Vitor Martins de Oliveira

Vitor Martins de Oliveira
University of São Paulo | USP · Institute of Mathematics and Statistics (IME) (São Paulo)

PhD

About

11
Publications
1,199
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
53
Citations
Introduction
I have a broad interest in nonlinear dynamics and chaos. During my PhD, I did research on stable/unstable manifolds in Hamiltonian systems, specifically in the planar circular restricted three-body problem. During my masters, I worked with numerical calculation of fractal dimensions in dissipative systems. And as an undergraduate, I studied chaotic advection of aerosols and electrowetting in microfluidics.
Additional affiliations
July 2018 - December 2018
University of São Paulo
Position
  • Teaching intern
Description
  • Course: Mechanics for B.A. in Mathematics Activities: - prepare special exercises for class - teach classes focused on exercise solving - organize meetings to elucidate student questions Financial aid: University of São Paulo
February 2017 - April 2021
University of São Paulo
Position
  • PhD Student
Description
  • PhD project entitled "Transport in hamiltonian systems with application to the three-body problem in celestial mechanics" under the supervision of Prof. Dr. Iberê L Caldas
January 2016 - May 2016
Universidade Federal do ABC (UFABC)
Position
  • Teaching intern
Description
  • Course: Multivariable functions Activities: - plan lessons and teach the first part of the course (from parametric equations and polar coordinates to partial differential equations)
Education
February 2017 - April 2021
University of São Paulo
Field of study
  • Physics
September 2014 - August 2016
Universidade Federal do ABC (UFABC)
Field of study
  • Mathematics
September 2012 - July 2013
University of Twente
Field of study
  • Advanced Techonology

Publications

Publications (11)
Article
Hamiltonian systems that are either open, leaking, or contain holes in the phase space possess solutions that eventually escape the system’s domain. The motion described by such escape orbits before crossing the escape threshold can be understood as a transient behavior. In this work, we introduce a numerical method to visually illustrate and quant...
Code
This software was developed to numerically investigate the dynamical and geometrical aspects of the planar circular restricted three-body problem. It is entirely written in c and most of the functions use the Gnu Scientific Library. In order to use it, open the main.c file and uncomment the function you want. You might have to input some values suc...
Preprint
Full-text available
Invariant manifolds are the skeleton of the chaotic dynamics in Hamiltonian systems. In Celestial Mechanics, for instance, these geometrical structures are applied to a multitude of physical and practical problems, such as to the description of the natural transport of asteroids and to the construction of trajectories for artificial satellites. In...
Thesis
Full-text available
Invariant manifolds are the skeleton of the chaotic dynamics in Hamiltonian systems. In Celestial Mechanics, for instance, these geometrical structures are applied to a multitude of physical and practical problems, such as to the description of the natural transport of asteroids and to the construction of trajectories for artificial satellites. In...
Article
Full-text available
In this work, we investigate the Earth-Moon system, as modeled by the planar circular restricted three-body problem, and relate its dynamical properties to the underlying structure associated with specific invariant manifolds. We consider a range of Jacobi constant values for which the neck around the Lagrangian point L1 is always open, but the orb...
Preprint
Full-text available
In this work, we introduce the escape measure, a finite-time version of the natural measure, to investigate the transient dynamics of escape orbits in open Hamiltonian systems. In order to numerically calculate the escape measure, we cover a region of interest of the phase space with a grid and we compute the visitation frequency of a given orbit o...
Preprint
Full-text available
In this work, we investigate the Earth-Moon system, as modeled by the planar circular restricted three-body problem, and relate its dynamical properties to the underlying structure associated to specific invariant manifolds. We consider a range of Jacobi constant values for which the neck around the Lagrangian point $L_1$ is always open but the orb...
Article
Stickiness is a well known phenomenon in which chaotic orbits expend an expressive amount of time in specific regions of the chaotic sea. This phenomenon becomes important when dealing with area-preserving open systems because, in this case, it leads to a temporary trapping of orbits in certain regions of phase space. In this work, we propose that...
Preprint
Full-text available
Stickiness is a well known phenomenon in which chaotic orbits expend an expressive amount of time in specific regions of the chaotic sea. This phenomenon becomes important when dealing with area-preserving open systems because, in this case, it leads to a temporary trapping of orbits in certain regions of phase space. In this work, we propose that...
Article
We introduce a map which reproduces qualitatively many fundamental properties of the dynamics of heavy particles in fluid flows. These include a uniform rate of decrease of volume in phase space, a slow-manifold effective dynamics when the single parameter s (analogous of the Stokes number) approaches zero, the possibility of fold caustics in the “...
Article
Full-text available
Precise control and manipulation of individual drops are crucial in many lab-on-a-chip applications. We present a novel hybrid concept for channel-based discrete microfluidics with integrated electrowetting functionality by incorporating co-planar electrodes (separated by a narrow gap) in one of the microchannel walls. By combining the high through...

Network

Cited By