The Navier-Stokes Equations with Time Delay

In the present paper we use a time delay epsilon > 0 for an energy conserving approximation of the nonlinear term of the non-stationary Navier-Stokes equations. We prove that the corresponding initial value problem (N_epsilon)in smoothly bounded domains G \subseteq R^3 is well-posed. Passing to the limit epsilon \rightarrow 0 we show that the sequence of stabilized solutions has an accumulation point such that it solves the Navier-Stokes problem (N_0) in a weak sense (Hopf).

Computing Generators of Free Modules over Orders in Group Algebras

Let E be a number field and G be a finite group. Let A be any O_E-order of full rank in the group algebra E[G] and X be a (left) A-lattice. We give a necessary and sufficient condition for X to be free of given rank d over A. In the case that the Wedderburn decomposition E[G] \cong \oplus_xM_x is explicitly computable and each M_x is in fact a matrix ring over a field, this leads to an algorithm that either gives elements \alpha_1,...,\alpha_d \in X such that X = A\alpha_1 \oplus ... \oplusA\alpha_d or determines that no such elements exist. Let L/K be a finite Galois extension of number fields with Galois group G such that E is a subfield of K and put d = [K : E]. The algorithm can be applied to certain Galois modules that arise naturally in this situation. For example, one can take X to be O_L, the ring of algebraic integers of L, and A to be the associated order A(E[G];O_L) \subseteq E[G]. The application of the algorithm to this special situation is implemented in Magma under certain extra hypotheses when K = E = \IQ.

Computations in Relative Algebraic K-Groups

Let G be finite group and K a number field or a p-adic field with ring of integers O_K. In the first part of the manuscript we present an algorithm that computes the relative algebraic K-group K_0(O_K[G],K) as an abstract abelian group. We solve the discrete logarithm problem, both in K_0(O_K[G],K) and the locally free class group cl(O_K[G]). All algorithms have been implemented in MAGMA for the case K = \IQ. In the second part of the manuscript we prove formulae for the torsion subgroup of K_0(\IZ[G],\IQ) for large classes of dihedral and quaternion groups.

Fluoreszenzspektroskopische Untersuchungen von Autoionisations- und Photodissoziationsprozessen des Stickstoffmoleküls nach monochromatischer Synchrotronstrahlanregung

Autoionisations- und Photodissoziationsprozesse von molekularem Stickstoff wurden mit Hilfe der photoneninduzierten Fluoreszenzspektroskopie nach Anregung von monochromatisierter Synchrotronstrahlung untersucht. Dabei wurden zwei Anregungsprozesse untersucht. Die Anregung eines Sub-Valenzschalenelektrons diente zum Studium des Photodissoziationsverhaltens von hochangeregten Zuständen ("super-excited-states") und die aus den Experimenten gewonnenen partiellen Emissionsquerschnitte wurden absolut normiert. Durch Anregen eines Innerschalenelektrons wurde die 1s^{-1}pi* Resonanz schwingungsselektiv angeregt und die darauf folgende Autoionisation in den N_2^+ C ^2\Sigma_u^+ (v)-Zustand und dessen Relaxation durch Fluoreszenzemission in den Grundzustand des Stickstoffions untersucht. Erstmalig wurden partielle Emissionsquerschnitte nach Photodissoziation in neutrale Fragmente von hochangeregten Zuständen von atomaren Stickstoff im Anregungsenergiebereich zwischen 23eV und 26,7eV und im Fluoreszenzwellenläneninterval zwischen 80nm und 150nm absolut bestimmt. Die schwingungsselektive Besetzung der Innerschalenresonanz des Stickstoffmoleküls ermöglichte eine detaillierte Analyse des Autoionisationsverhaltens der Innerschalenresonanz in den N_2^+ C-Zustand durch Analyse der nachfolgenden Relaxation durch molekulare Fluoreszenz in den Grundzustand des Molekülions.

Numerical Methods for Non-Stationary Stokes Flow

We consider a first order implicit time stepping procedure (Euler scheme) for the non-stationary Stokes equations in smoothly bounded domains of R3. Using energy estimates we can prove optimal convergence properties in the Sobolev spaces Hm(G) (m = 0;1;2) uniformly in time, provided that the solution of the Stokes equations has a certain degree of regularity. For the solution of the resulting Stokes resolvent boundary value problems we use a representation in form of hydrodynamical volume and boundary layer potentials, where the unknown source densities of the latter can be determined from uniquely solvable boundary integral equations’ systems. For the numerical computation of the potentials and the solution of the boundary integral equations a boundary element method of collocation type is used. Some simulations of a model problem are carried out and illustrate the efficiency of the method.

Freiraumqualität statt Abstandsgrün. - Band 1

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