03/12/2020

Between writing and engineering, Hugo chose mathematics.

At the beginning of his doctoral studies at IMPA, Hugo Saraiva was focused on bifurcation theory in differential equations and confident that he would follow that academic path. But a trip by his advisor, Alexei Mailybaev, to Rome changed the direction of his research to the field of Rayleigh-Taylor turbulence for immiscible fluid mixtures. The fruitful work gave rise to the doctoral thesis " Modeling immiscible Rayleigh-Taylor turbulence using the Lattice-Boltzmann method," which will be defended on December 8th at 10:00 AM, with live streaming on IMPA's YouTube channel .

"In a superficial way, fluid dynamics is an area dedicated to the study of the equations of motion of substances, such as water, oil, and gases. The so-called Rayleigh-Taylor instability occurs when a denser fluid is accelerated towards a less dense fluid, originating a mixing layer that becomes turbulent over long periods of time ." The doctoral candidate highlights that it is possible to find examples of Rayleigh-Taylor instability on very large scales, such as the movement of masses in a nebula, and on very small scales, such as in microfluids.

In Hugo's research, specifically, he addresses this type of instability in mixtures of immiscible fluids, such as water and oil, and compares it with statistics for mixtures of miscible fluids, such as water and glycerin. The main objective was to study these types of mixtures over long periods, when the flow becomes turbulent.

“At first, I found the topic a bit strange, but I became familiar with it. The interdisciplinarity involved in the subject motivated me a lot. Our research involved intersections between fluid dynamics, analysis, parallel computing, statistical mechanics, and differential geometry,” points out the doctoral student.

The blending of disciplines has been a part of Hugo's life since childhood, in the city of Cajazeiras, in the interior of Paraíba. “I thought about pursuing many different professions: writer, doctor, police officer, athlete, architect, scientist… My interest in mathematics came much later.” More specifically, in his third year of high school, when he had his first experience as a teaching assistant in the subject at the Cajazeiras Technical School of Health (ETSC), alongside Professor Raimundo Gonçalo Cariri. “The experience with mathematics led me to choose civil engineering for the university entrance exam.”

University life took shape at the Federal University of Campina Grande (UFCG), also in Paraíba. “The initial goal was 'just' to finish the course and go work as an engineer. But I developed an interest in mathematics. For three and a half years, I was a research scholarship recipient at the National Institute of Science and Technology of Mathematics (INCTMat), under the guidance of Professor Henrique Fernandes de Lima.” This mathematical enthusiasm fueled his master's degree, also at UFCG.

The experience, described as "memorable," gave Hugo the opportunity to work with differential equations in Banach spaces, alongside Professor Severino Horácio. Horácio was a key figure in encouraging the doctoral student to join IMPA, along with the events of the National Symposium/Scientific Initiation Conference held by the institute. "The doctorate was an intense and enriching period; I didn't imagine I would learn so much. Not to mention the international experiences," he says.

In addition to the thesis that will be defended soon, the partnership with Alexei throughout the doctoral program has resulted in publications that Hugo highlights, carried out together with researchers from the University of Rome Tor Vergata, Luca Biferale and Mauro Sbragaglia. Among them, the article “Validation and application of the lattice Boltzmann algorithm for a turbulent immiscible Rayleigh-Taylor system”, developed from results presented at the 29th International Conference on Discrete Fluid Dynamics Simulation (DSFD 2020) and invited to the journal Philosophical Transactions of the Royal Society A. And the publication “ Immiscible Rayleigh-Taylor turbulence using mesoscopic lattice Boltzmann algorithms”, submitted to the journal Physical Review Fluids, and eagerly awaited by the future PhD in mathematics.

Check out the doctoral candidate's invitation to defend their thesis!