Nonlinear potential analysis techniques for supersonic-hypersonic configuration design

Approximate nonlinear inviscid theoretical techniques for predicting aerodynamic characteristics and surface pressures for relatively slender vehicles at moderate hypersonic speeds were developed. Emphasis was placed on approaches that would be responsive to preliminary configuration design level of effort. Second order small disturbance and full potential theory was utilized to meet this objective. Numerical pilot codes were developed for relatively general three dimensional geometries to evaluate the capability of the approximate equations of motion considered. Results from the computations indicate good agreement with higher order solutions and experimental results for a variety of wing, body and wing-body shapes for values of the hypersonic similarity parameter M delta approaching one. Case computational times of a minute were achieved for practical aircraft arrangements

Nonlinear potential analysis techniques for supersonic-hypersonic aerodynamic design

Approximate nonlinear inviscid theoretical techniques for predicting aerodynamic characteristics and surface pressures for relatively slender vehicles at supersonic and moderate hypersonic speeds were developed. Emphasis was placed on approaches that would be responsive to conceptual configuration design level of effort. Second order small disturbance and full potential theory was utilized to meet this objective. Numerical codes were developed for relatively general three dimensional geometries to evaluate the capability of the approximate equations of motion considered. Results from the computations indicate good agreement with experimental results for a variety of wing, body, and wing-body shapes

Wavy stripes and squares in zero P number convection

A simple model to explain numerically observed behaviour of chaotically varying stripes and square patterns in zero Prandtl number convection in Boussinesq fluid is presented. The nonlinear interaction of mutually perpendicular sets of wavy rolls, via higher mode, may lead to a competition between the two sets of wavy rolls. The appearance of square patterns is due to the secondary forward Hopf bifurcation of a set of wavy rolls.Comment: 8 pages and 3 figures, late

Fractal Stability Border in Plane Couette Flow

We study the dynamics of localised perturbations in plane Couette flow with periodic lateral boundary conditions. For small Reynolds number and small amplitude of the initial state the perturbation decays on a viscous time scale $t \propto Re$. For Reynolds number larger than about 200, chaotic transients appear with life times longer than the viscous one. Depending on the type of the perturbation isolated initial conditions with infinite life time appear for Reynolds numbers larger than about 270--320. In this third regime, the life time as a function of Reynolds number and amplitude is fractal. These results suggest that in the transition region the turbulent dynamics is characterised by a chaotic repeller rather than an attractor.Comment: 4 pages, Latex, 4 eps-figures, submitted to Phys. Rev. Le

Spiral Defect Chaos in Large Aspect Ratio Rayleigh-Benard Convection

We report experiments on convection patterns in a cylindrical cell with a large aspect ratio. The fluid had a Prandtl number of approximately 1. We observed a chaotic pattern consisting of many rotating spirals and other defects in the parameter range where theory predicts that steady straight rolls should be stable. The correlation length of the pattern decreased rapidly with increasing control parameter so that the size of a correlated area became much smaller than the area of the cell. This suggests that the chaotic behavior is intrinsic to large aspect ratio geometries.Comment: Preprint of experimental paper submitted to Phys. Rev. Lett. May 12 1993. Text is preceeded by many TeX macros. Figures 1 and 2 are rather lon

Thermodynamic Driving Forces of Guest Confinement in a Photoswitchable Cage

Photoswitchable cages that confine small guest molecules inside their cavities offer a way to control the binding/unbinding process through irradiation with light of different wavelengths. However, a detailed characterization of the structural and thermodynamic consequences of photoswitching is very challenging to obtain by experiment alone. Thus, all-atom molecular dynamics (MD) simulations were carried out to gain insight into the relationship between structure and binding affinity. Binding free energies of the B12F122- guest were obtained for all photochemically accessible forms of a photoswitchable dithienylethene (DTE) based coordination cage. The MD simulations show that successive photo-induced closure of the four individual DTE ligands that form the cage gradually decreases the binding affinity. Closure of the first ligand already significantly lowers the unbinding barrier and the binding free energy, and therefore favours guest unbinding both kinetically and thermodynamically. Analysis of the different enthalpy contributions to the free energy shows that binding is enthalpically unfavourable and thus an entropy-driven process, in agreement with experimental data. Dissecting the enthalpy into the contributions from electrostatic, van der Waals, and bonded interactions in the force field shows that the unfavourable binding enthalpy is due to the bonded interactions being more favourable in the dissociated state, suggesting the presence of structural strain in the bound complex. Thus, the simulations provide microscopic explanations for the experimental findings and open a possible route towards the targeted design of switchable nanocontainers with modified binding properties

