The role of Mittag-Leffler functions in anomalous relaxation

The inertia-corrected Debye model of rotational Brownian motion of polar molecules was generalized by Coffey et al. [Phys. Rev. E, 65, 32 102 (2002)] to describe fractional dynamics and anomalous rotational diffusion. The linear- response theory of the normalized complex susceptibility was given in terms of a Laplace transform and as a function of frequency. The angular-velocity correlation function was parametrized via fractal Mittag-Leffler functions. Here we apply the latter method and complex-contour integral- representation methods to determine the original time-dependent amplitude as an inverse Laplace transform using both analytical and numerical approaches, as appropriate. (C) 2004 Elsevier B.V. All rights reserved.

Microscopic models for dielectric relaxation in disordered systems

It is shown how the Debye rotational diffusion model of dielectric relaxation of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended to yield the empirical Havriliak-Negami (HN) equation of anomalous dielectric relaxation from a microscopic model based on a kinetic equation just as in the Debye model. This kinetic equation is obtained by means of a generalization of the noninertial Fokker-Planck equation of conventional Brownian motion (generally known as the Smoluchowski equation) to fractional kinetics governed by the HN relaxation mechanism. For the simple case of noninteracting dipoles it may be solved by Fourier transform techniques to yield the Green function and the complex dielectric susceptibility corresponding to the HN anomalous relaxation mechanism.

Processing characteristics and mechanical properties of metallocene catalyzed linear low-density polyethylene foams for rotational molding

The object of this work is to assess the suitability of metallocene catalyzed linear low-density polyethylenes for the rotational molding of foams and to link the material and processing conditions to cell morphology and part mechanical properties (flexural and compressive strength). Through adjustments to molding conditions, the significant processing and physical material parameters that optimize metallocene catalyzed linear low-density polyethylene foam structure have been identified. The results obtained from an equivalent conventional grade of Ziegler-Natta catalyzed linear low-density polyethylene are used as a basis for comparison. The key findings of this study are that metallocene catalyzed LLDPE can be used in rotational foam molding to produce a foam that will perform as well as a ZieglerNatta catalyzed foam and that foam density Is by far the most Influential factor over mechanical properties of foam. © 2004 Society of Plastics Engineers.

Effect of relaxation on the oxygen K-edge electron energy-loss near-edge structure in yttria-stabilized zirconia

The electron energy-loss near-edge structure (ELNES) at the oxygen K-edge has been investigated in a range of yttria-stabilized zirconia (YSZ) materials. The electronic structure of the three polymorphs of pure ZrO2 and of the doped YSZ structure close to the 33 mol %Y2O3 composition have been calculated using a full-potential linear muffin-tin orbital method (NFP-LMTO) as well as a pseudopotential based technique. Calculations of the ELNES dipole transition matrix elements in the framework of the NFP-LMTO scheme and inclusion of core hole screening within Slater's transition state theory enable the ELNES to be computed. Good agreement between the experimental and calculated ELNES is obtained for pure monoclinic ZrO2. The agreement is less good with the ideal tetragonal and cubic structures. This is because the inclusion of defects is essential in the calculation of the YSZ ELNES. If the model used contains ordered defects such as vacancies and metal Y planes, agreement between the calculated and experimental O K-edges is significantly improved. The calculations show how the five different O environments of Zr,Y,O, are connected with the features observed in the experimental spectra and demonstrate clearly the power of using ELNES to probe the stabilization mechanism in doped metal oxides.

Macroturbulent and rotational broadening in the spectra of B-type supergiants.

The absorption-line spectra of early B-type supergiants show significant broadening that implies that an additional broadening mechanism (characterized here as `macroturbulence') is present in addition to rotational broadening. Using high-resolution spectra with signal-to-noise ratios of typically 500, we have attempted to quantify the relative contributions of rotation and macroturbulence, but even with data of this quality significant problems were encountered. However, for all our targets, a model where macroturbulence dominates and rotation is negligible is acceptable; the reverse scenario leads to poor agreement between theory and observation. Additionally, there is marginal evidence for the degree of broadening increasing with line strength, possibly a result of the stronger lines being formed higher in the atmosphere. Acceptable values of the projected rotational velocity are normally less than or equal to 50 km s-1, which may also be a typical upper limit for the rotational velocity. Our best estimates for the projected rotational velocity are typically 10-20 km s-1 and hence compatible with this limit. These values are compared with those predicted by single star evolutionary models, which are initially rapidly rotating. It is concluded that either these models underestimate the rate of rotational breaking or some of the targets may be evolving through a blue loop or are binaries.

Boron abundances in B-type stars: A test of rotational depletion during main-sequence evolution

Boron abundances have been derived for seven main-sequence B- type stars from Hubble Space Telescope STIS spectra around the B III lambda2066 line. In two stars, boron appears to be undepleted with respect to the presumed initial abundance. In one star, boron is detectable but is clearly depleted. In the other four stars, boron is undetectable, implying depletions of 1-2 dex. Three of these four stars are nitrogen enriched, but the fourth shows no enrichment of nitrogen. Only rotationally induced mixing predicts that boron depletions are unaccompanied by nitrogen enrichments. The inferred rate of boron depletion from our observations is in good agreement with these predictions. Other boron-depleted nitrogen-normal stars are identified from the literature. In addition, several boron- depleted nitrogen-rich stars are identified, and while all fall on the boron-nitrogen trend predicted by rotationally induced mixing, a majority have nitrogen enrichments that are not uniquely explained by rotation. The spectra have also been used to determine iron group (Cr, Mn, Fe, and Ni) abundances. The seven B-type stars have near-solar iron group abundances, as expected for young stars in the solar neighborhood. We have also analyzed the halo B-type star PG 0832 + 676. We find [Fe/H] = -0.88 +/- 0.10, and the absence of the B III line gives the upper limit [B/H] <-2.5. These and other published abundances are used to infer the star's evolutionary status as a post-asymptotic giant branch star.