Projekte
Current projects
Interfaces, ComplexStructures, and Singular Limits in Continuum MechanicsDFG Research Training Group GRK 2339Dates: 2018-2022 (first funding period), The DFG Research Training Group IntComSin is a joint |
Completed projects
Free boundary propagation and noise: analysis and numerics of stochastic degenerate parabolic equationsDFG Research Grant
The porous-medium equation and the thin-film equation are prominent examples of nonnegativity preserving degenerate parabolic equations which give rise to free boundary problems with the free boundary at time t > 0 defined as the boundary of the solution’s support at that time. |
Diffusive interface models for transport processes at fluidic interfaces (Part 2)DFG Priority Programme SPP 1056 „Transport processes at fluidic interfaces“ |
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Fronts and Interfaces in Science and Technology (FIRST) / Marie Curie Initial Training Networks |
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Diffusive interface models for transport processes at fluidic interfaces (Part 1)DFG Priority Programme SPP 1056 „Transport processes at fluid interfaces“ |
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Topological transitions like droplet coalescence or droplet break-up are fundamental features of two-phase flows. In recent years, diffuse interface models turned out to be a promising approach to describe such phenomena. Species transport across fluidic interfaces and the effects exerted by soluble and insoluble surfactants are additional issues of still increasing technological importance.
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Mathematical Analysis of Models Describing the Evolution of Liquid Patterns on Material Interfaces (Part 2 and Part 3)DFG Priority Programme SPP 1052 „Benetzung und Strukturbildung an Grenzflächen““ |
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DAAD project „Mathematical Analysis and Numerical Simulation of Dynamic Electrowetting“ („projektbezogener Personenaustausch Spanien“) |
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Electric fields may influence the wetting behaviour of charged droplets. This effect may be used to manipulate droplet motion and to enforce droplet coalescence or break-up. It is summarized under the notion of electrowetting. First studied in the late 19th century by Lippmann and others, very recently this effect gained the interest of physicists and engineers on account of a variety of applications in micro-fluidics („lab-on-a-chip“). However, mathematical modeling of this effect is still in its childhood — the dependency of contact angles on the applied voltage is modeled by the so called Lippmann formula which may hold true at most in a small voltage regime. In this project, new thermodynamically consistent models shall be derived to describe the evolution of droplet, voltage and thereby to shed light on the mechanisms underlying electrowetting. Existence of solutions shall be proven and efficient numerical schemes shall be developed as well. Poster>>
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Complex rheologiesProject in SFB 611 „Singular phenomena and scaling in mathematical models“, University of Bonn (together with Christiane Helzel and Felix Otto) |
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In this project, models for complex flow phenomena are investigated, for instance pattern formation in sheared suspensions, moving contact lines or Rayleigh-Bénard convection. By means of rigorous analysis and numerical simulations, properties of the models will be predicted. The aforementioned specific models may be used to develop new methods for PDE in general.
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Scaling laws and their cross-overs: global analysis of rheological processesProject in SFB 611 „Singular phenomena and scaling in mathematical models“, University of Bonn (together with Felix Otto) |
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The goal of this project is to investigate scaling laws in rheological processes. More precisely, analytical tools to rigorously infer such scaling laws shall be developed. A common feature of the friction dominated processes to be investigated is their gradient flow structure. This structure translates the physical free energy and the underlying dissipation mechanism into the mathematical terms of functional and metric tensor, respectively. The idea is to use global PDE methods, rather than local methods, like matched asymptotic expansions, to analyze the scaling laws. Phenomena to be studied include spreading of viscous films, case-II diffusion of solvents in polymeric solids, and the demixing of polymer solutions and sponge-like pattern formation.
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DFG project „Mathematical Analysis of Models Describing the Evolution of Liquid Patterns on Material Interfaces „)Project in SFB 611 DFG Priority Programme SPP 1052 „Benetzung und Strukturbildung an Grenzflächen“ |
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