Diffusive processes: random walkers with memory

• Grant number: 11/06757-0
• Support Opportunities: Regular Research Grants
• Start date: July 01, 2011
• End date: September 30, 2013
• Field of knowledge: Physical Sciences and Mathematics - Physics
• Principal Investigator: Marco Antonio Alves da Silva
• Grantee: Marco Antonio Alves da Silva
• Host Institution: Faculdade de Ciências Farmacêuticas de Ribeirão Preto (FCFRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil

Abstract

This project aims to develop models of random walkers on the lattice. Characteristic quantities are obtained, such as the diffusion coefficient, the first and second moment of the distributions. Another important point is to construct phase diagrams in the generalization of related models and their application to real systems such as economic phenomena and Alzheimer's disease. (AU)

Scientific publications

(20)

(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)

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)

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)

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, 11/13685-6, 17/01176-6)

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)

GRANZOTTI, C. R. F.; RIBEIRO, F. L.; MARTINEZ, A. S.; DA SILVA, M. A. A.. Persistence length convergence and universality for the self-avoiding random walk. Journal of Physics A-Mathematical and Theoretical, v. 52, n. 7, FEB 15 2019. (16/03918-7, 12/03823-5, 11/06757-0)

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, 11/13685-6, 11/06757-0)

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)

DE LACERDA, K. J. C. C.; DA SILVA, L. R.; VISWANATHAN, G. M.; CRESSONI, J. C.; DA SILVA, M. A. A.. A random walk model with a mixed memory profile: Exponential and rectangular profile. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 597, p. 6-pg., 2022-04-08. (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)

GRANZOTTI, C. R. F.; MARTINEZ, A. S.; DA SILVA, M. A. A.. Scaling analysis of random walks with persistence lengths: Application to self-avoiding walks. PHYSICAL REVIEW E, v. 93, n. 5, p. 6-pg., 2016-05-09. (11/06757-0, 12/03823-5)

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)

GRANZOTTI, C. R. F.; MARTINEZ, A. S.; DA SILVA, M. A. A.. Scaling analysis of random walks with persistence lengths: Application to self-avoiding walks. Physical Review E, v. 93, n. 5, MAY 9 2016. (11/06757-0, 12/03823-5)

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)

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)

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.; 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)

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, p. 7-pg., 2017-12-26. (11/06757-0, 11/13685-6, 17/01176-6)

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, p. 5-pg., 2012-08-27. (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, p. 5-pg., 2012-10-02. (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, v. N/A, p. 10-pg., 2014-04-01. (11/06757-0, 11/13685-6)