A comparison of spin relaxation and local motion between symmetrically and asymmetrically ring-substituted bisphenol units in dissolved polycarbonates

Carbon-13 and proton spin-lattice relaxation times were measured at two field strengths on solutions 10% by weight of two polycarbonates in C₂D₂Cl₄ from ?20 to +120°C. The first polycarbonate is an asymmetrically substituted form with one chlorine on one of the two phenylene aromatic rings of the bisphenol unit, whereas the second polycarbonate is symmetrically substituted with two chlorines on each of the two rings. The nuclear spin relaxation data are interpreted in terms of several local motions likely in these polymers. Segmental motion was described by the Hall–Helfand correlation function. Segmental motion in the monosubstituted polycarbonate is somewhat slower than in unsubstituted polycarbonate, whereas segmental motion in the tetrasubstituted polycarbonate is considerably slower. Phenylene ring rotation is observed in unsubstituted polycarbonate and in the monosubstituted polycarbonate above 40°C. Below 40°C in the monosubstituted species, and at all temperatures in the tetrasubstituted species, ring rotation is replaced by ring libration as the predominant motion contributing to spin lattice relaxation. In addition, the rotational motion of the two types of rings in the asymmetric monosubstituted form are very similar although not identical. The substituted ring is slightly less mobile than the rings of unsubstituted polycarbonate. This indicates a strong coupling of ring motion, although the coupling leads to less than synchronous motion. Methyl group rotation is present in both polymers and is little affected by the various structural modifications.     

Ramsey numbers for graphs with five vertices

The Ramsey numbers r(F¹, F²) are tabulated for essentially all but six pairs of graphs F¹ and F² with five vertices.     

X-ray scattering studies of the structure of aqueous hydroxy-propylcellulose solutions

X-ray diffraction studies have been undertaken on aqueous solutions of hydroxy propylcellulose (HPC) over a wide range of the scattering vector Q. The experiments revealed only modest differences in local structure on a distance scale ca. 5–300 Å despite the fact that they covered concentrations generally interpreted as ranging from the isotropic (35.1 wt %) to the anisotropic liquid crystalline (LC) phase (53.5 wt %). Several models were used to interpret the small-angle scattering data, and each gave similar structural parameters and extrapolated intensities ( Q → 0) for both solutions. Peaks were observed with d-spacings ca. 12–17 Å in both materials. Wide-angle x-ray scattering (WAXS) showed slightly increased local order over a size range ca. 5–20 Å for the anisotropic solution, and this is consistent with a greater intensity of the 13 Å peak in this material. It is difficult to reconcile these findings with an interpretation of the LC state involving major differences with the isotropic phase and a high degree of orientational order extending over long length scales.     

AN ENCOMPASSING APPROACH TO MODELING FISHERY DYNAMICS: MODELING DYNAMIC NONLINEAR SYSTEMS

Uncertainty about the nature and significance of nonlinearities and the manner in which dynamics affect future realizations makes model specification the most difficult aspect of modeling dynamic systems. By interpreting several popular fishery models as subcases of a nesting dynamic Taylor series approximation, we isolate the specification differences between these models in a way that accounts for commonalities. On the argument that the differences due to alternative nonlinear forms are likely to be small compared to more mundane considerations such as delay difference and general dynamic lag specification, we propose an alternative model that uses the terms from the first order approximation common to all models combined with a data-based determination of the appropriate lags using the methods of state space time series analysis. Finally, the success of the alternative models is judged in an application to Pacific halibut data.     

Thermoelastic contact interaction of bodies in the presence of surface thermophysical irregularities

We study the thermoelastic contact interaction (in the absence of friction) of half-spaces under conditions of planar deformation in the presence of thin surface thermophysical irregularities that are taken into account by means of generalized conditions of thermal contact with one another. The problem is reduced to solving a system of singular integrodifferential equations with respect to the jumps of temperature and heat flow on the boundary of a section. We analyze the influence of a nonuniform thermal resistance distributed periodically along the surface or localized in one region of it on the distribution of temperature and stresses in the bodies and on their boundary. Four figures.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 23–28.     

Optical quenching of the magnetoplastic effect in NaCl crystals

Observations indicate that illuminating NaCl crystals by ultraviolet light (λ=350 nm) suppresses the magnetoplastic effect. The processes induced by illumination take place in a subsystem of point defects and are related to a change in the state of magnetically sensitive dislocation pinning sites. Fiz. Tverd. Tela (St. Petersburg) 39, 1389–1391 (1996)     

Possible application of X-ray optical elements for reducing the spectral bandwidth of an X-ray SASE FEL

A new design for a single pass X-ray Self-Amplified Spontaneous Emission (SASE) FEL is proposed. The scheme consists of two undulators and an X-ray monochromator located between them. The first stage of the FEL amplifier operates in the SASE linear regime. After the exit of the first undulator the electron bunch is guided through a non-isochronous bypass and the X-ray beam enters the monochromator. The main function of the bypass is to suppress the modulation of the electron beam induced in the first undulator. This is possible because of the finite value of the natural energy spread in the beam. At the entrance to the second undulator the radiation power from the monochromator dominates significantly over the shot noise and the residual electron bunching. As a result the second stage of the FEL amplifier operates in the steady-state regime when the input signal bandwidth is small with respect to that of the FEL amplifier. Integral losses of the radiation power in the monochromator are relatively small because grazing incidence optics can be used. The proposed scheme is illustrated for the example of the 6 nm option SASE FEL at the TESLA Test Facility under construction at DESY. As shown in this paper the spectral bandwidth of such a two-stage SASE FEL (Δλ/λ 5 × 10⁻⁵) is close to the limit defined by the finite duration of the radiation pulse. The average brilliance is equal to 7 × 10²⁴ photons/(s × mrad² × mm² × 0.1% bandw.) which is by two orders of magnitude higher than the value which could be reached by the conventional SASE FEL. The monochromatization of the radiation is performed at a low level of radiation power (about 500 times less than the saturation level) which allows one to use conventional X-ray optical elements (grazing incidence grating and mirrors) for the monochromator design.