Highly degenerate harmonic mean curvature flow

We study the evolution of a weakly convex surface in with flat sides by the Harmonic Mean Curvature flow. We establish the short time existence as well as the optimal regularity of the surface and we show that the boundaries of the flat sides evolve by the curve shortening flow. It follows from our results that a weakly convex surface with flat sides of class C ^k,γ , for some and 0  <  γ ≤ 1, remains in the same class under the flow. This distinguishes this flow from other, previously studied, degenerate parabolic equations, including the porous medium equation and the Gauss curvature flow with flat sides, where the regularity of the solution for t  >  0 does not depend on the regularity of the initial data. M. C. Caputo partially supported by the NSF grant DMS-03-54639. P. Daskalopoulos partially supported by the NSF grants DMS-01-02252, DMS-03-54639 and the EPSRC in the UK.     

On Monge‐Ampère equations with homogenous right‐hand sides

We study the regularity and behavior at the origin of solutions to the two‐dimensional degenerate Monge‐Ampère equation det D²_u = |x|^α with α > ?2. We show that when α > 0, solutions admit only two possible behaviors near the origin, radial and nonradial, which in turn implies C^{2, δ}‐regularity. We also show that the radial behavior is unstable. For α < 0 we prove that solutions admit only the radial behavior near the origin. © 2008 Wiley Periodicals, Inc.     

Adsorption and radical stabilization of humic-Acid analogues and Pb2+ on restricted phyllomorphous clay

Humic acids have stable radicals that are indigenous to their structure. Hydroxybenzoic acid derivatives such as gallic acid (GA) and protocatechuic acid are appropriate models for the radical properties of humic acids. Here we show that the adsorption or intercalation of gallic acid in Laponite clay results in a significant thermodynamic stabilization of gallic acid radicals. Moreover, the formed organoclay shows enhanced stability against acid dissolution. The structural details of the association of gallic acid with Laponite depend on the GA/Laponite loading. At low GA/Laponite ratios (approximately 10(-6) M of gallic acid per gram of clay), gallic acid is adsorbed at the variable charge sites of Laponite. This adsorption can be adequately described by surface complexation modeling. At higher GA/Laponite ratios (approximately 10(-3) M of gallic acid per gram of clay), X-ray diffraction data show that gallic acid is intercalated at the interlamellar sites of Laponite. In the presence of Pb2+ ions, the formed GA/Pb complex is associated with Laponite in an analogous structural manner, that is, adsorption at variable charge sites or intercalation at the interlamellar sites of Laponite, depending on the loading. Laponite stabilizes the GA/Pb radicals. At prolonged exposure to ambient O2, Laponite promotes the formation of stable oligomeric GA/Pb radical species, which are intercalated into interlamellar sites.     

Endosomal accumulation of APP in wobbler motor neurons reflects impaired vesicle trafficking: Implications for human motor neuron disease

Background  

The cause of sporadic amyotrophic lateral sclerosis (ALS) is largely unknown but hypotheses about disease mechanisms include oxidative stress, defective axonal transport, mitochondrial dysfunction and disrupted RNA processing. Whereas familial ALS is well represented by transgenic mutant SOD1 mouse models, the mouse mutant wobbler (WR) develops progressive motor neuron degeneration due to a point mutation in the Vps54 gene, and provides an animal model for sporadic ALS. VPS54 protein as a component of a protein complex is involved in vesicular Golgi trafficking; impaired vesicle trafficking might also be mechanistic in the pathogenesis of human ALS.     

Numerical simulation of a mixed-mode reaction front in a PPC engine

The ignition process, mode of combustion and reaction front propagation in a partially premixed combustion (PPC) engine running with a primary reference fuel (87% iso-octane, 13% n-heptane by volume) is studied numerically in a large eddy simulation. Different combustion modes, ignition front propagation, premixed flame and non-premixed flame, are observed simultaneously. Displacement speed of CO iso-surface propagation describes the transition of premixed auto-ignition to non-premixed flame. High temporal resolution optical data of CH₂O and chemiluminescence are compared with simulated results. A high speed ignition front is seen to expand through fuel-rich mixture and stabilize around stoichiometry in a non-premixed flame while lean premixed combustion occurs in the spray wake at a much slower pace. A good qualitative agreement of the distribution of chemiluminescence and CH₂O formation and destruction shows that the simulation approach sufficiently captures the driving physics of mixed-mode combustion in PPC engines. The study shows that the transition from auto-ignition to flame occurs over a period of several crank angles and the reaction front propagation can be captured using the described model.     

