Generalized Chaplygin gas model

My name is Sanja Ružičić and I am a first-year PhD student at Department of Mathematics and Informatics, Faculty of Sciences at University of Novi Sad. Also, I am currently employed as an Assistant at Chair of Analysis, Probability and Differential Equations at Department of Mathematics and Informatics where I received both undergraduate and graduate education in Applied Mathematics (Finance Mathematics).
My master thesis entitled ”Models of blood flow in arteries” where the focus was on modeling blood flow in large arteries assuming cylindrical geometry. Modeling of that kind is a major challenge because the arterial walls are composed of three main layers, each with different mechanical characteristics. Also, the study of the problems with the interaction between blood flow and cardiovascular tissue remains to be a challenge due to their strong nonlinearity and multi-physics nature. The most interesting part of my work on thesis was implementing numerical algorithms in order to visualize the behavior of blood in such a complex environment.

Currently, I am working on some problems about singular solutions to conservation laws systems. Actually, during the last year I have been working with my PhD adviser prof. dr Marko Nedeljkov on generalized Chaplygin gas model which is a model of dark energy in Universe introduced in the last decade. Our main focus was to solve the uniqueness problem and to exclude unwanted solutions. We gain some interesting results about conditions most frequently used for admissibility check (overcompressibility and entropy condition). We were dealing with modified Bessel functions of the second kind which is an interesting class of functions, not yet well explored and that was the main reason why the analytical confirmation of the results numerically obtained is still a challenge to us (see figure for illustration).

I am also a part of research unit at the Department of Mathematics and Informatics named Center for Mathematical Research of Nonlinear Phenomena. That is a group which gathers researchers from 3 research groups financed by the Ministry of Education and Science, Republic of Serbia. The main research areas are functional analysis, PDEs and numerical methods for nonlinear equations (PDEs and nonlinear optimization). The group organizes weekly seminars where members of our group present their recent research.

I have to admit that during my studies I didn’t know that I will have this great opportunity to work and learn from a group of people which are very passionate about their work. All thanks to them, I am now able to apply mathematical knowledge in real life problems and I am capable to explore a new world of medicine, fluid mechanics, etc. through the science of applied mathematics. And I am still learning …