- Projection of non-equilibrium processes Here I am working on problems concerning the mapping of complex multidimensional processes onto the symbolic motion in an abstract state space. Many processes in science and engineering are characterized by a large set of independent or coupled state variables. A complete understanding of these processes requires their complete knowledge at any instant of time and/or the knowledge of all external and internal interactions of the system. In many cases this information is nearly impossible to obtain (experimentally) or just gets too exhaustive and costly in computation and data-storage. The focus of my work is addressing, a) which quantities can be inferred from a limited amount of measurements/information of the system and b) how can we map the original dynamics of the system onto the symbolic motion in an abstract state space, so that important properties are conserved in the reduced process.
- Large-scale optimization Atoms and molecules can be arranged in various ways to form materials with different properties. A simple example is carbon. Both diamond and graphite consist of carbon atoms, the same type of atoms, but have very different properties from each other. Graphite is used in pencils; it is soft, black, and when you strike it on a piece of paper it shaves off its layers and leaves a trail. Diamond however is clear, sparkles when hold against light, and is one of the hardest substances known. So how can the same type of atoms form two such different states, and how many more such states exist? The answer to this lies in the structure. Atoms and molecules can be arranged in different ways to form different structures. Due to the interaction between them each structure will have a particular energy. Changes in the relative position of these particles to each other will either increase or decrease the energy, or may give the same energy. Stable or metastable states correspond to arrangements of the atoms in which slight changes in their position will increase the energy. In such a way that, if left by itself, the system has the tendency to fall back into the minimum. For complex materials or large enough systems many such minima exist, and systems consisting of the same building blocks but being in different minima can have distinctive different properties (like graphite and diamond).
Finding minima of complex systems is a computational challenging task, and many strategies have been developed in recent years. Here I am using evolutionary strategies to find low lying energy minima for amorphous systems. Evolutionary strategies in computation are methods which are inspired by biological and social phenomena. The underlying idea is to start with multiple versions of the same system, to cross and mutate them, and under some criteria choose the one(s) fittest for survival (in my case the ones lower in energy) to start the next generation.