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Workshop "Homogenization Theory and Applications -- 2017"
From 4th to 6th October 2017 at the Weierstrass Institute (WIAS) Berlin
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Welcome to the DFG collaborative research centre CRC 1114:
Scaling Cascades in Complex Systems
Complex processes involving cascades of scales are ubiquitous in current natural science research. Such processes feature more than two characteristic scales, their smallest and largest scales are widely separated, and much of their scale range participates in the process interactions. Also, they are often too complex for experimental studies, but with the steady increase of compute power there is hope that they can be understood through computational simulations. Such simulations remain very challenging, however, as their wide range of scales is associated with very large numbers of degrees of freedom and in many cases this will prohibit brute-force all-detail computational modeling far into the future. Moreover, interactions of the smallest, largest, and intermediate scales often render most established theoretical or computational tools ineffective or inapplicable because most of them are well founded only for two-scale problems.
To summarize the main challenge for this Collaborative Research Center, let us suppose we are interested in some “target features” of a particular process, such as the detailed evolution or statistics of some of its key variables. An efficient simulation across a cascade of scales then requires a controlled distribution of the computational degrees of freedom over the scale hierarchy such that each scale and subprocess is represented just adequately with respect to its impact on the modeling target. Yet, there are no systematic means of meeting this requirement today, even if a complete mathematical “root model” is available that describes the process in all detail. Moreover, in many practical situations the best available model for such a process is given only in the form of a computer code that is not amenable to mathematical analysis. In the worst-case scenario, scientists are even still in search of a satisfactory root model, so that the developments of detailed and reduced target-oriented descriptions have to be pursued in parallel.
This is the point of departure for the planned Cooperative Research Center (CRC). In three Research Areas, each focusing on a different characteristic problem class, scientists from Biochemistry, Physics, and the Geo-Sciences join forces with mathematicians. They follow the two-fold goal of making sizeable progress on challenging applications and of laying generalizeable methodological foundations on the way.
In short, we aim for
Methodological developments for the modeling and simulation of complex processes involving cascades of scales derived from prototypical challenges in the natural sciences.