Non-linear static and dynamic deformations of shells of revolution†

The rate equation method, previously developed by the authors, is extended to the analysis of static and dynamic finite deformations of shells of revolution. As an example of the technique, the static and dynamic response of an initially flat plate under spatially uniform, but time varying pressure, is analyzed. Full non-linear shell equations are used in the analysis, and results are presented for large static deflections as well as for large amplitude free and forced vibrations.

The accuracy of the rate equation method is verified by comparison with known solutions obtained by other methods. This comparison also establishes the superiority of the rate equation method over other existing methods as far as calculation times and computer storage requirements are concerned.     

Preparation and Chromatographic Characterization of Tetrahydrogestrinone, a New “Designer” Anabolic Steroid

Tetrahydrogestrinone (THG, (17)-13-ethyl-17-hydroxy-18,19-dinorpregna-4,9,11-trien-3-one, C₂₁H₂₈O₂, 312 m.w.) is a synthetic 19-norsteroid closely related to gestrinone ((17)-13-ethyl-17-hydroxy-18,19-dinorpregna-4,9,11-trien-20-yn-3-one, C₂₁H₂₄O₂, 308 m.w.) which was originally developed as an oral contraceptive for women. Recent press reports detail the probable use of THG by athletes to enhance athletic performance, and the FDA has banned THG, declaring it a designer drug. THG has been difficult to analyze because of its instability, lack of commercially available analytical standards, and the fact that no published synthetic methods for the compound exist. We now report a method for the preparation of THG via the carefully controlled hydrogenation of gestrinone.Published as #350 from the Equine Pharmacology, Therapeutics and Toxicology Laboratory at the Maxwell H. Gluck Equine Research Center, Department of Veterinary Science, University of Kentucky.Published as Kentucky Agricultural Experiment Station Article #;04-14-052 with the approval of the Dean and Director, College of Agriculture and the Kentucky Agricultural Experiment Station.     

On the relaxation of anisotropic plasmas with dynamic shielding

The relaxation of a strongly anisotropic two-component-plasma is treated by using the Balescu-Lenard-equation, i.e. taking into account collective effects. The relaxation process is described by parallel and perpendicular temperatures as functions of time; it is assumed that the distribution functions remain elliptical. The result is that collective effects are only significant if the ratio of electron and ion temperatures is very small (<10^?4) or very large (>10⁺²).     

B-convergence properties of defect correction methods. I

Summary B-convergence properties of defect correction methods based on the implicit Euler and midpoint schemes are discussed. The property ofB-convergence means that there exist global error bounds for nonlinear stiff problems independent of their stiffness. It turns out that the orders ofB-convergence of these methods coincide with the conventional orders of convergence of these methods derived under the assumption that.hL is small (whereL is a Lipschitz constant of the right-hand side). In Part I these assertions are reduced to the validity of the so-called Hypothesis A which is discussed in greater detail in Part II. Numerical experiments confirming the theoretical analysis are also given in Part II.     

Circulardichroismus und Elektronenanregungsspektren chiraler [2,2]Metacyclophane

Zusammenfassung Aus den optischen und chiroptischen Eigenschaften substituierter [2,2]Metacyclophane, aus einem Vergleich mit substituierten [10]Paracyclophanen sowie aus Symmetriebetrachtungen an prochiralen Carbophanen kann geschlossen werden, daß für das Zustandekommen nicht-orthogonaler elektrischer und magnetischer Momente in diesen Verbindungen Dipol-Dipol-Kopplung nicht verantwortlich ist; vielmehr scheint es sich um eine hauptsächlich durch Schwingungen vermittelte Störung eines inhärent achiralen, aromatischen Chromophors zu handeln. Auf Grund desCD scheint die Annahme transanularer --Wechselwirkungen in [2,2]Metacyclophanen auch im angeregten Zustand nicht gerechtfertigt.

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Circulardichroism and electron absorption spectra of chiral [2.2]metacyclophanes

From the optical and chiroptical properties of substituted [2.2]metacyclophanes and a comparison with substituted [10]paracyclophanes as well as by symmetry arguments regarding prochiral carbophanes can be deduced that dipol-dipol coupling is not responsible for the generation of non-orthogonal electrical and magnetical moments in these compounds; pressmably one is dealing with an inherently achiral aromatic chromophore mainly perturbed by vibrations. Even in the exited state the assumption of transanular --interactions in [2.2]metacyclophanes is not justified as can be seen from theCD-spectra.

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Mit 4 Abbildungen     

Stabilization of the kerr effect by self-induced ionization: formation of optical light spatially localized structures

The nonlinear propagation of ultrashort laser pulses launched into the air is investigated. The formation of optical light "bullets," or spatially localized structures, has been experimentally observed recently. Their stability is shown as due to the occurrence of a dynamical balance between two opposite nonlinear effects: an optical focusing Kerr effect balanced by a defocusing self-induced multiphoton partial ionization of the neutral gas. Characteristics of the "bullets" are predicted analytically and confirmed numerically. They are found to be in agreement with observations.     

Ambient Catalytic Spinning of Polyethylene Nanofibers

A novel single-atom Ni(II) catalyst ( Ni-OH ) is covalently immobilized onto the nano-channels of mesoporous Santa Barbara Amorphous (SBA)-15 particles and isotropic Anodized Aluminum Oxide (AAO) membrane for confined-space ethylene extrusion polymerization. The presence of surface-tethered Ni complexes ( Ni@SBA-15 and Ni@AAO ) is confirmed by the inductively coupled plasma-optical emission spectrometry (ICP-OES) and X-ray photoelectron spectroscopy (XPS). In the catalytic spinning process, the produced PE materials exhibit very homogeneous fibrous morphology at nanoscale (diameter: ~50 nm). The synthesized PE nanofibers extrude in a highly oriented manner from the nano-reactors at ambient temperature. Remarkably high M_w (1.62×10⁶ g mol⁻¹), melting point (124 °C), and crystallinity (41.8 %) are observed among PE samples thanks to the confined-space polymerization. The chain-walking behavior of surface tethered Ni catalysts is greatly limited by the confinement inside the nano-channels, leading to the formation of very low-branched PE materials (13.6/1000 C). Due to fixed supported catalytic topology and room temperature, the filaments are expected to be free of entanglement. This work signifies an important step towards the realization of a continuous mild catalytic-spinning (CATSPIN) process, where the polymer is directly synthesized into fiber shape at negligible chain branching and elegantly avoiding common limitations like thermal degradation or molecular entanglement.     

A simple model for a two-stage chemical reaction with diffusion

We analyse the evolution of a two-stage chemical reaction betweentwo neighbouring plumes of reactants. Under the assumption thatthe plumes are approximately Gaussian we derive a system ofordinary differential equations for the total amount, the centroidand the variance of each reactant. We compare the solution ofthese equations with full numerical simulation of the reaction.Excellent agreement is obtained, with solution of the near-Gaussianmodel requiring considerably less computational effort thanthe full simulations. Of key importance is the yield of thereaction, and we discuss this feature in particular.