On the existence of intermediate magnetohydrodynamic shock waves

We consider the questions related to the structure of shock waves for a system of magnetohydrodynamic equations. Using Conley's connection matrix, we recover and extend earlier results due to C. Conley and J. Smoller. In particular, we give a simpler proof of the existence of fast and slow shocks with structure. We also demonstrate that for some viscosity parameters intermediate shocks occur. Furthermore, under an assumption of transversality, we show that there exist multi-parameter families of these intermediate shocks.This research was done while both authors were visiting the Lefschetz Center for Dynamical Systems at Brown University.Supported in part by the NSF under Grant DMS-8507056.Supported in part by AFOSR 87-0347.     

Pressure-Dependent Structure of Methanol–Water Mixtures up to 1.2 GPa: Neutron Diffraction Experiments and Molecular Dynamics Simulations

Total scattering structure factors of per-deuterated methanol and heavy water, CD₃OD and D₂O, have been determined across the entire composition range as a function of pressure up to 1.2 GPa, by neutron diffraction. The largest variations due to increasing pressure were observed below a scattering variable value of 5 Å⁻¹, mostly as shifts in terms of the positions of the first and second maxima. Molecular dynamics computer simulations, using combinations of all-atom potentials for methanol and various water force fields, were conducted at the experimental pressures with the aim of interpreting neutron diffraction results. The peak-position shifts mentioned above could be qualitatively reproduced by simulations, although in terms of peak intensities, the accord between neutron diffraction and molecular dynamics was much less satisfactory. However, bearing in mind that increasing pressure must have a profound effect on repulsive forces between neighboring molecules, the agreement between experiment and computer simulation can certainly be termed as satisfactory. In order to reveal the influence of changing pressure on local intermolecular structure in these “simplest of complex” hydrogen-bonded liquid mixtures, simulated structures were analyzed in terms of hydrogen bond-related partial radial distribution functions and size distributions of hydrogen-bonded cyclic entities. Distinct differences between pressure-dependent structures of water-rich and methanol-rich composition regions were revealed.     

Simultaneous determination of homocysteine,methionine and cysteine in maternal plasma after delivery by HPLC‐fluorescence detection with DBD‐F as a label

An HPLC‐fluorescence (FL) method for determination of sulfur‐containing amino acids such as homocysteine (Hcy), methionine (Met) and cysteine (Cys) in human plasma was developed. The sulfur‐containing amino acids were labeled with 4‐(N,N‐dimethylaminosulfonyl)‐7‐fluoro‐2,1,3‐benzoxadiazole (DBD‐F). Calibration curves in the range of 1–100 µm (Hcy and Met) and 5–500 µm (Cys) indicated good linearities (r ≥ 0.998). The limits of detection at a signal‐to‐noise ratio of 3 were 0.13 (Hcy), 0.02 (Met) and 0.11 µm (Cys), respectively. Acceptable results for accuracy and precision of intra‐ and inter‐day measurements were obtained. The results of Hcy and Cys obtained by the proposed method indicated good correlations with the conventional method (r > 0.911, n = 20). Furthermore, the method was applied to determination of the sulfur‐containing amino acids in maternal plasma (n = 200) after delivery. The concentrations of Hcy, Met and Cys as a median (inter quartile range, Q₁ and Q₃) were 5.37 (3.32–7.79) μm , 25.20 (20.10–31.06) μm and 147.25 (102.81–189.31) μm , respectively. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical method for verifying the existence and local uniqueness of a double turning point for a radially symmetric solution of the perturbed Gelfand equation

A numerical verification method to confirm the existence and local uniqueness of a double turning point for a radially symmetric solution of the perturbed Gelfand equation is presented. Using certain systems of equations corresponding to a double turning point, we derive a sufficient condition for its existence whose satisfaction can be verified computationally. We describe verification procedures and give a numerical example as a demonstration.     

Melt drawing of ultra‐high molecular weight polyethylene: Comparison of Ziegler‐ and metallocene‐catalyzed reactor powders

The drawing behavior of the ultra‐high molecular weight polyethylene (UHMW‐PE) melts has been studied by comparing the stress/strain curves for two types of samples as polymerized using conventional Ziegler and newer metallocene catalyst systems. Two UHMW‐PE samples, having the same viscosity average molecular weight of 3.3 × 10⁶, but different molecular weight distribution, have been drawn from melt at special conditions. The sample films for drawing were prepared by compression molding of reactor powders at 180°C in the melt. Differences in the structural changes during drawing and resultant properties, ascribable to their broad or narrow molecular weight distribution, were estimated from tensile tests, SEM observations, X‐ray measurements and thermal analyses. The metallocene‐catalyzed sample having narrower molecular weight distribution, could be effectively drawn from the melt up to a maximum draw ratio (DR) of 20, significantly lower than that obtained for the Ziegler‐catalyzed sample, ∼ 50. The stress/strain curves on drawing were remarkably influenced by draw conditions, including draw temperature and rate. However, the most effective draw for both was achieved at 150°C and a strain rate of 5 min⁻¹, independent of sample molecular weight distribution. The efficiency of drawing, as evaluated by the resultant tensile properties as a function of DR, was higher for the metallocene‐catalyzed sample having narrower molecular weight distribution. Nevertheless, the maximum achieved tensile modulus and strength for the Ziegler sample, 50–55 and 0.90 GPa, respectively, were significantly higher than those for the metallocene sample, 20 and 0.65 GPa, respectively, reflecting the markedly higher drawability for the former than the latter. The stress/strain behavior indicated that the origin of differences during drawing from the melt could be attributed to the ease of chain relaxation for the lower molecular weight chains in the melt. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1921–1930, 1999     

The Effects of Side-Chain Configurations of a Retro–Inverso-Type Inhibitor on the Human T-Cell Leukemia Virus (HTLV)-1 Protease

In this study, the effects of side-chain configurations of D-Ile residues of a retro–inverso (RI)-type inhibitor on the human T-cell leukemia virus type 1 (HTLV-1) protease containing a hydroxyethylamine dipeptide isostere were clarified. Prior to evaluation using the RI-type inhibitor, the effects of side-chain configurations of Ile residues of the substrate peptide on the HTLV-1 protease were examined to estimate the influence of side-chain configurations on enzyme activity. Based on the estimation of the influence of side-chain configurations on protease affinity, the RI-type inhibitors containing a D-allo-Ile residue in the corresponding substrate sequence, instead of a D-Ile residue, were synthesized via 9-fluorenylmethoxycarbonyl-based solid-phase peptide synthesis. Refolded recombinant HTLV-1 protease (1-116, L40I) was used for the simple and short evaluation of the inhibitory activities of the synthesized RI-type inhibitors. The results clearly indicated that mimicking the whole topology, comprising both the main- and side-chain structures of the parent inhibitor, is effective for the design of potent RI-modified protease inhibitors.