Why do ecosystems suddenly fall out of balance? Or why do nerve cells in the brain unexpectedly change their behavior in neurological disorders? Dr. Christian Kühn hopes to develop new mathematical methods to improve the predictability of complex processes in such systems. The Volkswagen Foundation has now pledged funding for his planned research project at Technische Universität München (TUM) by way of a Lichtenberg professorship.
There are countless examples of ecosystems that follow well-known physical laws up to a specific point. But once a threshold is exceeded the behavior of the system changes abruptly.
“Multiscale Dynamical Systems Near Instability” is the title of a research project of the mathematician Dr. Christian Kühn that the Volkswagen Foundation is now funding with 890,000 euro. The goal of the project is to improve the predictability of various systems in their critical ranges.
The mathematical descriptions build primarily on so-called differential equations. In complex systems like ecosystems, neural processes and chemical reactions, these equations often give rise to the phenomenon of scale separation.
This is substantial in describing and simulating interrelated processes that do not necessarily happen simultaneously or at the same speed. Examples of time scale separation can be found in chemical reactions with many molecules in which the reactions do not all run at the same speed – some are faster while others are slower.
This effect can be exploited mathematically to effectively analyze and numerically calculate the systems of differential equations that describe comprehensive chemical reaction processes. In his Lichtenberg professorship, Kühn hopes to improve the mathematical basis of processes comprising multiple time and space scales.
Further Lichtenberg professorships were granted to the Leuphana Universität Lüneburg, the Universität Mainz and the Universität Potsdam. Since 2004 the Volkswagen Foundation has been funding interdisciplinary and innovative research projects of exceptional scientists with its Lichtenberg professorships. The next deadline for applications to the funding initiative is June 2nd, 2015.