Talks of Ben Schweizer:

With the links below you find the the slides of recently given presentations

• On the effect of oil-trapping and the derivation of a homogenized equation: Oiltrapping2008. This regards the two-phase flow equations in a one-dimensional domain with an interface condition at (many) internal interfaces.


• A system with forward- and backward diffusion: Backward2008. This talk is about a  scalar equation in one space dimension, including diffusion with both signs. Together with D. Horstmann I compared two different solution concepts and characterized one of them with a free boundary problem.

• Homogenization of hysteresis problems: Hysteresis2010. This presentation regards homogenization methods for problems with hysteresis which could be applied to Hydromechanics and to Plasticity.

• Plasticity: These two talks are specific for homogenization in plasticity equations, one shorter talk for experts Plasticity2011DA, one longer talk for non-experts Plasticity2011DO.
  

• Meta-Materials are studied in the context of Maxwell equations. Together with G. Bouchitte I studied the question whether materials with a negative optical index can be constructed with a complex micro-structure. Indeed, such a construction was proposed by Pendry and others. In our contribution we give a detailed analysis of the microscopic behavior of electric and magnetic field and derive an effective Maxwell equation with negative index: See MetaMat1 for a more general talk and MetaMat2 for a talk for specialists.

• Outflow boundary conditions for various porous media equations: Outflow2009. For various bulk equations (degenerate and non-degenerate Richards, two-phase flow) a regularization scheme for outflow boundary conditions is analyzed. Results are in parts obtained together with M. Lenzinger and S. Pop.
  

• Fingering effect for Richards equation with hysteresis: Fingering2012. When we introduce static hysteresis in the Richards equation, planar front solutions become unstable. Together with the dynamic term, true fingering occurs for both Richards and two-phase flow in porous media under the influence of gravity.