Vitor Martins de Oliveira

Vitor Martins de Oliveira
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Vitor verified their affiliation via an institutional email.
Verified
Vitor verified their affiliation via an institutional email.
  • PhD
  • PostDoc at University of São Paulo

About

17
Publications
2,305
Reads
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78
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. I am now a postdoc working with tide models in celestial mechanics.
Current institution
University of São Paulo
Current position
  • PostDoc
Additional affiliations
March 2022 - present
University of São Paulo
Position
  • PostDoc Position
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
January 2016 - May 2016
Federal University of ABC
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
Federal University of ABC
Field of study
  • Mathematics
September 2012 - July 2013
University of Twente
Field of study
  • Advanced Techonology

Publications

Publications (17)
Article
The tidal evolution of a deformable body may lead to a state where its rotational and orbital motion are in resonance. In this work, we numerically investigate and visually illustrate some dynamical properties of the dissipative spin–orbit problem, namely, the co-existence of multiple periodic and quasi-periodic attractors, and the complexity of th...
Preprint
Full-text available
The renewed global interest in lunar exploration requires new orbital strategies to ensure flight safety which can benefit extended lunar missions and service a plethora of planned instruments in the lunar orbit and surface. We investigate here the equivalent fuel consumption cost to transfer from (to) a given orbit and enter (leave) at any point o...
Article
Full-text available
We present the open-source software RheoVolution , a computational implementation of the tidal theory based on the Association Principle, which provides a direct link from the adopted rheological model to the body’s deformation matrix in the time domain, thus facilitating the use of more complex rheological models. The code introduced here simulate...
Article
Full-text available
Maneuvering a spacecraft in the cislunar space is a complex problem, since it is highly perturbed by the gravitational influence of both the Earth and the Moon, and possibly also the Sun. Trajectories minimizing the needed fuel are generally preferred in order to decrease the mass of the payload. A classical method to constrain maneuvers is mathema...
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...
Preprint
Full-text available
In this work, we numerically investigate and visually illustrate the dynamical properties of the dissipative spin-orbit problem such as the co-existence of multiple periodic and quasi-periodic attractors, and the complexity of the corresponding basins of attraction. Our model is composed by a triaxial satellite (planet) orbiting a planet (star) in...
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...
Preprint
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
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...

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