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Tangent Method and Some Dynamical Properties of an Oval-Like Billiard

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da Costa, Diogo Ricardo ; Hansen, Matheus ; Silva, Mario Roberto ; Leonel, Edson D.
Total Authors: 4
Document type: Journal article
Source: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS; v. 32, n. 04, p. 15-pg., 2022-03-30.

In this paper, we consider the evolution of an ensemble of noninteracting classical particles confined in a closed region. Each one of these particles experiences several elastic collisions with a rigid-smooth oval-like boundary. As known in the literature, numerical simulations for this kind of system demand too much time, mostly because of the time spent in solving transcendental equations. To deal with that, we highlight an alternative approach to speed up the search of solutions for the transcendental equations via the tangent method, which has proved to be a faster way to solve this problem when compared with other methods, like the bisection one. The methods applied here are generic and can be used or adapted for other billiard boundaries. (AU)

FAPESP's process: 19/14038-6 - Investigation of dynamical properties in nonlinear systems
Grantee:Edson Denis Leonel
Support Opportunities: Regular Research Grants
FAPESP's process: 20/02415-7 - StatGraph 2.0 and Massive Open Online Course (MOOC)
Grantee:Diogo Ricardo da Costa
Support Opportunities: Scholarships in Brazil - Post-Doctoral
FAPESP's process: 19/09150-1 - Effect of time delay and plasticity in neuronal synchronization
Grantee:Matheus Hansen Francisco
Support Opportunities: Scholarships in Brazil - Post-Doctoral