Some Remarks on Modelling and Simulation of Physical Phenomena

Mathematical modelling and computer simulation of physical phenomena is a rapidly growing field of work in all areas of pure and applied sciences. In principle, mathematical modelling of physical phenomena has been the field of theoretical physics from the very beginning of physics although the computer has increased the potentials of this method by many orders of magnitude. Modelling and simulation are often used as synonyms. It may, however, be meaningfull to distinguish the development of a mathematical model from its use in computer simulation. Also, a mathematical model in this sense must be distinguished from mathematical expressions interpolating experimental data. In the field of textures, models of texture formation, models of materials properties, as well as the combination of the two are being used. In this connection it is important whether a texture formation model is linear or non-linear. In the first case the texture formation operator can be reduced to the orientation space whereas a non-linear operator operates in the full texture space.