Modelling drop impact and Hamiltonian dynamics in Faraday-drop Theories

• Grant number: 17/50295-8
• Support Opportunities: Regular Research Grants
• Start date: February 01, 2018
• End date: January 31, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Agreement: University of Bath
• Mobility Program: SPRINT - Projetos de pesquisa - Mobilidade
• Principal Investigator: Clodoaldo Grotta Ragazzo
• Grantee: Clodoaldo Grotta Ragazzo
• Principal researcher abroad: Paul Antoine Milewski
• Institution abroad: University of Bath, England
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The dynamics of fluid droplets can be extremely complex. In particular, in a set of experiments it was found that droplets may bounce on a vibrating fluid bath of the same fluid and under some circumstances become mobile, driven by their own wave-field. In this case, the droplet and its "pilot wave" form a single object close to what de Broglie envisioned as a model for particle-wave duality in quantum mechanics. We shall study two aspects of this system: (1) the dynamics of the droplets both in free space and when they "collide" with the fluid bath and generate waves, and (2) the effective Hamiltonian dynamics of a discrete version of the dynamics that can be derived from first principles. (AU)