
ATMAN,A.P.F.
ACEBAL,J.L.
author_sort PEREIRA,A.P.P.
title Simulation and Calibration Between Parameters of Continuous Time Random Walks and Subdifusive Model
title_short Simulation and Calibration Between Parameters of Continuous Time Random Walks and Subdifusive Model
title_full Simulation and Calibration Between Parameters of Continuous Time Random Walks and Subdifusive Model
title_fullStr Simulation and Calibration Between Parameters of Continuous Time Random Walks and Subdifusive Model
title_full_unstemmed Simulation and Calibration Between Parameters of Continuous Time Random Walks and Subdifusive Model
title_sort simulation and calibration between parameters of continuous time random walks and subdifusive model
description ABSTRACT We address the problem of subdiffusion or normal diffusion to perform a calibration between simulations parameters and those from a subdiffusive model. The theoretical model consists to a generalized diffusion equation with fractional derivatives in time. The data generated by simulations represents continuous-time random walks with controlled mean waiting time and jump length variance to provide a full range of cases between subdiffusion and normal diffusion. From simulations, we compare the accuracy of two methods to obtain the diffusion constant and the order of fractional derivatives: the analysis of the dispersion of the variance in time and an optimized fitting of the histograms of positions with theoretical model solutions. We highlight the connection between the parameters of the simulations those of theoretical models.
publisher Sociedade Brasileira de Matemática Aplicada e Computacional
publishDate 2017
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512017000200305
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AT atmanapf simulationandcalibrationbetweenparametersofcontinuoustimerandomwalksandsubdifusivemodel
AT acebaljl simulationandcalibrationbetweenparametersofcontinuoustimerandomwalksandsubdifusivemodel
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