(Diplom-, Bachelor-, Masterarbeit, SEP)

Nanoscience is a new discipline underlying so-called nanotechnology - a generic term for a variety of techniques dealing with very small (more exactly - mesoscopic) objects. Nanoscience develops regular methods allowing one to analyze and predict the properties of nanoobjects. Computational nanoscience is an emerging part of nanoscience providing the methods of computer simulation of nanostructures and nanotechnological processes. From the mathematical viewpoint, analysis of nanostructures is based on the Schrödinger equation to be applied to different regimes, i.e. containing different (variable!) coefficients and supplied with a variety of boundary conditions. In this sense, computational nanoscience (CNS) is ananlogous to Computational Fluid Dynamics (CFD), only the first is based on the Schrödinger equation (as practically the whole condensed matter science) whereas the second, in its major part, on the Navier-Stokes equation. As in the case of the N.-S. equation, the Schrödinger equation is hard to solve despite its seeming simplicity, and quite intricate methods of its solution have recently appeared (e.g. based on supersymmetric factorization and eigenfunction ansatz).There also exists a quasi-hydrodynamic approach in nanoscience, when the Schrödinger equation is reduced to the CFD-like equations, with the latter being solved by the methods generally adopted in CFD (e.g. moving and unstructured grids, etc.). There are, however, many questions pertaining to this approach, so it can also be a possible field of research.

Prof. Dr. E. W. Mayr

S. Pankratov (pankrato@in.tum.de)

D. Chibisov (chibisov@in.tum.de)

A number of analytical results needed to understand the processes in nanostructures have already been produced. Now the phase of the application of these results to specific engineering problems is coming, with the concrete parameter values, visualization, etc. The primary task, as far as numerics goes, may be just to translate formulas, e.g. some Schrödinger equation solutions, into a C-code. Beyond translating formulas into code, scientific computing, in particular in the nanofield, is also concerned with making up a program to run a specific job by using libraries, storing and postprocessing data, interpreting, vizualizing and presenting results in the form convenient for engineers or managers. The ultimate purpose would be to create a tool (e.g. on Java) for nano-engineers enabling them to analyze the nanostructures and their behavior by ascribing specific values to predesigned fields. In fact, it should be a number of tools for a variety of nanostructures and processes in them.

Mathematics (analysis and differential equations), some interest in physics-based modeling, knowledge of Maple and/or Mathematica);

Matlab would also be an asset.

Java (C/C++ or C#) programming abilities are indispensable for some part of this work.