Summer School 2020 “Computational Photonics”

Welcome and openingOpening of the Summer School 2020 “Computational Photonics” at KIT

We are glad having the opportunity oganising the Summer School as a hybrid event in these extraordinary times and saying hello personally to Sven Burger, Christin David, Lothar Nannen, Philipp Schneider and Barbara Verfürth. Due to travel restrictions our lecturers Andrei Laurynenka, Owen Miller and Ole Sigmund will provide their lectures online. More than 155 researchers have been registrated from all over the world and will join the Summer School on-site and online.

We are looking forward having a exciting, instructive and successful week.

Computational Photonics – Summer School 2020

From September 21-25, 2020 leading experts (see the list below) will speak about important concepts and recent developments in the field of computational methods. Our recent Summer School will be complemented by computer tutorials to provide insights into the implementation and performance of various algorithms. Have a look at the schedule. The summer school will be an online event due to the Covid-19 situation. We organize the event on-site but with a proper streaming of all the lectures and exercises. If the situation relaxes in September and the regulations will permit we do it as a hybrid event.

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Im Fokus: Numerische Analyse von Mehrskalenmethoden und Stabilität und Instabilität in physikalisch motivierten Problemen bei partiellen Differentialgleichungen

Zwei neue Junior Research Group Leader haben ihre Forschung am SFB 1173 in Karlsruhe aufgenommen: Zum 1. Juni 2020 konnten wir Frau Dr. Barbara Verfürth von der Universität in Augsburg und zum 15. Juli 2020 Herrn Dr. Christian Zillinger vom  Basque Center for Applied Mathematics (BCAM) in Bilbao an den SFB holen. Wir freuen uns sehr, mit ihnen zwei hochmotivierte, exzellente Forscher*innen in unserem Team zu haben.

Image of Barbara Verfürth and Christian Zillinger

Image of Barbara Verfürth (left) and Christian Zillinger (right)

Unsere Nachwuchsgruppenleiterin Barbara Verfürth forscht in den nächsten Jahren an der Entwicklung und numerischen Analyse von Mehrskalenmethoden für partielle Differentialgleichungen mit unstrukturierten, nicht glatten Koeffizienten und möglicherweise auch Nichtlinearitäten. Materialien mit mehrskaligen Strukturen tauchen in vielen Anwendungen auf und sind eine große Herausforderung für numerische Simulationen, weil feine Materialdetails selbst mit modernsten Computern rechnerisch meist nicht aufgelöst werden können. Numerische Mehrskalenmethoden basieren auf der Zerlegung der Lösung in einen makroskopischen und einen feinskaligen Anteil. Dadurch lässt sich das makroskopische oder globale Verhalte der Lösung gut auf einem groben Gitter näherungsweise beschreiben. Ein besonderer Fokus ihrer Arbeit ist die Wellenausbreitung in heterogenen Medien, welche zu erstaunlichen und ungewöhnlichen Effekten wie einem negativen Brechungsindex führen kann.

Nachwuchsgruppenleiter Christian Zillinger beschäftigt sich in seiner Forschung mit Stabilität und Instabilität in physikalisch motivierten Problemen der partiellen Differentialgleichungen. Insbesondere interessieren ihn Durchmischungseffekte und Resonanzen in Flüssigkeiten und Plasmen und deren asymptotisches Verhalten. Des weiteren arbeitet er zu Rigidität und Flexibilität von konvexen Integrationslösungen in Formgedächtnismaterialien und der Rolle von Mikrostrukturen.

Um die beiden Newcomer etwas besser kennenzulernen, haben wir sie gebeten, uns folgende Fragen zu beantworten: Continue Reading →

Waveguides – Modellansatz

H. Wind

Everybody has experimented with resonating frequencies in a bathtub filled with water. These resonant eigenfrequencies are eigenvalues of some operator which models the flow behavior of the water. Eigenvalue problems are better known for matrices. For wave problems, we have to study eigenvalue problems in infinite dimension. Like the eigenvalues for a finite dimensional matrix the spectral theory gives access to intrinsic properties of the operator and the corresponding wave phenomena.

Anne-Sophie Bonnet-BenDhia from ENSTA in Paris is in conversation with Gudrun Thäter about transmission properties in perturbed waveguides.  This is the third of three conversations recorded during the Conference on Mathematics of Wave Phenomena July 23-27, 2018 in Karlsruhe for the Modellansatz Podcast. Anne-Sophie is interested in wave guides: Optical fibers that can guide optical waves while wind instruments are guides for acoustic waves. Electromagnetic waveguides also have important applications.

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Pattern Formation

If one puts a pan with a layer of oil on the hot oven in order to heat it up one observes different flow patterns over time: In the beginning it is easy to see that the oil is at rest and not moving at all. But if one waits long enough the still layer breaks up into small cells which makes it more difficult to see the bottom clearly. This is due to the fact that the oil starts to move in circular patterns in these cells. In our example the temperature difference between bottom and top of the oil gets bigger as the pan is heating up. For a while the viscosity and the weight of the oil keep it still. But if the temperature difference is too big it is easier to redistribute the different temperature levels with the help of convection of the oil.

This means that the system has more than one solution and depending on physical parameters one solution is stable while the others are unstable. Mariana Haragus, Professor in Besançon at the University of Franche-Comté, is doing research on this important question for engineers as well as mathematicians.

Gudrun Thäter was in conversation with her in the context of the Modellansatz Podcast about Bernard-Rayleigh problems: Where do these convection cells evolve in theory in order to keep processes on either side of the switch? This had been one of the interesting research topics at our 2018 Conference on Mathematics of Wave Phenomena.

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