Perezoperezone and curcuperezone: bisabolane dimers from the soft coral Pseudopterogorgia rigida

Perezoperezone (1), curcuperezone (2), and diperezone (3), belonging to the rare class of bisabolane dimers, were isolated as minor constituents of the organic extract of the Caribbean soft coral, Pseudopterogorgia rigida. The structures of the new compounds 1 and 2 were established by detailed analyses of their NMR and MS data.     

Homogeneous chemiluminescent assays for free choline in human plasma and whole blood

Choline was oxidized in the presence of choline oxidase and the hydrogen peroxide generated was detected using a chemiluminescent acridinium-9-carboxamide. The dose response for choline (0-150 μM) was established in buffer and was validated for the quantification of choline in human plasma and whole blood. This homogeneous assay was performed in a 96-well microplate format and required minimal sample volume (4 μL) and short analysis time (<5 s per well). The new assay(s) correlated well (R > 0.98, plasma; R > 0.97, whole blood) with LC-MS/MS.     

Protein arrays on high-surface-area plasma-nanotextured poly(dimethylsiloxane)-coated glass slides

Treatment of poly(dimethylsiloxane) (PDMS) surfaces with SF(6) plasma results in the creation of high-surface-area nanotextured surfaces that considerably favour protein adsorption with respect to untreated ones. In order to employ such nanotextured surfaces as substrates for microarrays to be created and analysed using standard instrumentation, we fabricated thin PDMS films on top of standard low-cost microscope glass slides. The properties of both untreated and plasma-treated PDMS-coated slides towards spotting of protein solutions were evaluated in terms of spot signal intensity and homogeneity as well as of spot shape and size. It was found that the plasma-treated PDMS-coated glass slides provided highly homogeneous spots (mean intra-spot variation 7.6%) with spot signal intensity 6-times higher than that obtained using the untreated ones. In addition, comparison with commercially available polystyrene and aminosilanized-glass microarray slides showed that the proposed slides provided 3-times higher spot signal intensity and 2-times lower intra-spot signal variation. In addition, the implementation of long-aged-after-plasma-treatment nanotextured PDMS-coated glass slides provided spots whose shape and size matched those of the spotting tip. As a consequence, denser arrays of variable spot shape can be created using SF(6) plasma-treated PDMS-coated slides instead of standard microarray slides opening new potentials for bioanalytical applications.     

Dielectric studies of a laterally-linked siloxane ester dimer

This paper reports measurements of the dielectric response over the frequency range 10² to 10⁹?Hz of a liquid crystal dimer consisting of two ester mesogens laterally linked by an alkoxy chain containing a siloxane group. The synthesis and phase behaviour of the siloxane dimer are also reported. Results show that there are two relaxations in the isotropic phase and four in the nematic phase of the material. The possible molecular origins for these modes are given. It is found that there is a coupling between internal and external modes which gives rise to a cooperative mode as the temperature in the nematic phase is lowered towards a glass transition.     

Weak and smooth solutions for a fractional Yamabe flow: The case of general compact and locally conformally flat manifolds

As a counterpart of the classical Yamabe problem, a fractional Yamabe flow has been introduced by Jin and Xiong (2014) on the sphere. Here we pursue its study in the context of general compact smooth manifolds with positive fractional curvature. First, we prove that the flow is locally well posed in the weak sense on any compact manifold. If the manifold is locally conformally flat with positive Yamabe invariant, we also prove that the flow is smooth and converges to a constant fractional curvature metric. We provide different proofs using extension properties introduced by Chang and González (2011) for the conformally covariant fractional order operators.