Scaling laws associated with a symmetry-break in the probability distribution function in a set of dynamical systems

• Grant number: 16/15713-0
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• Start date: October 01, 2016
• End date: March 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Edson Denis Leonel
• Grantee: Matheus Palmero Silva
• Supervisor: Peter Vaughan Elsmere Mcclintock
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil
• Institution abroad: Lancaster University, England
• Associated to the scholarship: 14/27260-5 - Scaling laws associated to a symmetry-break in the energy distribution in a set of dynamical systems: application to discrete mappings, BP.MS

Abstract

In this project we investigate the dynamics of some systems described by mappings near two types of phase transition: (i) integrability to non-integrability; (ii) limited to unlimited diffusion in energy (Fermi acceleration). Our main goal is to describe the behaviour of the probability density of the energy for a set of particles moving in a chaotic way. The break of symmetry in the probability distribution leads to an additional scaling. So far we can say, it has been only described phenomenologically. The first observation in an area preserving mapping was in a paper published in Physical Review Letters {\bf 93}, 014101 (2004), authored by Edson D. Leonel, Peter V. E. McClintock and Jafferson K. L. Silva. Considering the solution of the Diffusion Equation at the chaotic sea of the phase space, we may describe this behaviour, caused by a symmetry-break, in an analytical way hence leading to scaling laws associated to the dynamics. This is a new approach for this kind of phenomenon in a set of dynamical systems described by discrete mappings. Furthermore, the generalization to time dependent billiard is immediate and is in the scope of this present project too. Finally, we would like to extend and apply this theory to some simple living systems, also described by stochastic nonlinear dynamics, which is the main research topic of Professor's McClintock group on Lancaster University.

Scientific publications

(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)

PALMERO, MATHEUS S.; DIAZ, GABRIEL I.; MCCLINTOCK, PETER V. E.; LEONEL, EDSON D.. Diffusion phenomena in a mixed phase space. Chaos, v. 30, n. 1, JAN 2020. (16/15713-0, 14/27260-5, 17/14414-2)