# Current main focuses

## Population dynamics

Population dynamic systems are characterized as an accumulation of a large number of single elements which vary in certain properties. These systems appear in various forms. A simple example is the human population. Single individuals differ, for example, in their age. How this age distribution will develop in the future is dependent on birth and mortality rates, as well as on immigration and emigration.

Many processes in engineering can also be modelled using a population dynamic system. Particle suspensions or emulsions, in which particles or liquid drops are surrounded by a continuous fluid, represent some examples of this. The most prominent distinctive feature in this case is the size of the particles or liquid drops. Analogous to the previously mentioned development of the age distribution, process systems engineering is interested in the size distribution of the disperse phase. Additionally, biological populations like yeast cell suspensions, in which the cells vary in age and activity, can be described.

As physicochemical, biological or sociological phenomena, these populations are so strongly different it is remarkable that those systems can be described with the same mathematical tools. The further development and use of those tools to generate predictive models, for the analysis and optimization of population dynamic processes is the aim of this research group.

## Multiscale modeling

Many technologically important processes cannot be predicted satisfactorily on one scale. An example is the growth rate of a crystal in an oversaturated solution. This rate can be determined through repetitive measurements of the crystal-size distribution. Thereby, the measurement technique usually covers a range from micrometers up to several millimetres. However, the phenomena responsible for crystal growth occur on a molecular level and therefore on a much smaller scale. In order to model both scales individually, it is possible to use established techniques but these all exhibit different restrictions. A continuum-based approach to describe the crystal is easy to realise and an appropriate model is easy to solve numerically. Unfortunately, prediction, unlike description, is not possible with this tool. An approach based on molecular dynamics can simulate the actual growth of a crystal layer. Here, the restriction is that prediction of crystal growth is only possible for very short timescales (a few nanoseconds). Therefore the technical relevance of molecular-dynamics models is limited.

Multiscale modelling or multiscale simulation combines modelling techniques (such as continuum and molecular dynamics) by utilising mathematical and algorithmic techniques. The resulting hybrid model includes the advantages of both approaches. Prediction is possible on a technically relevant timescale. While multiscale techniques can be used in various fields, our current research focuses on aggregation and restructuring processes. Examples include colloidal systems and crystal growth in solutions.