Resonant non-linear vibrations in continuous systems—I. Undamped case

A method is presented for obtaining periodic solutions to forced oscillations of non-linear systems governed by equations of the form u_ss?u_yy?εf(u,u,_y,u_yy…,s) = 0. The method is presented by application to the equation u_ss?u_yy?εu²_yu_yy= 0 which governs the vibrations of a soil layer that is free on the top surface and is forced harmonically at the bedrock. It is shown that unlike the ODE case (Duffing equation), the PDE requires an infinite number of periodicity conditions to correctly characterize the resonant region and these conditions lead to an infinite number of branches in the dispersion spectrum. Calculations indicate that these branches tend to an envelope curve. The uniform approach presented by Millmann and Keller is discussed in order to determine in what sense it can be viewed as an effective approximation for the fundamental mode.     

Single crystal X-ray structure and optical properties of anthraquinone-based dyes

This study focuses on the preparation, single crystal X-ray diffraction, characterization, and optical properties of some anthraquinone-based dyes. The anthraquinone-based antimicrobial dye N-{2-[(9,10-dioxo-9,10-dihydroanthracen-1-yl)amino]-2-oxoethyl}-N,N-dimethylbutan-1-aminium chloride monohydrate (III) was obtained from 1-aminoanthraquinone (I) via 2-chloro-N-(9,10-dioxo-9,10-dihydroanthracen-1-yl)acetamide (II) using known preparation and characterization methods. Single crystal X-ray diffraction analysis of III revealed a monoclinic system, space group P2₁/n, Z = 4. Photoluminescence properties of anthraquinone dyes I–III were also investigated. These dyes gave an intense emission (λ_max = 341 nm) upon the irradiation by UV light and showed photoluminescence quantum yields of 73 %, 66 %, and 61 % with long excited-state lifetimes of 6.87 ns, 6.14 ns, and 5.69 ns, respectively. These anthraquinone dyes are of interest as an organic light emitting material for electroluminescent devices.     

Synthesis and characterization of novel antimicrobial cationic polyelectrolytes

Cationic polyelectrolytes containing quaternary nitrogen atoms within the main chain were prepared via condensation polymerization of epichlorhydrin (ECH) with benzyl amine (BA). Polyelectrolytes having different molecular weights were obtained by varying the ECH/BA mole ratio. Cationic polymers were characterized by ¹H-NMR and gel permeation chromatography. The antimicrobial activity of the polymers was tested against bacteria, yeast, and fungi.     

An analysis of the reflective component of small-angle X-ray scattering patterns from crazed polystyrene

An investigation of the reflective component of small-angle x-ray scattering patterns of polystyrene crazes is performed. It is shown that the strong streak parallel to the tensile axis consists predominantly of reflected radiation, while the remaining pattern is composed entirely of diffracted radiation. X-ray reflection off unparallel regions of crazes is discussed and the nature of the reflection is also considered in terms of collimation quality. An analysis methodology based on craze tip angular distribution is proposed.     

On-line small-angle and wide-angle x-ray scattering studies on melt-spinning poly(vinylidene fluoride) tape using synchrotron radiation

On-line small-angle and wide-angle x-ray scattering experiments were performed during the melt spinning of polyvinylidene fluoride using the DESY synchrotron light source. In these studies, the melt-spinning apparatus consisting of a screw extruder, a metering pump, and a take-up motor system were assembled on two separate stepper-motor-driven platforms. To investigate the structure development during crystallization, the tape location at the desired distance from the die could be positioned at the beam level with synchronous vertical movement of extruder and take-up platforms. Small-angle and wide-angle x-ray patterns were taken simultaneously with a two-dimensional wire detector and one-dimensional wire detector. In a separate study, two-dimensional WAXS data were also taken under identical processing conditions to observe the off-equator diffraction behavior during the crystallization. The data obtained for a variety of take-up speeds generally indicate that SAXS d-spacings first appear large in the early stages of crystallization and gradually decrease along the spin-line (as the crystallization progresses). As the take-up speed increases, the crystallization onset position moves away from the die and d-spacings observed at the onset increase. In addition, the shape of the discrete scattering pattern starts as a meridional streak and converts to a teardrop shape with the tip of the pattern pointing toward the beam stop at the early stages of crystallization for high take-up speeds. This does not occur at low take-up speeds and is attributed to the differences in crystallization behavior which is spherulitic or sheaflike to row nucleated crystallites. Our studies also showed that SAXS patterns appear earlier than the wide-angle crystalline diffraction peaks indicating the SAXS technique to be more sensitive to the structural changes at these stages. An idealized model is developed to explain the observed patterns at high take-up speeds. This consists of two regimes. In regime 1, the periodic fluctuations due to the alternating crystalline and amorphous regions form along the regions where eventually the “shish” structures develop. In the second stage, a volume filling crystallization takes place between the existing crystallites along the shish structure and simultaneously radial overgrowth of crystallites (i.e., the “kebabs”) takes place. This causes the observed reduction in the average d-spacing. © 1993 John Wiley & Sons, Inc.     

The investigation of 0<Superscript>+</Superscript> ↔ 0<Superscript>−</Superscript><Emphasis Type="Italic">β</Emphasis> decay in some spherical nuclei

The 0⁺ ↔ 0⁻ first-forbidden β decay transitions have been investigated for some spherical nuclei. The theoretical framework is based on a proton-neutron quasiparticle random phase approximation (pnQRPA). The Woods-Saxon potential basis has been used in our calculations. The transition probabilities have been calculated within the ξ approximation. The relativistic β moment matrix element has been calculated both directly without any assumption and assuming that it is proportional to the non-relativistic one.