General theory of domain decomposition: Indirect methods

According to a general theory of domain decomposition methods (DDM), recently proposed by Herrera, DDM may be classified into two broad categories: direct and indirect (or Trefftz‐Herrera methods). This article is devoted to formulate systematically indirect methods and apply them to differential equations in several dimensions. They have interest since they subsume some of the best‐known formulations of domain decomposition methods, such as those based on the application of Steklov‐Poincaré operators. Trefftz‐Herrera approach is based on a special kind of Green's formulas applicable to discontinuous functions, and one of their essential features is the use of weighting functions which yield information, about the sought solution, at the internal boundary of the domain decomposition exclusively. A special class of Sobolev spaces is introduced in which boundary value problems with prescribed jumps at the internal boundary are formulated. Green's formulas applicable in such Sobolev spaces, which contain discontinuous functions, are established and from them the general framework for indirect methods is derived. Guidelines for the construction of the special kind of test functions are then supplied and, as an illustration, the method is applied to elliptic problems in several dimensions. A nonstandard method of collocation is derived in this manner, which possesses significant advantages over more standard procedures. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 296–322, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10008     

LAM Study of Chain Straightening During Stress Relaxation in Gel-Spun Polyethylene Fibers

The low-frequency Raman spectra of gel-spun polyethylene fibers were recorded in the frequency range of the longitudinal acoustic modes (LAM) localized on all-trans sequences, i.e., on straight-chain segments (SCS). During the experiment, the samples were stressed and held with their ends fixed. As soon as the stress was applied, there appeared a substantial amount of short (as compared to the size of the crystal) all-trans sequences randomly distributed in the amorphous phase. These primary SCS are not stable and decay (coil) within approximately half an hour. Further chain straightening continues in the interfacial regions between the crystalline and amorphous phases. In the course of this process, the individual all-trans sequences in the amorphous bulk are virtually replaced by the SCS adjacent to crystal cores. The final SCS length distribution in the relaxed sample is characterized by an increased fraction of the crystalline SCS penetrating deeply into the amorphous regions with formation of some quantity of taut-tie molecules.     

ON FINE STRUCTURE OF NASCENT UHMWPE REACTOR POWDERS

Reactor powder of a number of commercial ultra-high molecular weight polyethylenes synthesized on heterogeneous Ziegler–Natta catalyst in a conventional slurry process have been investigated with the help of scanning electron microscopy (SEM), wide-angle x-ray scattering (WAXS), differential scanning calorimetry (DSC), and low-frequency Raman spectroscopy. The SEM study reveals a complicated structure of nascent particles consisting of a small (0.5–1.0 μm) spongy-like fibrillar spheres. It is suggested that the elementary morphological units are fibrils formed by the small defective crystallites with the dominating crystalline distortions caused by microstrains. The comparison of longitudinal crystallite sizes derived from WAXS data with the straight chain segment length calculated from Raman shift frequency and the length of extended segments computed from the true melting interval measured by DSC allows to conclude that there are a large number of extended tie chains bridging the neighboring crystallites, which is not in agreement with a lamellar model. The extended chains passing through the noncrystalline regions stabilize a structure and provides its thermal stability. A possible tilting of molecules in the crystals, the location of defects and the distribution of crystallite sizes are discussed.     

Large Amplitude Motions of Pyruvic Acid (CH3-CO-COOH)

Torsional and rotational spectroscopic properties of pyruvic acid are determined using highly correlated ab initio methods and combining two different theoretical approaches: Second order perturbation theory and a variational procedure in three-dimensions. Four equilibrium geometries of pyruvic acid, Tc, Tt, Ct, and CC, outcome from a search with CCSD(T)-F12. All of them can be classified in the C_s point group. The variational calculations are performed considering the three internal rotation modes responsible for the non-rigidity as independent coordinates. More than 50 torsional energy levels (including torsional subcomponents) are localized in the 406–986 cm⁻¹ region and represent excitations of the ν₂₄ (skeletal torsion) and the ν₂₃ (methyl torsion) modes. The third independent variable, the OH torsion, interacts strongly with ν₂₃. The A₁/E splitting of the ground vibrational state has been evaluated to be 0.024 cm⁻¹ as it was expected given the high of the methyl torsional barrier (338 cm⁻¹). A very good agreement with respect to previous experimental data concerning fundamental frequencies (ν^CAL − ν^EXP ~ 1 cm⁻¹), and rotational parameters (B₀^CAL − B₀^EXP < 5 MHz), is obtained.     

Remnant Features in Melt Crystallized Samples of Polyethylenes Originated from Reactor Powders

A series of reactor powders of ultrahigh molecular weight (UHMW) polyethylenes with different morphology was melted at 160°C for 5 min and cooled in ice water. Low‐frequency Raman spectroscopy was used to characterize the straight‐chain‐segment (SCS) length distribution of both initial and melt‐crystallized materials. A bimodal SCS length distribution was found in the melt‐crystallized sample originated from the reactor powder with a very tenuous amorphous phase. In other samples recrystallized from powders with more ordered structure, the SCS length distribution was unimodal and approximately identical. The result is explained in terms of perfection of lamellar crystals formed under limited time and thermal conditions from differently organized initial structure.     

