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My scientific interest:

Partial Differential Equations and singular limits

Applications
Methods

  • Porous Media: degenerate diffusion, hysteresis
  •  
  • Plasticity
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  • Maxwell-, Helmholtz-, Wave-equations
  • Free boundary problems and fluid mechanics

  • Homogenization, Gamma limits
  • Degenerate and negative Diffusion
  • Compactness and interpolation arguments     
  • Discretization schemes

Some research high-lights in the form of images:

Waves, Maxwell equations, Cloaking, Porous Media and Plasticity


Dispersive Welle

We derived a dispersive equation that describes the long-time behavior of waves in a heterogeneous medium

Names: T. Dohnal, A. Lamacz, B. Schweizer


Split ring geometry

We analyzed the Maxwell equations in a complex geometry that generates a meta-material with a negative index

Names: G. Bouchitte, A. Lamacz, B. Schweizer


Transmission

We confirmed the extraordinary transmission of light through sub-wavelength holes with an analysis of plasmonic waves

Names: G. Bouchitte, B. Schweizer

Cloaking

Cloaking: Both, the ring and the small black point at position z are invisible for measurements from far away. The reason is that the ring contains a negative index material


Names: G. Bouchitte, R.V. Kohn, J. Lu, M. Weinstein, B. Schweizer



Bloch Transmission


What is the radiation condition (boundary condition at infinity) for the Helmholtz equation in a periodic medium? We developed one and derived a (weak) uniqueness result.

Names: A. Lamacz, B. Schweizer


Plasticity

We derived effective equations that describe the plastic deformations of heterogeneous materials

Names: M. Heida, M. Veneroni, B. Schweizer


Oiltrapping

We derived effective equations that describe oil-trapping. The image shows a saturation profile in a porous medium consisting of two different materials; infinite slopes occur

Names: S. Pop, M. Ohlberger, P. Henning, B. Schweizer


Fingering

We studied a hysteresis model for flow in porous media that can explain gravity fingering

Names: A. Lamacz, J. Koch, A. Rätz, B. Schweizer