Transition of dynamic phase in evolutive systems: large deviations, diffusion and location

Abstract

The project seeks to unify potentially convergent lines of research in a common program that has as axis the study of large deviations in evolutive processes. We will study deterministic and stochastic automatons in metastable regime, Schroedinger equations under the influence of random or quasiperiodic fields, random walks in random environments, and behavior of attractors in dynamic systems. The focus will be to unify the problems under the single point of view of the large deviations with a view to achieving a qualitative leap in the understanding of this phenomenology. The results will be important for clarifying the behavior of these systems from the mathematical point of view, and could have applications in thermodynamics, ecology, fluid-dynamics and electrical engineering. Implementation of the plan includes: a) intense exchange with institutions within Brazil and abroad. We intend to receive visits from 12 researchers each year from top universities in Brazil, Italy, France, Holland, etc. Simultaneously 10 researchers each year will visit centers abroad for periods of between 30 and 90 days (each Brazilian researcher will average a trip every two years); b) the staging of two national workshops at the end of the first and the third year of the project, with the aim of disseminating and homogenizing the results obtained; c) the staging of two international conferences, which will take place at the end of the second and fourth year of the project. The objective is to situate the results obtained in the ambit of international research; d) installation of computer equipment. The objective is to provide the group with a computing infrastructure of medium size appropriate for the implementation of simulations of the systems being studied. The proposed network of work stations will also serve for work on the edition of articles and connection with the international Bitnet network. (AU)