UdeC Mathematics Civil Engineering Report proposes solutions to applied physics problems

Research gave rise to two articles accepted for publication in prestigious journals, a very relevant fact for an undergraduate report.

Communications UdeC.- Two international Applied Mathematics journals recently accepted for publication some of the results obtained in the Mathematical Civil Engineering (ICM) report of Nicholas Nunez Lirawho worked under the direction of teachers, Gabriel N. Gaticamember of the Center for Research in Mathematical Engineering, CI²MA, and Ricardo Ruiz-BaierScholar of the School of Mathematics, Monash University (Australia).

On January 10, Nicolás defended his memory titled: ‘Mixed Finite Element Methods Based on Banach Spaces for the Coupled Navier-Stokes-Brinkman Equations and Natural Convection‘, in which he addressed “some typical fluid mechanics problems in numerical form, where the challenge was to do all the analysis and develop the necessary computational tools so that the applicability is direct”, he explains.

“In fact, one of the main objectives was to extend and improve the advances that had already been achieved together with thesis students from the Doctorate in Applied Sciences with a mention in Mathematical Engineering from the UdeC, Mario Álvarez and Bryan Gómez, who addressed the problem of behavior of a fluid to which, in addition, heat is being applied. One of the main objectives of my memory was to carry out the necessary theoretical and computational development so that the case of a fluid that changes phase, for example, solidifying or evaporating, could also be considered”, explains Nicolás.

Nicolas details that this problem has important applications in the field of Physics. “Mario and Bryan formalized the mathematical analysis of one of the situations of interest, and we extended it to a more general case, which allows us to consider more representative models of the physical problem.”

In addition to Prof. Gatica, Nicolás highlights the work he was able to develop, within the framework of his research, with Prof. Ricardo Ruiz-Baier. “Now I am formally closing my entire undergraduate stage, but I am interested in being able to apply to a postgraduate program, I am focused on continuing and doing a doctorate, and one of my options, I hope, is precisely with Professor Ruiz-Baier”.

Regarding having had the opportunity to work at the CI²MA facilities, Nicolás stated that “it is nice to have a workspace where we are all in the same tune, not necessarily doing the same thing, because everyone has a different line of research, but It is always good to know the points of view of people who know and who can contribute, which helps a lot to have a comprehensive work environment”.

“I rescue the closeness that there is, for example, at lunchtime with the teachers, with the officials themselves, and that this is something so close, so familiar. That makes it much more comfortable as a workplace.”

Nicolás is a native of San Vicente de Tagua-Tagua (O’Higgins Region). “The experience of leaving home to go to a different city to study is difficult, but it is achievable, all with effort,” he affirms, and regarding the discipline he decided to study, he states that “from the outside, everyone sees mathematics as something unattainable, incomprehensible, one of the most difficult things. In my case, initially I wanted to study another career, perhaps music, but ‘the paths of life’ led me to mathematics, thus attesting that it is not unattainable as people think”.

He comments that his motivation is also complemented by his interest in dissemination. “That was what I was excited about at one time: helping to make people understand the importance of mathematics, and today more than ever.”

The publications

The first of the two papers is entitled ‘New Non-Augmented Mixed Finite Element Methods for the Navier–Stokes–Brinkman Equations Using Banach spaces’ and was accepted at Journal of Numerical Mathematics, Magazine founded in 2001 and currently has an impact factor of 4,036. In it, explains Prof. Gatica, “a problem that had already been studied some time ago by Ricardo Oyarzúa (University of Bío-Bío) and Luis Gatica (U. Católica de la Santísima Concepción) is addressed, but for which we managed to simplify considerably the respective computational formulation”. And the also researcher at the Center for Mathematical Modeling of the U. de Chile adds: “the above was possible thanks to the fact that we realized that the theoretical advances previously obtained with another of my undergraduate thesis students, Claudio Correacould also be used to study this model, thus generating additional applicability to what was done in Claudio’s thesis”.

The second article co-written by Núñez, Gatica and Ruiz-Baier is entitled ‘Mixed-Primal Methods for Natural Convection Driven Phase Change with Navier-Stokes-Brinkman Equations’ and was recently accepted for publication in Journal of Scientific Computing, which has an impact factor of 2.41. In it Gatica and Nunez develop an extension of the results of the first work, as they explain: “to be able to study not only how the fluid flows, but also how its concentration and temperature change, which are added mathematically with another set of equations that are coupled with those that we had already studied in the first work”.