The current production of synthetic polymers is about 300 million tonnes per year (2015) with a typical annual growth rate of 5% to 7%. Usually the manufacturing process requires one to deal with flow of polymer melts or polymer solutions. Consequently, mathematical modelling of flows of these materials is of eminent interest, and it brings many challenging questions both from the physical and mathematical point of view. Usually, the molten polymers are described as viscoelastic fluids. Starting with the seminal paper by Oldroyd (Oldroyd 1950, Proc. R. Soc. A-Math. Phys. Eng. Sci. 200, 523), we will briefly outline the historical development of the theory of viscoelastic fluids, and we will comment on recent advances in the field especially from the point of view of modern phenomenological non-equilibrium thermodynamics.
A drawing of a (combinatorial) graph is a representation of the graph in which the vertices of the graph correspond to points in the plane and the edges to simple curves connecting pairs of points. I will talk about several algorithmic and geometric problems related to such drawings.
Radiation can be recently sensitively controlled both in time and energy. Chemistry can benefit from the advancement in physics and use light to control matter. In my talk, I will focus on molecular simulations of the chemical processes initiated by the interaction of photons with molecules. Photochemical processes are usually associated with photons in the UV, visible and sometimes also in the IR range. Photochemical simulations describing the processes in this range have significantly advanced in the last decade. I will briefly describe the techniques typically used in the field, emphasizing particularly the role of solvent environment. The field of X-ray initiated photodynamics is much more complicated and much less developed. In fact, dynamical processes initiated by X-ray photons are so far not typically considered as part of photochemistry as the amount of energy deposited into the system is way too large for defined chemical changes. On the other hand, X-ray photons allow us to excite/ionize specific atoms. Here, I will present our recent findings on new processes which we have identified in solvated systems upon X-ray exposure. In this context, I will also discuss new liquid state spectroscopies using tunable X-radiation and allowing us to investigate X-ray initiated processes.
Changes in climate influence the distribution of ice and water over the Earth's surface, which, in turn influence the climate itself. Ice accumulation or ablation followed by changes in sea level induce glacial-isostatic adjustment of the solid Earth. Conversely, the solid-Earth deformation influences a rise and fall of sea level. Moreover, the redistribution of ice and water and changes in the mass distribution in the Earth's interior are capable to induce perturbations in the rotation of the Earth, both in direction and magnitude of the rotation vector. A wander of the rotation axis, in turn, induces variations in the centrifugal potential and, subsequently, variations in the sea level. All this means that the determination of sea level variations coupled with polar wander due to changes in ice's water mass load is a complex geophysical and mathematical problem.
The theory and modelling of glacial isostatic adjustment have been rapidly developing since the launch of the GRACE satellite gravity mission in 2002. The lecture presents an overview what has been achieved in the theory and data assimilation on a precise modelling and prediction of glacial isostatic adjustment.
Examples of solar flares in UV and radio observations are shown. The standard model of solar flares is explained. Then we present processes in solar flares and their simulations in magnetohydrodynamic and particle-in-cell models. Maps of waves and oscillations based on the broadband radio spectrum are added. A role of thermal fronts in solar flares is mentioned. Finally, a question of solar superflares is shortly discussed.
X-ray diffraction from crystals consisting of randomly stacked monoatomic or monomolecular layers have been investigated for several decades. Recently, these structures are again in focus of attention, since new materials like topological insulators, multiferroic systems etc. exhibit a random layered structure. An x-ray diffraction experiment from a random stack of monolayers can be carried out in two basic arrangements; in a standard set-up the measured diffracted intensity is collected from a large sample volume, for which the ergodic hypothesis applies, so that the measured signal is averaged over a statistical ensemble of all possible monolayer distributions (microstates). Synchrotron x-ray sources can deliver very narrow and almost coherent x-ray beams, allowing for another experimental set-up, in which only one microstate is irradiated. The application of a fully coherent beam makes it possible to retrieve the phase of the diffracted beam and determine fully the monolayer sequence under investigation. We have used both experimental approaches for the investigation of epitaxial layers of rhombohedral topological insulators (Bi2Se3, Bi2Te3), for the investigation of stacking faults in non-polar GaN layers and for the study of wurtzite and zincblende segments in III-V nanowires.
The density-functional theory is a powerful tool for modeling the electronic structure of crystalline solids and for computational prediction of materials' properties. There are, however, whole classes of compounds, for which the present-day approximate implementations of the density-functional theory do not reach sufficient accuracy. Among the problematic cases are compounds with strongly correlated electrons, for instance those that contain elements from the lanthanide or actinide groups. A substantially improved description of the electron-electron correlations is achieved by building a material-specific Hubbard model on the top of the density-functional result, and by solving this model by means of the dynamical mean-field theory. I show how such framework can be used to analyze core-level spectra on the same footing as the valence-band electronic structure. I use photoemission from core levels in actinide and rare-earth oxides as an illustration, and discuss how the satellite features observed in the photoelectron spectra do (or do not) reflect the chemical bonding.
The standard models of economics and finance make some extremely convenient but unjustified assumptions about the aggregated behaviour of the participants within the system. These greatly simplify the mathematics required to the point where many mathematicians do not even consider them interesting research areas.
I shall describe some non-standard financial market models, both agent-based and mesoscopic in nature, and their relationship to, if time permits: Coupled PDEs with very unusual boundary conditions Queueing Theory Generalized Polya urns Variants of self-organized criticality models
I will discuss thermodynamics of charged and rotating black holes in asymptotically AdS spacetimes and show how to extend some of the results to black holes that also accelerate. The acceleration can be thought of as caused by a cosmic string pulling the black hole to infinity and the exact solution of the Einstein equations is known as the C-metric. I will derive a standard first law, with the usual identification of entropy proportional to the area of the event horizon, and discuss the thermodynamic volume, stability and phase structure of these interesting black hole solutions.