Energy is one of the most valuable ressources of human life and as such requires its economic. In this context, mathematical modeling, simulation and optimization is of particular importance. The focus at the WIAS lies on problems of storage, conversion, transport and distribution of energy. The covered spectrum of applications reaches from the development of efficient technologies over the simulation and optimization of production processes to the modeling of energy markets.
Optimization problems in energy management are concerned with the planning of production and distribution of different energy sources (power, gas), in order to cover a given customer's demand. In this context, the consideration of transportation networks, of uncertainties and of market equilibria represent particular challenges.
The behavior of electrochemical systems is widely investigated with continuum physics models. Applications range from single crystal electrochemistry to lithium batteries and fuel cells, from biological nano-pores to electrolysis and corrosion science, and further.
Modern semiconductor and optoelectronic devices such as semiconductor lasers or organic field-effect transistors are based on semiconductor structures, which e.g. can be given by doping profiles, heterostructures or nanostructures. For the qualitative and quantitative understanding of the properties of these devices, mathematical modeling and simulation of the most relevant and, respectively, of the limiting carrier transport processes is necessary.
This work is focussed on the design of nanostructures and semiconductor simulations in photovoltaics as well as the production of solar silicon.
Phase transitions and hysteresis are characteristics of energy storage problems. The aim is to formulate and analyse a thermodynamical model which discribes the storage problem.
Dynamic process simulation has become an indispensable tool for design, analysis, and operation of complex plants in industry. Here initial value problems for large systems of differential-algebraic equations (DAEs) have to be solved. The simulation concept developed at WIAS exploits the modular structure of the process models to use divide-and-conquer techniques for solving the DAE system with block-structured methods. The concept is implemented in the Simulator BOP and has been successfully used in different industrial applications.
Thin films play an important role in nature and many areas of technological applications. In particular on micro- and nanoscales technological processes such as dewetting or epitaxial growth are used to design surfaces with specific material properties. Apart from the need to derive mathematical decriptions, analyis and numerical simulation, that serve to accelerate the development of new technologies, it is also exciting to understand material behaviour on these small scales.