## Berichte der Arbeitsgruppe Technomathematik (AGTM Report)

- 37
- Adaptive Synchronization of Interconnected Linear Systems (1990)
- In this paper we introduce the concept of an adaptive synchronization controller. Synchronization is modelled as an adaptive tracking problem for families of interconnected linear systems. Stabilization and tracking results are obtained for minimum phase systems.

- 41
- Multiscale Analysis, Wavelets and Texture Quality (1990)
- Fleeces made from artificial fabric are the basic material for many products, ranging from carpets to napkins. Itturns out that their quality is determined by the distribution of the fibres, which can be measured eithter by the optical transmission properties or by the thickness of the material. In both cases one obtains a 2-dimensional signal and one would like to have an objective quality criterion, based on a suitable analysis of these data, which, moreover, can be automated.; In this paper we propose a solution to this problem, based on multiresolution techniques, which have been developed in image analysis through the last few years. Moreover, we use these techniques to investigate fractal properties of the textures.

- 42
- A Deterministic Particle Method for the Simulation of the Boltzmann Transport Equation of Semiconductors (1990)
- We present a deterministic simulation scheme for the Boltzmann Semiconductor Equation. The convergence of the method is shown for a simplified space homogeneous case. Numerical experiments, which are very promising, are also given in this situation. The extension for the application to the space inhomogeneous equation with a self consistent electric field is quoted. Theoretical considerations in that case are in preparation.

- 43
- Computational Methods for the Boltzmann Equation (1990)
- This paper contains the basic ideas and practical aspects for numerical methods for solving the Boltzmann Equation. The main field of application considered is the reentry of a Space Shuttle in the transition from free molecular flow to continuum flow. The method used will be called Finite Pointset Method (FPM) approximating the solution by finite sets of particles in a rigorously defined way. Convergence results are cited while practical aspects of the algorithm are emphasized. Ideas for the transition to the Navier Stokes domain are shortly discussed.

- 44
- Universal Adaptive Stabilizers for One-Dimensional Nonlinear Systems (1990)
- The purpose of this paper is twofold: first, to present universal adaptive stabilizers for large classes of one-dimensional nonlinear systems, and second, to derive results on the decay rate of the closed loop solutions, which for linear systems turns out to be exponential in the generic case.

- 45
- Quality Control of Artificial Fabrics (1990)
- Some new approaches to measure irregularities of artificial tissues are introduced.

- 46
- A Comparison of a Microscopic and a Phenomenological Model for a Polyatomic Gas (1990)
- Treating polyatomic gases in kinetic gas theory requires an appropriate molecule model taking into account the additional internal structure of the gas particles. In this paper we describe two such models, each arising from quite different approaches to this problem. A simulation scheme for solving the corresponding kinetic equations is presented and some numerical results to 1D shockwaves are compared.

- 47
- Several Computer Studies on Boltzmann Flows in Connection with Space Flight Problems (1990)
- This report contains the following three papers about computations of rarefied gas flows:; ; a) Rarefied gas flow around a disc with different angles of attack, published in the proceedings of the 17th RGD Symposium, Aachen, 1990.; ; b) Hypersonic flow calculations around a 3D-deltawing at low Knudsen numbers, published in the proceedings of the 17th RGD Symposium,; Aachen, 1990.; ; c) Rarefied gas flow around a 3D-deltawing, published in the proceedings of the Workshop on Hypersonic Flows for Reentry Problems,; Part 1, Antibes, France, January 22-25, 1990.; ; All computations are part of the HERMES Research and Development Program.

- 49
- On the Moving Preisach Model (1990)
- It is shown that the moving model, which is a variant of the Preisach model for hysteresis, possesses the wiping out property and is continuous in C[0,T] under natural assumptions.