Category: Workshop

Together with one of the organizers, Roland Schnaubelt, and the invited speaker Peer Kunstmann, Martin Spitz and I participated in the 10^th Euro-Maghrebian Workshop on Evolution Equations. This series of workshops was initiated in 1999 with the aim of bringing together mathematicians from Europe and the Maghreb working on evolution equations, the first one having taken place in Marrakesh, Morocco. This time the scientists met in the small city Blaubeuren, Germany, located close to Ulm in the eastern Swabian Alb. The location of the workshop was the Heinrich-Fabri Institute of the university of Tübingen. It provided us with pleasant accommodation and a well-equipped lecture room. During the breaks many lively discussions between the participants developed and the nature in the surrounding, including the famous Blautopf, invited to go for walks.

Evolution equations, the topic of the workshop, arise naturally in many sciences like physics, chemistry and biology. They appear whenever the time rate of change of a quantity (e.g. a temperature, a mass concentration or a density of a population) depends only on the present state of the quantity. This covers a wide range of natural phenomena and leads to many different scientific questions.

During the workshop three lecture series were held, each of them consisting of three talks. Thierry Cazenave from Paris spoke about Finite time blowup in nonlinear heat, Schrödinger, and Ginzburg-Landau equation. He talked about the analysis of the first two equations and how to combine the properties of their solutions in the investigation of the solutions to the last equation. Mourad Choulli from Metz gave a lecture series about Elliptic and parabolic Cauchy problems. He was mainly concerned with stability estimates for the elliptic case and the extension of their proofs to the more complicated parabolic situation. Jürgen Saal from Düsseldorf gave insights into Systematizing the maximal regularity approach to quasilinear mixed order systems. He talked about the Newton polygon approach and anisotropic function spaces and their application to free boundary value problems. These three minicourses were accompanied by nine invited lecturers and about 20 contributed talks by the participants from Europe and Northern Africa on various topics concerning evolution equations, functional analysis, partial differential equations and inverse problems.

Conference photo of the 10th Euro-Maghrebian Workshop on Evolution Equations in Blaubeuren.

Blaubeuren Workshop 2016 Poster (with kind permission of RTG 1838)

In March 2016, we, that is a small delegation of the applied analysis workgroup at KIT (Ioannis Anapolitanos, Leonid Chaichenets, Michael Hott, Johanna Richter, and Tobias Ried), had the opportunity to participate in a workshop on Quantum Dynamics and Functional Inequalities, organised by the Stuttgart/Tübingen RTG 1838 “Spectral Theory and Dynamics of Quantum Systems”. It covered a very diverse range of topics from mathematical physics:

Benjamin Schlein (University of Zurich) gave an introduction to the derivation of effective equations for quantum systems with a large number of particles. In the case of bosons this leads to a description of the dynamics of Bose-Einstein condensates.

The connection between functional inequalities and geometric problems, as well as their application in kinetic theory, were discussed by Michael Loss (Georgia Institute of Technology).

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Everyone knows graphite. We find it in pencils, it is used in electrical motors and generators…

A line of a pencil is made of graphite. photo by Patrick Krämer

But did you know that we can make way more out of this material, or more precisely out of the extracted layers of this material, called graphene?
In the future it could be used for designing a new generation of smartphone displays, transistors, electrodes, biomicrorobotics and many more.

In November 2015 we invited the physics group of Kurt Busch from Humboldt Universität zu Berlin to a „Discontinuous Galerkin SFB Workshop” at our institute. The aim of the workshop was to find a common starting point for the combination of theory and practice in the efficient simulation of problems arising from physics under realistic conditions. For this purpose the idea was to combine the expertise of Kurt Busch’s group in the parallel implementation of a specific class of methods for the spatial discretization of PDEs, so called discontinuous Galerkin (dG)  methods,  on large clusters with efficient time integration methods developed in our SFB.

My specific field of research within the SFB is the efficient time integration of the Maxwell–Dirac (MD) system in a highly oscillatory regime. This system describes the interaction of e.g. an electron with its self-generated electromagnetic field.  During this very interesting workshop Julia Werra, a PHD student of Kurt Busch’s group, told me that in particular the MD system is used to model electrons in the material graphene.

Since Julia’s research is on the analysis of the physical properties of graphene and we wanted to learn more about the physical point of view of the MD system, we planned to discuss the connection of the physical with the mathematical aspects of this material together with her a little bit more. So I went for 4 days to Berlin in March 2016.  This exchange of knowledge proved very valuable. Now Kurt Busch’s group and I think about how we can combine physics and mathematics in the efficient simulation of graphene.

At this point I also want to put some light also on what graphene actually is:

Graphene can be seen as an extracted layer of graphite. Click for source.

Graphene is a 2D crystal of carbon atoms which are structured in a hexagonal honeycomb lattice. It can be seen as an extracted layer of graphite. Each carbon atom in graphene only has 3 partners, so by the missing fourth partner at each atom there are free electrons that make the material a good electrical conductor. Here its electronic band structure plays an important role. The band structure of a solid helps to understand its electrical, thermal and optical properties. The band structure of graphene shows a peculiarity, the so called Dirac cone, at the so called Dirac points, where two energy bands cross each other. On Youtube you can find a pretty nice and informative video on graphene, its band structure and Dirac cones.

Physicists all over the world see graphene as the material of the future as it has very nice properties due to its atomic structure: It is transparent, impermeable for many molecules, much stronger than for example steel even though it is much lighter, and it has an exceptionally good electrical and thermal conductivity. Furthermore, it is one of the most frequent materials on earth.

If you are interested in a related work on the so-called Maxwell-Klein-Gordon equation you can listen to the modellansatz podcast on numerical time integration which we recorded together with Gudrun Thäter in the context of the Cooking Math project of KIT together with the Hochschule für Gestaltung Karlsruhe.