Former WG Modelling and PDEs
Administration: Prof. Dr. Michael Böhm
Nowadays most processes in nature and industry can only by understood and prognosticated with advanced mathematical modelling methods. To cope the complexity of models from material sciences, mathematical skills and methods are needed for an adequate formulation.
We focus on
- the mathematical modelling of physicochemical processes in various types of materials with a complex micro structure,
- on the mathematical investigation of the resulting systems of Partial Differential Equations,
- and on the derivation of averaged models by homogenization methods.
A steel sample
One important application is the material behaviour of steel. A long lasting partnership exists to the
IWT (Stiftung Institut für Werkstofftechnik) and the
AG Numerik von PDEs in the framework of the “Sonderforschungsbereich”
SFB 570 „Distortion Engineering – Verzugsbeherrschung in der Fertigung“,in which the working group with the main research on
Modellierung und Simulation von verzugsrelevantem Materialverhalten (Teilprojekt C3) and
Mehrskalen-Modellierung von Phasenübergängen, Verzug und Verzugspotential (Teilprojekt C4) is involved.
Resulting initial-boundary value problems for the description of the material behaviour of steel are analysed mathematically in another
dissertation project.
A research project concerning the theory and application of
Mehr-Mechanismen-Modellen(multi mechanisms models), in co-operation amongst others with the
INSA institute (Rouen) and the
École des Mines (Paris)was arranged recently.
Constriction of micro pores
Contained in the main research
Mikro-Makro-Modellierung von Reaktions-Diffusions-Problemen(micro macro modelling of reaction diffusion problems) is the analysis of how homogenization methods and two-scale models can be used for time-dependent geometries. For instance this can be adopted to the constriction of pore systems in concrete (cf. project
Moving-Boundary-Modellierung der Karbonatisierung von Beton(moving boundary modelling of the carbonation of concrete).
Topics for Bachelor-Thesis (Industrial Mathematics)
Bachelor-Thesis (application/pdf 63.4 KB)
Dissertations:
Dissertations (application/pdf 76.3 KB)
A steel sample
Constriction of micro pores