On forming the Romberg table

Romberg-type extrapolation is commonly used in many areas of numerical computation. An algorithm is presented for forming the Romberg table for general step-length sequence and general powers in the asymptotic expansion. It is then shown that parameters of the algorithm can be used to gain an a priori bound on propagation of rounding errors in the table.     

Composition dependence of elasticity in NaxWO3

Single crystal Na_xWO₃ elastic constants have been measured for x = 0.522, 0.628, 0.695, and 0.74 using Brillouin light scattering. The elasticity of Na_xWO₃ is found to be similar to that of ReO₃. Calculations indicate that an observed decrease in c₁₁ with increasing sodium concentration results from perturbation associated with an increasing lattice constant of strong, covalent WO bonds.     

Characterization of polyolefin melts using the polymer reference interaction site model integral equation theory with a single‐site united atom model

A general approach, based on the polymer reference interaction site model (PRISM) integral equation theory, suitable for characterizing arbitrarily complex polyolefin melts is described. We tested the method by calculating the melt structures of linear polyethylene (PE) and isotactic polypropylene (iPP) and the spinodal decomposition temperatures for PE/iPP blends. The computational expense of the PRISM calculation was reduced with a single‐site united atom model in which the polyolefin CH, CH₂, and CH₃ groups were approximated as chemically equivalent sites with spherically symmetric energetic interactions. The site–site interactions were defined by a potential function comprising a hard core with an attractive Lennard–Jones term. These energetic parameters were optimized with a central composite design strategy that enabled a simultaneous fit of experimental melt density and structure factor data. Values were obtained for PE and iPP individually and for common universal parameters that could potentially be used for all polyolefins. The rotational isomeric state–metropolis Monte Carlo (RMMC) technique was used to generate sets of conformers at specified temperatures covering the melt‐temperature range of the polymers. The characteristic ratio was used to assess the quality of the conformers and the RMMC method. Values of 9.68 for PE and 9.27 for iPP were obtained. The single‐chain structure factors calculated by the RMMC method were used to calculate the total structure factor for each melt. These were validated against published X‐ray diffraction results. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1803–1814, 2001     

Thermal memory of poly(3‐hydroxybutyrate) using temperature‐modulated differential scanning calorimetry

The influence of thermal history on morphology, melting, and crystallization behavior of bacterial poly(3‐hydroxybutyrate) (PHB) has been investigated using temperature‐modulated DSC (TMDSC), wide‐angle X‐ray diffraction (WAXRD) and polarized optical microscopy (POM). Various thermal histories were imparted by crystallization with continuous and different modulated cooling programs that involved isoscan and cool–heat segments. The subsequent melting behavior revealed that PHB experienced secondary crystallization during heating and the extent of secondary crystallization varied with the cooling treatment. PHB crystallized under slow, continuous, and moderate cooling rates were found to exhibit double melting behavior due to melting of TMDSC scan‐induced secondary crystals. PHB underwent considerable secondary crystallization/annealing that took place under modulated cooling conditions. The overall melting behavior was interpreted in terms of recrystallization and/or annealing of crystals. Interestingly, the PHB analyzed by temperature modulation programs showed a broad exotherm before the melting peak in the nonreversing heat capacity curve and a multiple melting reversing curve, verifying that the melting–recrystallization and remelting process was operative. WAXRD and POM studies supported the correlations from DSC and TMDSC results. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 70–78, 2006     

Topical Astodrimer Sodium,a Non-Toxic Polyanionic Dendrimer,Demonstrates Antiviral Activity in an Experimental Ocular Adenovirus Infection Model

There is no approved antiviral therapy for adenovirus (HAdV) ocular infections. Astodrimer sodium (SPL7013) is a polyanionic dendrimer with antiviral activity. The current study evaluated the ocular tolerability and anti-adenoviral efficacy of topical SPL7013 in rabbit ocular models. In a tolerability study, rabbits were treated with 3% SPL7013, vehicle, or 0.5% cidofovir. Their eyes were graded using the Draize scale. In antiviral efficacy studies, HAdV5 inoculated eyes were treated with 3% SPL7013, vehicle, or 0.5% cidofovir. Eyes were cultured for the virus on days 0, 1, 3, 4, 5, 7, 9, 11, and 14. Viral titers were determined. There were no differences in Draize scores between 3% SPL7013 and vehicle on any day. Cidofovir produced significantly higher Draize scores on day 12 than SPL7013 and vehicle. The 3% SPL7013 and 0.5% cidofovir significantly reduced daily viral titers and positive cultures per total compared with vehicle on several different days. The 3% SPL7013 and 0.5% cidofovir significantly reduced the duration of HAdV5 shedding compared to vehicle. The 3% SPL7013 demonstrated significantly more antiviral activity compared with vehicle in the Ad5/NZW rabbit ocular model. The 3% SPL7013 induced “minimal” to “practically non-irritating” Draize scores in the ocular tolerability study. Further development of astodrimer sodium as a topical antiviral therapy for adenoviral ocular infections is indicated.     

