Scaling laws associated to a symmetry-break in the energy distribution in a set of dynamical systems: application to discrete mappings

• Grant number: 14/27260-5
• Support Opportunities: Scholarships in Brazil - Master
• Start date: June 01, 2015
• End date: August 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Edson Denis Leonel
• Grantee: Matheus Palmero Silva
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil
• Associated scholarship(s): 16/15713-0 - Scaling laws associated with a symmetry-break in the probability distribution function in a set of dynamical systems, BE.EP.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 energy diffusion (Fermi acceleration). Our main goal is to describe the behavior of the probability energy density for a set of particles moving in a chaotic way. The break of symmetry in the probability energy density leads to an additional scaling, up to now, described only phenomenologically. The first observation in a area preserving mapping was in Physical Review Letters 93, 014101 (2004), authored by Edson D. Leonel, Peter V. E. McClintock and Jafferson K. L. Silva. The generalization to time dependent billiard is immediate and is in the scope of the present project. (AU)

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)

LIVORATI, ANDRE L. P.; PALMERO, MATHEUS S.; DIAZ-, I, GABRIEL; DETTMANN, CARL P.; CALDAS, IBERE L.; LEONEL, EDSON D.. Investigation of stickiness influence in the anomalous transport and diffusion for a non-dissipative Fermi-Ulam model. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 55, p. 225-236, FEB 2017. (14/25316-3, 12/23688-5, 15/26699-6, 14/27260-5)

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)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

SILVA, Matheus Palmero. Leis de escala associadas à quebra de simetria da distribuição de energia em um conjunto de sistemas dinâmicos: aplicações em mapeamentos discretos. 2017. Master's Dissertation - Universidade Estadual Paulista (Unesp). Instituto de Geociências e Ciências Exatas. Rio Claro Rio Claro.