# News

To continue their PhD studies in Mathematical Engineering

Five students of the Doctorate in Applied Sciences program with a major in Mathematical Engineering from the Universidad de Concepción, who study at the CI²MA: Center for Research in Mathematical Engineering, were benefited with funding from the Advanced Human Capital Formation Program of the National Commission of Scientific and Technological Research, Conicyt, for the realization of doctoral studies in the national territory. They are part of the 65 UdeC students who agreed to this financing. It should be noted that the Universidad de Concepción was the third national institution to concentrate the largest number of fellows. In the case of students of the Doctorate in Applied Sciences with a major in Mathematical Engineering, all agree on the quality of the program and its teachers, and value the financial support provided by Conicyt as it allows them to concentrate their efforts on their fields of study.

**Yissedt Lara**, the only woman of the group, points out that what motivated and motivated her to do this PhD is "*the quality of the teaching staff, as well as the outstanding work that several of her graduates have achieved, as good researchers, especially in the area of EDPs and Numerical Analysis*". She also adds that those same reasons have allowed her, for the moment, to direct her thesis idea "*in applications of these theories in epidemiological problems, with the guidance of professorsRaimund Bürger (CI2MA) and Gerardo Chowell (external tutor) from the State University of Georgia), with which, at the moment we are in the development of the idea for the thesis project and in the consolidation of an article to publish, which is part of a MEC project of Conicyt*". This scholarship, she adds, has meant great support and support for his work. "*It has allowed me to glimpse and value its importance for the expansion of theory and methodologies, which allow the solution of problems in the epidemiology, and how these can improve the detection criteria and prevention of public health entities. Additionally, the scholarship will allow me to carry out research internships and dedicate myself in a exclusive in these 2 years that remain of my doctoral training*".

Salvadoran **William Miranda** is currently in his third year in the program that, he says, chose because he considers it "*one of the best doctoral programs in Numerical Analysis for Partial Differential Equations in Latin America.*", Affirmation that is supported by the scientific production of the academics and students of the Doctorate. Currently working on his thesis "*Mixed Finite Element Methods for Nonlinear Problems in Biomedicine and Biology*", directed by researchers Gabriel Gatica (UdeC), Daniel Hurtado (PUC) and Eligio Colmenares (UBB), states that "*receiving the Conicyt scholarship means tranquility, stability and more time to dedicate them to the doctorate*". In his thesis he develops the numerical analysis of two problems, one in the area of Biology and the other in the area of Biomedicine. "*The first is a model of bioconvective fluids that describes the hydrodynamics of a microorganism culture. The movement of these microorganisms in the opposite direction to the force of gravity produces a convection movement. The model is used to study and understand biological processes such as reproduction, infection or the marine life ecosystem. The problem is constituted by Navier-Stokes equations for the movement of the fluid and convection-diffusion equations for the concentration of microorganisms*". Miranda points out that, in this part, the main contribution of his research lies in "the development of new numerical methods for this model based on mixed finite element methods demonstrating the existence of a solution, deriving optimal estimates of error a priori and illustrating using computer simulations. the good performance of the schemes we propose. " The second, he adds, "*is a problem that is generated in the Biomedical area, for which I study the problem of determining the regional deformation that the lung parenchyma suffers in-vivo non-invasively from medical images analyzed by different formulations of finite elements. The problem is known as deformable image registration (DIR), which is equivalent to the linear elasticity problem with a non-linear source term that depends on the unknown field. An important application of this problem is to study the regional deformation of lung tissue from computed tomography images of the thorax.*"

Another student benefited is **Cristian Cárcamo**, who is currently beginning his fourth year of doctoral studies. "*What motivated me to do this PhD was the possibility of studying and developing tools which have a practical use, due to the applicability they have in areas of engineering, medicine, physics, among others. In addition, this doctorate has a recognized international prestige that mathematically has nothing to envy to other programs in major universities in Europe or North America.*" For the student, receiving this benefit acquires great relevance because "*I have delayed the completion of the doctoral internship and now with Conicyt scholarship I can travel with a little more slack to do it*". His thesis, directed by Rodolfo Araya (UdeC) has allowed him to perform two works: a multi-scale mixed hybrid finite element method, the Oseen Equation, which models the behavior of speed and pressure of a fluid and, currently, has been comparing, via finite element analysis, two methods used by engineers to estimate pressure jumps in the arteries when there is narrowing. "*The idea is to show which of the two has a better order of convergence, since that will allow us to know which of the two works best*," he says. In his opinion, with this research, "*apart from broadening the knowledge frontier, multiscale methods allow us to better capture the solutions of an equation when the parameters that compose it are highly heterogeneous, in addition to the method we are applying is a method high order In relation to the other area of study (hemodynamics), being able to determine which of the two methods works better will allow patients with problems of narrowing in the arteries, to be operated without the need to perform an invasive diagnosis such as the one that currently it is applied but the use of medical images will be enough to determine the speed of the blood and with it subsequently recover the value of the pressure*".

In turn, **Nestor Sánchez**, the fourth of the beneficiaries, said that "*my interest in the area of numerical analysis arose since I started my thesis project of Magister at the Universidad del Bío Bío, under the advice of Ricardo Oyarzúa. At the same time, thanks to some seminars organized by professors from the Universidad del Bío Bío and the Universidad de Concepción, I decided to apply to this program that I entered the first semester of 2017. Having won this scholarship will allow me to dedicate much more time to the study of the doctorate*". Sànchez currently works with Manuel Solano (UdeC) in the development of Galerkin Discontinuous Hybridizable methods for the Grad-Shafranov equation, from magneto-hydrodynamics. "*In particular, this consists of a semi-linear equation in a non-polygonal domain that describes a cross section of a nuclear reactor, where the plasma is confined. This work is being carried out in collaboration with Tonatiuh Sánchez from the University of New York, who specializes in numerical methods in Plasma Physics, which is why my goal is to carry out research stays in that university and, as possible, to have the support of the Conicyt scholarship for this process*". The student is emphatic in thanking Manuel Solano, Gabriel Gatica, Raimund Bürger and Mauricio Sepúlveda "*for being part of my academic training in this first two years of study*".

The last of the Doctorate students to receive the Scholarship is **Mario Muñoz**, who has just finished his first year of training and is about to start his seminars, with which he intends to formulate his thesis project in the area of Stochastic Differential Equations and its numerical analysis. Muñoz says that "*I decided to do the Doctorate in Mathematical Engineering of the UdeC in order to obtain the faculties and capacities necessary to carry out research in applied mathematics*". For this reason, he feels enormously grateful for the Conicyt Scholarship, since, he says, "*this benefit is a great economic support that will also enrich my Doctor training, being able to attend congresses and do internships abroad*".