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We have studied bifurcation phenomena for the incompressable Navier-Stokes equations in two space dimensions with periodic boundary conditions. Fourier representations of velocity and pressure have been used to transform the original partial differential equations into systems of ordinary differential equations (ODE), to which then numerical methods for the qualitative analysis of systems of ODE have been applied, supplemented by the simulative calculation of solutions for selected initial conditions. Invariant sets, notably steady states, have been traced for varying Reynolds number or strength of the imposed forcing, respectively. A complete bifurcation sequence leading to chaos is described in detail, including the calculation of the Lyapunov exponents that characterize the resulting chaotic branch in the bifurcation diagram.
A novel atomic beam splitter, using reflection of atoms off an evanescent light wave, is investigated theoretically. The intensity or frequency of the light is modulated in order to create sidebands on the reflected de Broglie wave. The weights and phases of the various sidevands are calculated using three different approaches: the Born approximation, a semiclassical path integral approach, and a numerical solution of the time-dependent Schrdinger equation. We show how this modulated mirror could be used to build practical atomic interferometers.
We present a semiclassical perturbation method for the description of atomic diffraction by a weakly modulated potential. It proceeds in a way similar to the treatment of light diffraction by a thin phase grating, and consists in calculating the atomic wavefunction by means of action integrals along the classical trajectories of the atoms in the absence of the modulated part of the potential. The capabilities and the validity condition of the method are illustrated on the well-known case of atomic diffraction by a Gaussian standing wave. We prove that in this situation the perturbation method is equivalent to the Raman-Nath approximation, and we point out that the usually-considered Raman-Nath validity condition can lead to inaccuracies in the evaluation of the phases of the diffraction amplitudes. The method is also applied to the case of an evanescent wave reflection grating, and an analytical expression for the diffraction pattern at any incidence angle is obtained for the first time. Finally, the application of the method to other situations is briefly discussed.
A detailed theoretical investigation of the reflection of an atomic de Broglie wave at an evanescent wave mirror is presented. The classical and the semiclassical descriptions of the reflection process are reviewed, and a full wave-mechanical approach based on the analytical soution of the corresponding Schrödinger equation is presented. The phase shift at reflection is calculated exactly and interpreted in terms of instantaneous reflection of the atom at an effective mirror. Besides the semiclassical regime of reflection describable by the WKB method, a pure quantum regime of reflection is identified in the limit where the incident de Broglie wavelength is large compared to the evanescent wave decay length.
Strange nonchaotic attractors typically appear in quasiperiodically driven nonlinear systems. Two methods of their characterization are proposed. The first one is based on the bifurcation analysis of the systems, resulting from periodic approximations of the quasiperiodic forcing. Secondly, we propose th characterize their strangeness by calculating a phase sensitivity exponent, that measures the sensitivity with respect to changes of the phase of the external force. It is shown, that phase sensitivity appears if there is a non-zero probability for positive local Lyapunov exponents to occur.
Two deterministic processes leading to roughening interfaces are considered. It is shown that the dynamics of linear perturbations of turbulent regimes in coupled map lattices is governed by a discrete version of the Kardar-Parisi-Zhang equation. The asymptotic scaling behavior of the perturbation field is investigated in the case of large lattices. Secondly, the dynamics of an order-disorder interface is modelled with a simple two-dimensional coupled map lattice, possesing a turbulent and a laminar state. It is demonstrated, that in some range of parameters the spreading of the turbulent state is accompanied by kinetic roughening of the interface.
Zur Ökologisierung des Lernprozesses : Versuch über einen vernachlässigten Aspekt von Umweltbildung
(1993)
Langmuir-Blodgett(LB) multilayers were prepared from disc-shaped multiyne mesogens based on amphiphilic alkyl pentakis(aryl-ethynyl)benzene ethers. The two compounds used are characterized by five hydrophobic flexible chains and one hydrophilic substituent at the terminal position of the alkoxy chain. The LB films were analysed by X-ray scattering and spectroscopic measurements. An edge-on arrangement of the two discotic pentaalkynes within Y-type bilayers with a different packing density proved to be possible for the LB films of both compounds.
The possibilities and limits of structure refinement of Langmuir-Blodgett films by means of symmetrical reflection of X- rays are described using the example of a stearic acid multilayer. Three different techniques for the determiantion of the electron density profile from reflectivity data are compared; a Fourier method, a Patterson method, and model calculations. The important role of the a priori information for finding the besft structure model is outlined.
Combining issues of "girl-suited" science teaching, STS and constructivism in a physics textbook
(1992)
Intermolekulare Desaktivierung zwischen einem angeregten Fluorophor und einem Löscher durch Elektronenübertragung kann mit dynamischer und statischer Löschung beschrieben werden. Es wird vorgeschlagen den dynamischen Löschprozess in Transport- und Wechselwirkungsphase einzuteilen. Ergebnisse der Löschung der N-Heteroarene durch Naphthalen bei hohen Löscherkonzentrationen werden mit der statischen Löschung beschrieben. Außerdem werden CT-Systeme untersucht. Nach einem Überblick über statische Modelle zum Resonanzenergietransfer wird ein aus der Treffertheorie abgeleitetes Modell vorgestellt und an Beispielen getestet. Die Experimente sind computergesteuert.
An einigen CT-Modellkomplexen in verschiedenen Lösungsmitteln und bei Temperaturen von 113-300 K sollte der Einfluß der Umgebung auf die Form und Lage der Absorption von CT-Komplexen unterschiedlicher Bindungsfestigkeit untersucht werden.
Dazu wurden bekannte Bandenprofilfunktionen auf ihre Anwendbar-keit geprüft. Da eine optimale Anpassung nicht möglich war, wurde eine neue Profilfunktion entwickelt, die eine bessere Beschreibung ergab.
Nach der Bestimmung der Gleichgewichtskonstante und des Extink-tionskoeffizienten konnte mit der Profilfläche das Übergangsmoment berechnet werden.
Die Lösungsmittelabhängigkeit wurde bei verschiedenen Brechzahlen und Dielektrizitätskonstanten untersucht.
Für feste Komplexe wurde eine spezielle Präparationstechnik gewählt. Die beobachteten Feinstrukturen und der auftretende Streuuntergrund werden diskutiert.
The simultaneous switching activity in digital circuits challenges the design of mixed-signal SoCs. Rather than focusing on time-domain noise voltage minimization, this work optimizes switching noise in the frequency domain. A two-tier solution based on the on-chip clock scheduling is proposed. First, to cope with the switching noise at the fundamental clock frequency, which usually dominates in terms of noise power, a two-phase clocking scheme is employed for system timing. Second, on-chip clock latencies are manipulated to target harmonic peaks in specific frequency bands for the spectral noise optimization. An automated design flow, which allows for noise optimization in user-defined application-specific frequency bands, is developed. The effectiveness of our design solution is validated by measurements of substrate noise and conductive EMI (electromagnetic interference) noise on a test chip, which consists of four wireless sensor node baseband processors each addressing a distinct clock-tree-synthesis strategy. Compared to the reference synchronous design, the proposed clock scheduling solution substantially reduces noise in the target GSM-850 band, i.e., by 11.1 dB on the substrate noise and 12.9 dB on the EMI noise, along with dramatic noise peak drops measured at the 50-MHz clock frequency.