| 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 |
| Principal Investigator: | 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)