Multi-valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems

Multi-valued solutions are constructed for 2 × 2 first-order systems using a generalization of the hodograph transformation. The solution is found as a complex analytic function on a complex Riemann surface for which the branch points move as part of the solution. The branch point singularities are envelopes for the characteristics and thus move at the characteristic speeds. We perform an analysis of stability of these singularities with respect to perturbations of the initial data. The generic singularity types are folds, cusps, and nondegenerate umbilic points with non-zero 3-jet. An isolated singularity is generically a square root branch point corresponding to a fold. Two types of collisions between singularities are generic: At a “tangential” collision between two singularities moving at the same characteristic speed, a cube root branch point is formed, corresponding to a cusp. A “non-tangential” collision, between two square root branch points moving at different characteristic speeds, remains a square root branch point at the collision and corresponds to a nondegenerate umbilic point. These results are also valid for a diagonalizable n-th order system for which there are exactly two speeds. © 1993 John Wiley & Sons, Inc.     

Mechanisms of reduced human vascular cell migration after photodynamic therapy

Restenosis results from intimal hyperplasia and constrictive remodeling following cardiovascular interventions. Photodynamic therapy (PDT) has been shown to inhibit intimal hyperplasia in vivo by preventing neointimal repopulation of the treated vessel. This study was undertaken in an attempt to further dissect the mechanisms by which PDT acts on secreted and extracellular matrix proteins to inhibit migration of cultured human vascular cells. PDT of three-dimensional collagen gels inhibited invasive human smooth muscle cell (SMC) migration, whereas cell-derived matrix metalloproteinase production remained unaltered. Additionally, PDT generated cross-links in the collagen gels, a result substantiated in an ex vivo model whereby PDT rendered the treated vessels resistant to pepsin digestion and inhibited invasive migration of SMC and fibroblasts. These data support the premise that by inducing matrix protein cross-links, rendering the vessel resistant to degradation, in vivo PDT inhibits repopulation of the vessel and therefore intimal hyperplasia.     

Rapid determination of corticosteroids in pharmaceuticals by flow injection analysis

The proposed method is based on the reduction of blue tetrazolium by the steroid in an alkaline medium to form a highly colored formazan. The effects of reagent concentration, temperature, flow rate, and manifold design on the reaction are discussed for a typical steroid, methylprednisolone acetate. Analytical readout is obtained within 30 s after sample introduction and up to 100 samples/h can be processed with baseline resolution between peaks. Typical relative standard deviations of 0.5% are obtained with 10-μ1 injection volumes. Results obtained by flow injection analysis are similar to those obtained with the AutoAnalyzer technique.     

Reactivity of secondary metallocene alkyls and the question of dormant sites in catalytic alkene polymerization

The reactivity of [rac-(C2H4(1-indenyl)2)Zr(n-butyl)][MeB(C6F5)3] (4), [rac-(C2H4(1-indenyl)2)Zr(sec-butyl)][MeB(C6F5)3] (5), and [rac-(C2H4(1-indenyl)2)Zr(polypropenyl)][MeB(C6F5)3] with propene, ethene, and hydrogen was studied by low-temperature (<-40 degrees C) 1H and 13C NMR spectroscopy in toluene solutions. In contrast with previous suggestions that 2 degrees zirconium alkyl species such as 5 are dormant sites, these measurements demonstrate reactivity of 2 degrees zirconium alkyls with propene and ethene comparable to the 1 degrees zirconium alkyl species 4 and [rac-(C2H4(1-indenyl)2)Zr(polypropenyl)][MeB(C6F5)3]. Because 2,1-insertion of propene is an infrequent event, these results preclude significant accumulation of catalyst in the form of 2 degrees zirconium alkyls for this metallocene and counterion. The reactivity of 5 with hydrogen is at least 2 orders of magnitude faster than other 1 degrees zirconium alkyls. Such high reactivity accounts for the puzzlingly high fraction of butyl end groups in prior hydrooligomerization studies and implies that catalyst responsivity to H2 as a molecular weight control agent correlates with the regioselectivity of the catalyst.     

Direct observation of insertion events at rac-(C2H4(1-indenyl)2)Zr(MeB(C6F5)3)-polymeryl intermediates: distinction between continuous and intermittent propagation modes

The propagating species for 1-hexene, propene, and ethene polymerization as catalyzed by [rac-(C2H4(1-indenyl)2)Zr(CH3)][CH3B(C6F5)3] has been intercepted at T < -40 degrees C and characterized by NMR methods. Observation of the propagating species permits direct monitoring of initiation, propagation, and termination processes by NMR. Detailed examination of alkene incorporation into Zr-polymeryl species using 13C-labeled 1-alkenes supports a continuous insertion mechanism whereby the anion re-coordinates after each alkene insertion.     

An In-Situ X-Ray Microtomography Study of Split Cylinder Fracture in Cement-Based Materials

In an effort to quantify microstructure-property relationships, three dimensional imaging experiments were conducted on small cylinder specimens subjected to split cylinder fracture. 3-D images were made using synchrotron-based x-ray microtomography, and the experiments were conducted with an in-situ frame such that a specimen could be examined while under load at varying degrees of damage. The specimens were made of fine-grained portland cement mortar and 0.5 mm glass beads, which served as aggregates. The diameter of the specimens was 5 mm. 3-D image analysis routines were developed or adapted to characterize microstructure and internal damage, which could then be related to bulk splitting strength and fracture energy. For fracture energy calculation, crack surface area could be measured in a way that accounted for roughness, branching, and fragmentation. Results showed that, for the specimens tested, aggregate surface roughness had little effect on strength but significant effect on fracture energy. Split cylinder strength showed correlation with specimen porosity, although there was considerable scatter. Strength did not correlate with maximum flaw size, although flaw location was not evaluated.     

Heavy-atom kinetic isotope effects,cocatalysts, and the propagation transition state for polymerization of 1-hexene using the rac-(C(2)H(4)(1-indenyl)(2))ZrMe(2) catalyst precursor

Using 13C NMR techniques, the 12C/13C kinetic isotope effects (KIEs) for the polymerization of 1-hexene catalyzed by rac-(C2H4(1-indenyl)2)ZrMe2 in the presence of four different cocatalysts (tris(pentfluorophenyl)borane, tris(pentafluorophenyl)alane, anilinium tetrakis(pentafluorophenyl)borate, and methylalumoxane) have been determined. All cocatalysts yield similar KIEs within experimental uncertainty, with values of 1.009(1) and 1.017(2) at C1 and C2, respectively. Ab initio DFT computational modeling of the polymerization KIE indicates that alkene binding to the catalyst must be reversible, with the majority of the KIE developing in the subsequent migratory insertion reaction.