Analytical and computational modelling of diffusive systems

• Grant number: 11/13685-6
• Support type: Research Grants - Visiting Researcher Grant - Brazil
• Duration: September 01, 2011 - August 31, 2012
• Field of knowledge: Physical Sciences and Mathematics - Physics - Condensed Matter Physics
• Principal researcher: Marco Antonio Alves da Silva
• Grantee: Marco Antonio Alves da Silva
• Visiting researcher: Jose Carlos Cressoni
• Visiting researcher institution: Universidade Federal de Santa Maria (UFSM). Centro de Ciências Naturais e Exatas (CCNE), Brazil
• Home Institution: Faculdade de Ciências Farmacêuticas de Ribeirão Preto (FCFRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil

Abstract

In this work we are interested in the mathematical and computational modelling of non Markovian diffusion systems in connection to the already approved fapesp project numbered 2011/06757-0, initiated in july 2011. I have had a collaboration with Prof. J.C. Cressoni in this area (and others) for several years and we are confident in the viability of these studies. The fapesp funding for a year is crucial for the conclusion of these activities, for ensure the continuity of the research, without interruptions, during the time proposed.We are particularly interested in the problem of amnestically induced persistence, caused by damage to the memory of the non-Markovian random walker (PRL 98 070603 2007, PRE 81 011125 2010). More specifically we seek to:1) study the effect of different patterns of memory and extra dimensions in the model;2) determine the stochastic function of the Fokker-Planck equation (FP) (Eur. Phys. J. B (2009) DOI: 10.1140/epjb/e2009-00361-6) andobtain the FP equation for the non-persistent model (i.e., with recent memory);3) include new ingredients to the model to allow for the appearance of logperiodicities outside the origin, possibly leading to a model for the predictions of catastrophes (this is a daring and difficult task, however with an extraordinary impact);4) investigate other possible extensions of this research searching for applications in the real world, like Alzheimer disease (according toPRL 98 - op. cit.) and economic bubble (this is a long-term activity, and will be discussed and possibly initiated, at least).As a visiting researcher, Prof. J.C. Cressoni will participate on the group discussions, with direct impact, for example on the supervision of our (post)graduate students. For example, Prof. J.C. Cressoni already participate on the discussions in an ongoing project in FCFRP-USP involving diffusion (growth) in in-vitro growing processes, carried out by an MSc student with a Capes scholarship, under my supervision (these phenomena are physically analogous to prionic clustering that we studied in 2003 (M.A.A. da Silva e J.C. Cressoni et al, PRL 90 198101 2003). (AU)

Scientific publications

(12)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

DINIZ, R. M. B.; CRESSONI, J. C.; DA SILVA, M. A. A.; MARIZ, A. M.; DE ARAUJO, J. M.. Narrow log-periodic modulations in non-Markovian random walks. Physical Review E, v. 96, n. 6, DEC 26 2017. (11/06757-0, 17/01176-6, 11/13685-6)

MOURA, THIAGO R. S.; VISWANATHAN, G. M.; DA SILVA, M. A. A.; CRESSONI, J. C.; DA SILVA, L. R.. Transient superdiffusion in random walks with a q-exponentially decaying memory profile. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 453, p. 259-263, JUL 1 2016. (11/06757-0, 11/13685-6)

DA SILVA, M. A. A.; VISWANATHAN, G. M.; CRESSONI, J. C.. A two-dimensional non-Markovian random walk leading to anomalous diffusion. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 421, p. 522-532, MAR 1 2015. (11/06757-0, 11/13685-6)

CRESSONI, J. C.; VISWANATHAN, G. M.; FERREIRA, A. S.; DA SILVA, M. A. A.. Alzheimer random walk model: Two previously overlooked diffusion regimes. Physical Review E, v. 86, n. 4, 1, OCT 2 2012. (11/06757-0, 11/13685-6)

DA SILVA, M. A. A.; CRESSONI, J. C.; SCHUETZ, GUNTER M.; VISWANATHAN, G. M.; TRIMPER, STEFFEN. Non-Gaussian propagator for elephant random walks. Physical Review E, v. 88, n. 2, AUG 9 2013. (11/21089-4, 11/06757-0, 11/13685-6)

ALVES, G. A.; DE ARAUJO, J. M.; CRESSONI, J. C.; DA SILVA, L. R.; DA SILVA, M. A. A.; VISWANATHAN, G. M.. Superdiffusion driven by exponentially decaying memory. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, APR 2014. (11/06757-0, 11/13685-6)

DE LACERDA, K. J. C. C.; CRESSONI, J. C.; VISWANATHAN, G. M.; DA SILVA, M. A. A.. Log-periodicity can appear in a non-Markovian random walk even if there is perfect memory of its history. EPL, v. 130, n. 2, APR 2020. (11/06757-0, 11/13685-6)

CRESSONI, J. C.; VISWANATHAN, G. M.; DA SILVA, M. A. A.. Exact solution of an anisotropic 2D random walk model with strong memory correlations. Journal of Physics A-Mathematical and Theoretical, v. 46, n. 50, DEC 20 2013. (11/06757-0, 11/13685-6)

BORGES, G. M.; FERREIRA, A. S.; DA SILVA, M. A. A.; CRESSONI, J. C.; VISWANATHAN, G. M.; MARIZ, A. M.. Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile. European Physical Journal B, v. 85, n. 9, SEP 2012. (11/06757-0, 11/13685-6)

CRESSONI, J. C.; DA SILVA, L. R.; VISWANATHAN, G. M.; DA SILVA, M. A. A.. Robustness of the non-Markovian Alzheimer walk under stochastic perturbation. EPL, v. 100, n. 6, DEC 2012. (11/06757-0, 11/13685-6)

CRESSONI, J. C.; VISWANATHAN, G. M.; FERREIRA, A. S.; DA SILVA, M. A. A.. Weakly anomalous diffusion with non-Gaussian propagators. Physical Review E, v. 86, n. 2, 1, AUG 27 2012. (11/06757-0, 11/13685-6)

DA SILVA, M. A. A.; VISWANATHAN, G. M.; CRESSONI, J. C.. Ultraslow diffusion in an exactly solvable non-Markovian random walk. Physical Review E, v. 89, n. 5, MAY 8 2014. (11/06757-0, 11/13685-6)