Our young researchers with prizes in the fields of physics and mathematics!

Dr Karol Duda received a commendation in the prestigious International Stefan Banach Prize for the best doctoral dissertation. He defended his dissertation entitled “Dynamika i obliczalność w geometrycznej teorii grup” (eng. “Dynamics and Computability in the Geometric Group Theory”) last year at the University of Wrocław under the supervision of Aleksander Iwanow from Silesian University of Technology and Damian Osajda from the Mathematical Institute of the University of Wrocław.

In the first part of the dissertation, dr Duda analyzes computable aspects of amenability. He proves a computable version of Tarski’s Alternative Theorem. This proof is based on a new, computable version of Hall’s Harem Theorem.  Several of such computable versions are presented in the dissertation.  Applying one of them to non-amenable coarse spaces, dr Duda arrives at a computable version of the generalized Whyte’s Theorem concerning von Neumann’s geometric hypothesis.

The second part of the dissertation is concerned with locally elliptic actions of groups on small cancellation complexes. Dr Duda proves that groups defined by C(6), C(4)-T(4) or C(3)-T(6) small cancellation presentations do not consist of infinite torsion subgroups. This conclusion was especially highlighted by the reviewers of the dissertation, as it offers an answer to a problem open for many years. The dissertation provides proof for a generalized theorem on the existence of fixed points for the locally elliptic actions of groups on the simply connected small cancellation complexes.

Methods of proof made it possible to obtain stronger results in the context of the C(3)-T(6) complexes. Notably, the dissertation points to the possibility of introducing the CAT(0) metric space for the simply connected C(3)-T(6) complexes. It shows that Tits Alternative holds true for groups acting on the simply connected C(3)-T(6) complexes.

More information on the prize.

The Polish Physical Society awarded, among others, authors of doctoral dissertations and master’s theses with prizes and commendations as well. Our PhD student Damian Śnieżek is among the laureates who received a commendation for his master’s thesis entitled “Inertial Flows in Fractal Porous Media,” supervised by dr hab. Maciej Matyka.

‘Commendation in the PPS contest for Arkadiusz Piekara Master’s Award gives me motivation to continue my research and scientific development,’ says Damian Śnieżek, currently conducting further research on the fluid flow through porous media as part of his doctoral studies in the Institute of Theoretical Physics, Faculty of Physics and Astronomy of the University of Wrocław.

In the next few years he is planning on developing his tools even further.

‘I intend to use them to analyze the influence of medium’s porosity on the flow structure of non-Newtonian fluids and compare it with the structures of Newtonian fluids,’ he explains.
In his, awarded by scientists, master’s thesis, he presents the results of his research on inertial effects acting during the fluid flow through porous media. In the investigation, he focused on a numerical analysis of fluid flow through disordered and fractal porous media of high-porosity in 2D and 3D in a wide range of Reynolds numbers.

‘I begin with the proof that a mutual relationship between flow rate and pressure drop experienced by fluid getting through a porous object deviates from Darcy’s empirical law which presupposes a linear relationship between the parameters. With this, I show that for high velocity flow it is indispensable to incorporate Forchheimer correction which introduces to this relationship a term proportional to the square of the velocity,’ explains the young researcher.

‘My thesis also contains an analysis of tortuosity, a parameter providing information about a relative elongation of the flow paths of fluid particles relative to the size of a porous object. Calculations of tortuosity were done on the basis of a method which allowed for determination of the value for a whole system right from the velocity field, resulting directly from a numerical simulation of the fluid flow. With that, the complexity of the calculations was considerably reduced.

Moreover, I analyzed the location of the fluid’s kinetic energy. For this purpose, I used a participation parameter which made it possible to quantitatively describe changes of the flow structure along with the increase of its velocity. Furthermore, I present how to derive this parameter on the basis of basic static quantities, which constitutes an alternative to the derivation known from literature,’ he adds. 

‘I made calculations for a range of Reynolds number starting from 0.01 to 100 in two- and three-dimensional systems. They showcase that all of the aforementioned parameters above are good indicators of inertial effects acting during the fluid flow through porous media. Moreover, a comparison of all of the indications proved that it is impossible to unequivocally draw the line between Darcy’s and inertial flow.’

Tools developed by Damian Śnieżek during the research process as well as the conclusions drawn from the data analysis were used to prepare a publication for the Physical Review E journal.

More on the prize laureates.

Edited by Katarzyna Górowicz-Maćkiewicz

Translated by Weronika Bogucka (student of English Studies at the University of Wrocław) as part of the translation practice.