Thermoplastic polymer-dispersed liquid crystals prepared from solvent-induced phase separation with predictions using solubility parameters

The optical effects of liquid crystals can be realized when the mesogens are dispersed in a supporting and stabilizing polymer phase. Thermoplastics were chosen for their structural reversibility and ease of fabrication of polymer-dispersed liquid crystals (PDLCs) from solution via solvent-induced phase separation (SIPS). The component match and tuning in PDLCs was achieved in a common solvent through predictions of solubility parameters. The PDLCs were first prepared using SIPS and were then exposed to thermal treatments on a hot stage polarizing microscope or in a differential scanning calorimeter. At elevated temperatures the polymer and mesogen may become miscible, while upon cooling thermally induced phase separation (TIPS) should occur, preferably above the isotropic-nematic transition temperature. The nematic phase existed within disperse phase droplets that were stabilized and supported by the matrix polymer. The temperature range of the nematic phase was extended in the PDLC configuration. The droplet size was important for liquid crystalline optical behaviour. Polymer-mesogen interactions, identified through solubility parameters, were important in ensuring sufficient but not coarse phase separation.     

Linear thermal expansion, thermal ageing, relaxations and post-cure of thermoset polymer composites using modulated temperature thermomechanometry

The glass transition temperature (Tg) regions of polymers and composites were studied using static force thermomechanometry and modulated temperature thermomechanometry (mT-TM). Modulated temperature allowed measurement of linear thermal expansion coefficient and glass transition as reversing phenomena, independent of any residual cure and relaxations that are non-reversing in nature. The reversing dimension change curves were well defined with continuous expansion that increased after Tg, though sensitivity decreased with crosslinking and fibre content. The non-reversing dimension change curves showed the maximum variation and revealed complex changes, and the non-reversing characteristics were confirmed by repeated scans, both upon cooling or re-heating. Non-reversing curves showed contractions with increasing temperature. Lissajous figures demonstrated that temperature modulation deviated significantly from linear response in the temperature range below Tg, and during the Tg range, steady state was not maintained. Measurements made in mT-TM mode were compared with modulated force TM where Tg was revealed as a peak in loss modulus or tan(δ), whilst reversing events were consistent with changes in storage modulus.     

Comparison of reversible melting behaviour of poly(3-hydroxybutyrate) using quasi-isothermal and other modulated temperature differential scanning calorimetry techniques

Melting behaviour of poly(3-hydroxybutyrate) (PHB) has been investigated by conventional DSC and each of several methods of modulated temperature differential scanning calorimetry (mT-DSC) such as heat-cool, iso-scan, step-scan and quasi-isothermal (QI). Thermal properties were investigated after fast and slow cooling crystallisation treatments. Multiple melting peak behaviour was observed for all methods except conventional melting with an average heating rate. Comparison of the mT-DSC data revealed that PHB underwent reversing melting including several reversible events and some non-reversible contributions under the modulation conditions. The main melting of PHB was irreversible, as were crystallisation and annealing, where the crystals can approach equilibrium. The various fusion enthalpy values were measured and they confirmed significant melt-recrystallisation of PHB with different melting conditions. Only the QI method revealed a true reversible contribution.     

Zeros of 2-adic -functions and congruences for class numbers and fundamental units

We study the imaginary quadratic fields such that the Iwasawa -invariant equals 1, obtaining information on zeros of -adic -functions and relating this to congruences for fundamental units and class numbers.

     

Electronic structure of tetragonal tungsten bronzes and electrochromic oxides

X-ray photoemission spectra of the band structures of WO₃, crystalline H _x WO₃ and the tetragonal and cubic bronzes M _x WO₃ (M=Li, Na) exhibit great similarity. In the bronzes tungsten 5d conduction band states are occupied. The tungsten 4f core level spectra of these materials have an unusual, but characteristic structure attributed to a combination of final state screening and hydrogen or alkali ion neighbor effects. The band structure of amorphous electrochromic WO₃ films differs in characteristic ways from that of the crystalline bronzes.