Dynamical systems on vector bundles.
Dynamics of an artificial slope
The slope shape is replaced by a 3D regression function which corresponds with high precision to the position of several hundred points which were determined on the surface of the slope body. The position of several points was repeatedly measured for several years. The time changes in the position of these points were used to create regression functions that describe vertical movements, slope settlement and horizontal movements, slope movement. The model results are presented in the form of mathematical...
Dynamics of Biomembranes: Effect of the Bulk Fluid
We derive a biomembrane model consisting of a fluid enclosed by a lipid membrane. The membrane is characterized by its Canham-Helfrich energy (Willmore energy with area constraint) and acts as a boundary force on the Navier-Stokes system modeling an incompressible fluid. We give a concise description of the model and of the associated numerical scheme. We provide numerical simulations with emphasis on the comparisons between different types of flow:...
Dynamics of shock waves in elastic-plastic solids
The Maxwell type elastic-plastic solids are characterized by decaying the absolute values of the principal components of the deviatoric part of the stress tensor during the plastic relaxation step. We propose a mathematical formulation of such a model which is compatible with the von Mises criterion of plasticity. Numerical examples show the ability of the model to deal with complex physical phenomena.