Browsing by Author "Burger, Martin"

Now showing 1 - 3 of 3
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    On multi-species diffusion with size exclusion
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Hopf, Katharina; Burger, Martin
    We revisit a classical continuum model for the diffusion of multiple species with size-exclusion constraint, which leads to a degenerate nonlinear cross-diffusion system. The purpose of this article is twofold: first, it aims at a systematic study of the question of existence of weak solutions and their long-time asymptotic behaviour. Second, it provides a weak-strong stability estimate for a wide range of coefficients, which had been missing so far. In order to achieve the results mentioned above, we exploit the formal gradient-flow structure of the model with respect to a logarithmic entropy, which leads to best estimates in the full-interaction case, where all cross-diffusion coefficients are non-zero. Those are crucial to obtain the minimal Sobolev regularity needed for a weak-strong stability result. For meaningful cases when some of the coefficients vanish, we provide a novel existence result based on approximation by the full-interaction case.
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    Silicon-organic hybrid photonics: Overview of recent advances, electro-optical effects and CMOS-integration concepts
    (Bristol : IOP Publishing, 2021) Steglich, Patrick; Mai, Christian; Villringer, Claus; Dietzel, Birgit; Bondarenko, Siegfried; Ksianzou, Viachaslau; Villasmunta, Francesco; Zesch, Christoph; Pulwer, Silvio; Burger, Martin; Bauer, Joachim; Heinrich, Friedhelm; Schrader, Sigurd; Vitale, Francesco; De Matteis, Fabio; Prosposito, Paolo; Casalboni, Mauro; Mai, Andreas
    In recent decades, much research effort has been invested in the development of photonic integrated circuits, and silicon-on-insulator technology has been established as a reliable platform for highly scalable silicon-based electro-optical modulators. However, the performance of such devices is restricted by the inherent material properties of silicon. An approach to overcoming these deficiencies is to integrate organic materials with exceptionally high optical nonlinearities into a silicon-on-insulator photonic platform. Silicon–organic hybrid photonics has been shown to overcome the drawbacks of silicon-based modulators in terms of operating speed, bandwidth, and energy consumption. This work reviews recent advances in silicon–organic hybrid photonics and covers the latest improvements to single components and device concepts. Special emphasis is given to the in-device performance of novel electro-optical polymers and the use of different electro-optical effects, such as the linear and quadratic electro-optical effect, as well as the electric-field-induced linear electro-optical effect. Finally, the inherent challenges of implementing non-linear optical polymers on a silicon photonic platform are discussed and a perspective for future directions is given.
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    Tomographic Inverse Problems: Mathematical Challenges and Novel Applications
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2023) Arridge, Simon; Burger, Martin; Hahn, Bernadette; Todd Quinto, Eric
    This workshop brought together researchers working on mathematical problems related to tomography, with a particular emphasis on novel applications and associated mathematical challenges. Examples of respective issues represented in the workshop were tomographic imaging with Compton cameras or coupled-physics imaging, resolution and aliasing, vector and tensor field tomography, diffraction tomography, magnetic particle tomography, and limited data, all of which are motivated by the many modern applications. These topics were complemented by novel algorithmic strategies in the solution of tomographic inverse problems, such as stochastic methods and machine learning techniques. Bringing together mathematical and scientific researchers working on these different mathematical problems created a fruitful interchange with novel ideas and strong impact for the future of the field.