Memory effects and characterization in stochastic processes

• Grant number: 17/01176-6
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
• Duration: April 10, 2017 - April 09, 2018
• Field of knowledge: Physical Sciences and Mathematics - Physics - Condensed Matter Physics
• Principal Investigator: Marco Antonio Alves da Silva
• Grantee: Marco Antonio Alves da Silva
• Visiting researcher: Jose Carlos Cressoni
• Visiting researcher institution: Universidade Federal de Alagoas (UFAL). Instituto de Química e Biotecnologia (IQB). Centro de Ciências Exatas e Naturais (CCEN), Brazil
• Host Institution: Faculdade de Ciências Farmacêuticas de Ribeirão Preto (FCFRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil

Abstract

The main purpose of this project is the study of anomalous diffusion in complex non-Markoviandiscrete-time Random Walk systems with strong long range time-memory correlations. Specifically,we focus on systems with full memory and systems with memory damage, the latter being those in which the recent memory has been erased. The question of mapping non-Markovian processes in Markovian processes is discussed. A relation between log-periodic corrections to scaling and anomalous diffusion is analysed through the introduction of pauses in the RW, both in 1D and 2D. Lévy processes are also taken into account by searching for a connection among suitably chosen time-discrete RW memory patterns and Lévy originated processes. The scaling behavior of the Self Avoiding Walk is also addressed using a recently developed method of analysis for studying universality, criticality and conformational properties of systems, with possible applications to polymers, biopolymers and magnetic systems. (AU)

Scientific publications

(5)

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

DA SILVA, M. A. A.; ROCHA, E. C.; CRESSONI, J. C.; DA SILVA, L. R.; VISWANATHAN, G. M.. Non-Levy stable random walk propagators for a non-Markovian walk with both superdiffusive and subdiffusive regimes. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 538, p. 5-pg., 2020-01-15. (16/03918-7, 17/01176-6)

CRESSONI, J. C.; VISWANATHAN, G. M.; DA SILVA, M. A. A.. Log-periodicity in piecewise ballistic superdiffusion: Exact results. Physical Review E, v. 98, n. 5, NOV 1 2018. (16/03918-7, 17/01176-6)

CRESSONI, J. C.; VISWANATHAN, G. M.; DA SILVA, M. A. A.. Log-periodicity in piecewise ballistic superdiffusion: Exact results. PHYSICAL REVIEW E, v. 98, n. 5, p. 7-pg., 2018-11-01. (16/03918-7, 17/01176-6)

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)