Starting from 2000, three conferences on multi-scale methods in science and technology have been successfully organized in Dubrovnik
in cooperation with Andro Mikeliċ.
Their goal was to bring together the mathematicians working on the multi-scale techniques
(asymptotic analysis, homogenization, singular perturbation, …) and experts from the applied sciences, who need these techniques in modeling,
numerical simulations and optimization of real systems. These events provided a high potential and the proper atmosphere for the exchange of
information, results and ideas, for discussions and cooperation on the front of research.
Andro Mikeliċ, a pioneer in multi-scale analysis and its applications and an inspiring partner, contributed substantially to this success.
Sadly, Andro has passed away in 2020 and it is appropriate to dedicate to his memory this Dubrovnik conference, pursuing the main goal which he had chosen for his own research:
The mathematical rigorous derivation of effective model systems for processes in complex media using multi-scale methods, starting from models based on first principles.
The topics of this conference include on the theoretical side among others:
- the mathematical modeling and analysis of transport processes coupled with fluid flow and reactions in complex deformable media;
- the derivation of effective interface laws for processes in domains involving thin structures or interfaces, separating and controlling the coupling of compartments in deformable (porous) media;
- the development of new concepts and analytical and numerical methods for homogenization in case of almost periodic or stochastic structures coupled with dimension reduction.
The following selected application areas will provide examples to be presented and discussed in the conference:
- modeling of physiological processes on the level of single cells, tissues, organs and organism;
- investigation of crucial endothelial and epithelial layers and their role in controlling the processes;
- physical-chemical and biological, fluid-mechanical and mechanical processes in geological layers particular in porous media, applications in agriculture, mining, water supply, geothermal energy supply, waste deposit;
- design of materials with optimized properties, based on their micro-structures; aging, corrosion and weathering of materials.
Invited speakers (tentative)
- Helmut Abels, University Regensburg
- Peter Bastian, Heidelberg University
- Anna Marciniak-Czochra, Heidelberg University
- Boris Muha, University of Zagreb
- Šárka Nečasová, Institute of Mathematics, Prague
- Felix Otto, Max Planck Institute for Mathematics in the Sciences in Leipzig
- Andrey Piatnitski, Arctic University of Norway, Narvik
- Sebastian Schwarzacher, Charles University, Prague
- Thomas Wick, Leibniz Universität Hannover
The conference will take place at the CAAS building in Dubrovnik, situated few hundred meters from the old walled city. The accomodation for the participants is available at the dormitory of CAAS or in some of the many hotels in Dubrovnik. The first lecture starts on Tuesday, March 19 in the morning, while the lectures finish on Friday March 22.
