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Talks of Ben
Here, you find
the slides of some 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
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.
- 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.
- Homogenization of hysteresis
problems: Hysteresis2010. This
presentation regards homogenization methods for problems with
hysteresis which could be applied to Hydromechanics and to
- Meta-Materials are studied in the context of Maxwell equations. Together
with G. Bouchitte and later with A. Lamacz 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. A related effect is perfect transmission. MetaMat2013
- Fingering effect for
Richards equation with hysteresis: Fingering2013. 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.
for waves in heterogeneous materials: Waves2015. We describe
waves with a linear wave equation, the elliptic operator is in
divergence form and with highly oscillatory coefficients. For
finite times, the effective equation is again a linear second
order wave equation -- and cannot describe the dispersion
effects that are observed numerically and experimentally.
Instead, for large times, the effective equation is a
dispersive wave equation. Dispersion-Paris-2017
and interfaces are studied in terms of uniqueness and
with the aim of practical schemes with Bloch-waves. An
important subject is the definition of an outgoing wave
condition in such media. For experts in Blochwaves-Korsika-2016
in a more general language in Blochwaves-Heidelberg2017.