Chaotic Behaviour of Hamiltonian Dynamical Systems. Study of a classical model of the hydrogen atom exposed to circularly polarized laser fields.

We have considered a classical model of the hydrogen atom exposed to a circularly polarized monochromatic electromagnetic wave. This model is related to similar models studied in various fields of physics, including the research in chaotic dynamics. The aim of the investigation has been to detect possible signs of stochasticity using the well established concept of Liapunov-exponents. The physical and mathematical background has been thoroughly explained and adaptions for the given problem have been made. The presented methods have been demonstrated using the H'enon-Heiles model and generalizations of it. The original problem has been simplified by a canonical transformation to the co-moving coordinate system of the lightwave. The properties of this transformation and it's quantum mechanical counterpart have been examined. Numerical methods have been used to integrate the classical equations of motion as well as the defining equations of the Liapunov exponents. In particular a time-tra..

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On estimating a dynamic function of stochastic system with averaging

We consider a two-scaled diffusion system, when drift and diffusion parameters of a 'slow' component are contaminated by an unobservable 'fast' one. The goal is to estimate the dynamic function which is defined by averaging the drift coefficient of the 'slow' component w.r.t. the stationary distribution of the 'fast' one. For estimation we use a locally linear smoother with a datadriven choice of bandwidth. A procedure proposed is fully adaptive and nearly optimal up to a log log factor. (orig.)Available from TIB Hannover: RR 5549(381) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Deviation probability bound for martingales with applications to statistical estimation

SIGLEAvailable from TIB Hannover: RR 5549(471)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

About a stationary Schroedinger-Poisson system with Kohn-Sham potential in nanoelectronics

The stationary Schroedinger-Poisson system with a self-consistent effective Kohn-Sham potential is a system of PDEs for the electrostatic potential and the envelopes of wave functions defining the quantum mechanical carrier densities in a semiconductor nanostructure. We regard both Poisson's and Schroedinger's equation with mixed boundary conditions and discontinuous coefficients. Without an exchange-correlation potential the Schroedinger-Poisson system is a nonlinear Poisson equation in the dual of a Sobolev space which is determined by the boundary conditions imposed on the electrostatic potential. The nonlinear Poisson operator involved is strongly monotone and boundedly Lipschitz continuous, hence the operator equation has a unique solution. The proof rests upon the following property: The quantum mechanical carrier density operator depending on the potential of the defining Schroedinger operator is anti-monotone and boundedly Lipschitz continuous. The solution of the Schroedinger-Poisson system without an exchange-correlation potential depends boundedly Lipschitz continuous on the reference potential in Schroedinger's operator. By means of this relation a fixed point mapping for the vector of quantum mechanical carrier densities is set up which meets the conditions in Schauder's fixed point theorem. Hence, the Kohn-Sham system has at least one solution. If the exchange-correlation potential is sufficiently small, then the solution of the Kohn-Sham system is unique. Moreover, properties of the solution as bounds for its values and its oscillation can be expressed in terms of the data of the problem. (orig.)Available from TIB Hannover: RR 5549(339)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Moderate deviations for integral functionals of diffusion process

Available from TIB Hannover: RR 5549(377) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Stochastic stability of structures under active control with distributed time delays

The pathwise behaviour of a single degree of freedom (SDOF) system with symmetric nonlinearity and distributed delays is investigated under the presence of seismic excitation and multiplicative noise. Besides distributed time delays and finite build-up time of control force are taken into consideration. The system is modelled as stochastic integro-differential equation with exponential type kernels. Interpreting stochastic equations in Stratonovich sense, stochastic stability is analyzed in terms of Lyapunov exponents. Estimates of frequencies with which sample paths of displacement of SDOF system cross certain critical values are also obtained. Studies of stochastic linear and nonlinear systems are carried out by resorting to numerical techniques for the solution of (ordinary) stochastic differential equations. (orig.)Available from TIB Hannover: RR 5549(181)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Sputtering - a key technology for thin film deposition in crystalline silicon solar cell production?

The novel sputter source TwinMag is used to deposit silicon nitride as an antireflection layer for crystalline silicon solar cells. TwinMag consists of two planar magnetrons, standing side by side and supplied with MF-power. The source is developed for large area coating and is able to deposit metal oxides and nitrides with high deposition rates. The characteristics of sputtered silicon nitride films have been investigated in respect to solar cell technology. First solar cells have been processed using TwinMag sputtered silicon nitride as an anti-reflection coating and simple industrial like processes. These cells yield efficiencies of up to 13.2% on 2 x 2 cm"2 multi-crystalline and 15.6% on 10 x 10 cm"2 mono-crystalline silicon and a corresponding open circuit voltage of up to 595 mV and 611 mV, respectively. These results imply that severe emitter damage does not occur due to the sputtering process. Also good optical characteristics have been found for the used layer. Surface recombination velocities below 1000 cm/s are deduced from lifetime measurements. The very high bond density of the sputtered films being measured by FTIR spectrometry demonstrates their high quality. Adding molecular hydrogen to the process a high content of up to 3 x 10"2"2 hydrogen atoms/cm"3 could be determined. These results indicate, that high quality surface passivation should also be possible for sputtered silicon nitride films. (orig.)Available from: http://www.ise.fhg.de / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman