Abstracts Mathematics

On the strategies used to attack unsolved mathematical problems - a case study of the Collatz Conjecture

by Daniel Olesen Fejerskov

The world of physics is an ever expanding field, and applying the isomorph theory is a fairly new and interesting way of understanding the glass transition phase, viscous liquids and liquids in general. In this study, we examine if the isomers o-xylene and m-xylene can be regarded as a Roskilde-simple system when modelled by a three-site coarse-grain model. For this purpose, RUMD is used to simulate the model and examine the behaviour of the isomers. The model parameters are optimized to fit both structural and dynamical properties of xylene. The results from the simulations are analysed, and judging by Pearson's correlation coefficient, the simulations indicate that o-xylene and m-xylene can be regarded as a Roskilde-simple system in large parts of the phase diagram. Advisors/Committee Members: Schrøder, Thomas (advisor).