Lunar topographic model CLTM-s01 from Chang’E-1 laser altimeter

More than 3 million range measurements from the Chang’E-1 Laser Altimeter have been used to produce a global topographic model of the Moon with improved accuracy. Our topographic model, a 360th degree and order spherical harmonic expansion of the lunar radii, is designated as Chang’E-1 Lunar Topography Model s01 (CLTM-s01). This topographic field, referenced to a mean radius of 1738 km, has an absolute vertical accuracy of approximately 31 m and a spatial resolution of 0.25o (～7.5 km). This new lunar topogr...     

Rapid and sensitive LC-MS/MS method for quantification of lamotrigine in human plasma: application to a human pharmacokinetic study

A highly sensitive, specific and fully validated LC‐MS/MS method as per general practices of industry has been developed for estimation of lamotrigine (LAM) with 100 μL of human plasma using flucanozole as an internal standard (IS). The API‐4000 LC‐MS/MS was operated under the multiple reaction‐monitoring mode using electrospray ionization. A simple liquid–liquid extraction process was used to extract LAM and IS from human plasma. The total run time was 2.0 min and the elution of LAM and IS occurred at 1.25 and 1.45 min; this was achieved with a mobile phase consisting of 0.1% formic acid–methanol (20:40:40, v/v) at a flow rate of 0.50 mL/min on a Discovery CN (50 × 4.6 mm, 5 µm) column. The developed method was validated in human plasma with a lower limit of quantitation of 0.1 ng/mL for LAM. A linear response function was established for the range of concentrations 0.1–1500 ng/mL (r > 0.998) for LAM. The intra‐ and inter‐day precision values for LAM met the acceptance as per Food and Drug Administration guidelines. LAM was stable in the set of stability studies, viz. bench‐top, autosampler and freeze–thaw cycles. The developed assay method was applied to an oral bioequivalence study in humans. Copyright © 2011 John Wiley & Sons, Ltd.     

Fractionation process in TREF systems: Validation of thermodynamic model and calculation procedure by Raman LAM studies

In this paper, possible sources for the unexpected distributions of crystalline sequence lengths calculated from temperature rising elution fractionation (TREF) calibration experiments, as reported in a previous work, are investigated. With this aim, chain folding and cocrystalization phenomena were explored in the conditions of crystallization as used for TREF or crystallization analysis fractionation (CRYSTAF). Slow crystallizations were performed from xylene solutions of model low molecular weight ethylene homopolymers with narrow molecular weight distributions. The same experiments were performed with homopolymers having narrow molecular weight distributions and with blends having wide molecular weight distributions. The resulting distributions of the lengths of crystalline methylene sequences were directly studied by Raman in the so‐called longitudinal acoustic mode (LAM) and by DSC. For ethylene homopolymers with molecular weights below 2000 g/mol, the results from Raman LAM indicate that slow crystallization in TREF or CRYSTAF systems occurs in the extended‐chain mode. For higher molecular weights, evidence of chain folding was found. In the case of blends, independent crystallization was observed for each molecular weight when the molecular weight ranges used for the blends are relatively narrow. Cocrystallization was observed when this range was increased. Overall, these results strongly support the inverse technique calculation procedure developed by our group for the calculation of distributions of lengths of crystallizable sequences from TREF spectra. In this context, the results confirm that the unexpected crystallizable sequence lengths found in our previous work really exist and can be associated to chain folding or cocrystallization phenomena. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3083–3092, 2005     

Straight‐Chain Segment Length Distribution in Oriented Polyethylene as Revealed by LAM-Raman Spectroscopy

With the help of low-frequency Raman spectroscopy, the peculiarity of structural organization of oriented PE produced by multistage zone drawing of melt-crystallized films was studied. The draw ratios varied from DR=6 to 21 for PEI with M_η=8·10⁴ and from 3.5 to 5.7 for PEII with M_η≈10⁶.

The half widths (Δν) of all observed LAM bands were larger than 10–20 cm^?1. This means that the bands comprise a continuum of the overlapped elementary bands with Δν≈3 cm^?1 because of the wide straight–chain segments (SCS) length distribution. The length (L) of straight segments calculated from LAM-spectra, following a routine procedure, lies in the range from 7–8 to 60 nm.

Weight fractions G_MW of the SCS, as functions of their length, have a bell-like shape. Comparison of the SCS lengths with the value of the long periods (D) inferred from SAXS data for the same samples indicates that the lengths do not exceed 2D. The structural interpretation of the data obtained is given on the basis of microfibrillar models of oriented polymers. The peculiarity of the microfibrillar structure in PEI and PEII samples such as crystallite sizes and shapes and concentrations of inter- and intrafibrillar tie molecules, manifest themselves as the shape of G_MW (L) functions obtained for PE samples of various M_w and DR.     

Chain Straightening During Constant-Strain Relaxation in Melt-Crystallized Polyethylene Films

Abstract

The low-frequency Raman study of the chain-straightening process during stress relaxation in melt-crystallized polyethylene with molecular weight 10⁵ is presented. The application of tensile stress to low- and mid-drawn films causes the formation of “short” (as compared with crystal cores) straight-chain-segments (SCS). During the subsequent stress relaxation, while keeping the strain constant, the amount of SCS in the λ = 7 sample (λ is the draw ratio) gradually increases, while in the λ = 22 sample, a fraction of “short” SCS diminishes to zero within 3 days. This difference in the behavior of the low- and mid-drawn samples was ascribed to the difference in the contribution of the chain-breaking process. In the ultimately drawn sample (λ = 31), the length of the newly formed SCS is close to the crystal size, and they are situated, mainly, in the axially ordered interfibrillar phase. The formation of taut-tie molecules was not observed.