Orientational self-sorting in cuboctahedral Pd cages

Cuboctahedral coordination cages of the general formula [Pd12L24]24+ (L = low-symmetry ligand) were analyzed theoretically and experimentally. With 350 696 potential isomers, the structural space of these assemblies is vast. Orientational self-sorting refers to the preferential formation of particular isomers within the pool of potential structures. Geometric and computational analyses predict the preferred formation of cages with a cis arrangement at the metal centers. This prediction was corroborated experimentally by synthesizing a [Pd12L24]24+ cage with a bridging 3-(4-(pyridin-4-yl)phenyl)pyridine ligand. A crystallographic analysis of this assembly showed exclusive cis coordination of the 3- and the 4-pyridyl donor groups at the Pd2+ ions

Quasiperiodic waves at the onset of zero Prandtl number convection with rotation

We show the possibility of quasiperiodic waves at the onset of thermal convection in a thin horizontal layer of slowly rotating zero-Prandtl number Boussinesq fluid confined between stress-free conducting boundaries. Two independent frequencies emerge due to an interaction between a stationary instability and a self-tuned wavy instability in presence of coriolis force, if Taylor number is raised above a critical value. Constructing a dynamical system for the hydrodynamical problem, the competition between the interacting instabilities is analyzed. The forward bifurcation from the conductive state is self-tuned.Comment: 9 pages of text (LaTex), 5 figures (Jpeg format

Steuerung der ultraschnellen Öffnungs‐ und Schließungsdynamik eines photochromen Koordinationskäfigs durch Gastmoleküle

Photochemische Studien über supramolekulare Wirte, die kleine Gastmoleküle einkapseln können, konzentrieren sich zumeist auf drei Aspekte: Die Photoschaltung des Käfigs, um den Gast freizusetzen oder einzufangen, die Wirkung der Käfigumgebung auf den Gast und die lichtinduzierte Exzitonen- oder Ladungsübertragung innerhalb der Käfigstruktur. Hier nutzen wir ultraschnelle Spektroskopie, um zu untersuchen, wie der Gast die Photoschaltcharakteristik des Käfigs verändert. Zu diesem Zweck werden die Auswirkungen von drei unterschiedlichen Gastmolekülen auf die Ringöffnung oder den Ringschluss eines Dithienylethen (DTE)-Liganden in einem photoschaltbaren Koordinationskäfig auf DTE-Basis einander gegenübergestellt. Der Gast moduliert sowohl das Ergebnis als auch die Zeitskala der Photodynamik des Käfigs durch ein Zusammenspiel von struktureller Wechselwirkung, dem Schweratomeffekt und einer Verstärkung von Ladungstransferprozessen, die der Gast auf den photoangeregten Käfig ausübt. Der Ansatz könnte sich als nützlich erweisen, um die Anwendbarkeit von photoschaltbaren Nanocontainern und gewünschten Gastverbindungen aufeinander abzustimmen

Steering the Ultrafast Opening and Closure Dynamics of a Photochromic Coordination Cage by Guest Molecules

Photochemical studies on supramolecular hosts that can encapsulate small guest molecules commonly focus on three aspects: photoswitching the cage to release or trap the guest, the effect of the confining environment on the guest, and light-induced exciton or charge transfer within the cage structure. Here, we exploit ultrafast spectroscopy to address how the guest alters the photoswitching characteristics of the cage. For this, the impacts of three disparate guest compounds on ring-opening or ring-closure of a dithienylethene (DTE) ligand in a photoswitchable DTE-based coordination cage are juxtaposed. The guest modulates both outcome and timescale of the cage's photodynamics, by an interplay of structural strain, heavy-atom effect, and enhancement of charge-transfer processes exercised by the guest on the photo-excited cage. The approach might prove beneficial for attuning the applicability of photoswitchable nanocontainers and desired guest compounds