Fast elliptic solvers in cylindrical coordinates and the Coulomb collision operator

In this paper, we describe a new class of fast solvers for separable elliptic partial differential equations in cylindrical coordinates (r, θ, z) with free-space radiation conditions. By combining integral equation methods in the radial variable r with Fourier methods in θ and z, we show that high-order accuracy can be achieved in both the governing potential and its derivatives. A weak singularity arises in the Fourier transform with respect to z that is handled with special purpose quadratures. We show how these solvers can be applied to the evaluation of the Coulomb collision operator in kinetic models of ionized gases.     

Rational blowdowns and smoothings of surface singularities

In this paper, we give a necessary combinatorial condition fora negative-definite plumbing tree to be suitable for rationalblowdown, or to be the graph of a complex surface singularitywhich admits a rational homology disk smoothing. New examplesof surface singularities with rational homology disk smoothingsare also presented; these include singularities with resolutiongraph having valency 4 nodes. Received July 25, 2007.     

Steric Effects in the Tuning of the Diastereoselectivity of the Intramolecular Free-Radical Cyclization to an Olefin As Exemplified through the Synthesis of a Carba-Pentofuranose Scaffold

Two free-radical cyclization reactions with the radical at the chiral C4 of the pentose sugar and the intramolecularly C1-tethered olefin (on radical precursors 8 and 17) gave a new diastereospecific C4-C8 bond in dimethylbicyclo[2.2.1]heptane 9, whereas the new C4-C7 bond in 7-methyl-2-oxabicyclo[2.2.1]heptanes 18a/18b gave trans and cis diastereomers, in which the chirality of the C4 center is fully retained as that of the starting material. It has been shown how the chemical nature of the fused carba-pentofuranose scaffolds, dimethylbicyclo[2.2.1]heptane 9 vis-a-vis 7-methyl-2-oxabicyclo[2.2.1]heptanes 18a/18b (C7-Me in the former versus 2-O- in the latter), dictates the stereochemical outcome both at the Grignard reaction step as well as in the free-radical ring-closure reaction. The formation of pure 1,8-trans-bicyclo[2.2.1]heptane 9 from 8 suggests that the boat-like transition state is favored due to the absence of steric clash of the bulky 1(S)-O-p-methoxybenzyl (PMB) and 7(R)-Me substituents (both in the α-face) with that of the 8(R)-CH(2)(?) radical in the β-face. The conversion of 17 → 18a-7(S) and 18b-7(R) in 6:4 ratio shows that the participation of both the chair- and the boat-like transition states is likely.     

Endo-selective Diels-Alder reaction of methacrylonitrile: application to the synthesis of Georgywood

Diels-Alder reactions of alkyl-substituted dienes with acrylonitriles give good yields and endo-selectivities if catalyzed by (organo)aluminum, (organo)boron or gallium halides. The activity of these group IIIa Lewis acids in this reaction correlates with the coordination strength of their nitrile complexes, which deactivate Lewis acids sufficiently, so that the subsequently added diene partner undergoes the Diels-Alder reaction without serious side-reactions. Boron trichloride is the most effective catalyst for this purpose. This method gives the best endo/exo-ratios reported so far for these components and was applied in the selective synthesis of the olfactory vector of Georgywood^®.     

Modeling unimolecular reactions in photoelectron photoion coincidence experiments

A computer program has been developed to model and analyze the data from photoelectron photoion coincidence (PEPICO) spectroscopy experiments. This code has been used during the past 12 years to extract thermochemical and kinetics information for almost a hundred systems, and the results have been published in over forty papers. It models the dissociative photoionization process in the threshold PEPICO experiment by calculating the thermal energy distribution of the neutral molecule, the energy distribution of the molecular ion as a function of the photon energy, and the resolution of the experiment. Parallel or consecutive dissociation paths of the molecular ion and also of the resulting fragment ions are modeled to reproduce the experimental breakdown curves and time‐of‐flight distributions. The latter are used to extract the experimental dissociation rates. For slow dissociations, either the quasi‐exponential fragment peak shapes or, when the mass resolution is insufficient to model the peak shapes explicitly, the center of mass of the peaks can be used to obtain the rate constants. The internal energy distribution of the fragment ions is calculated from the densities of states using the microcanonical formalism to describe consecutive dissociations. Dissociation rates can be calculated by the RRKM, SSACM or VTST rate theories, and can include tunneling effects, as well. Isomerization of the dissociating ions can also be considered using analytical formulae for the dissociation rates either from the original or the isomer ions. The program can optimize the various input parameters to find a good fit to the experimental data, using the downhill simplex algorithm. Copyright © 2010 John Wiley & Sons, Ltd.     

Three-dimensional molecular reconstruction of rat heart with mass spectrometry imaging

Cardiovascular diseases are the world’s number one cause of death, accounting for 17.1 million deaths a year. New high-resolution molecular and structural imaging strategies are needed to understand underlying pathophysiological mechanism. The aim of our study is (1) to provide a molecular basis of the heart animal model through the local identification of biomolecules by mass spectrometry imaging (MSI) (three-dimensional (3D) molecular reconstruction), (2) to perform a cross-species validation of secondary ion mass spectrometry (SIMS)-based cardiovascular molecular imaging, and (3) to demonstrate potential clinical relevance by the application of this innovative methodology to human heart specimens. We investigated a MSI approach using SIMS on the major areas of a rat and mouse heart: the pericardium, the myocardium, the endocardium, valves, and the great vessels. While several structures of the heart can be observed in individual two-dimensional sections analyzed by metal-assisted SIMS imaging, a full view of these structures in the total heart volume can be achieved only through the construction of the 3D heart model. The images of 3D reconstruction of the rat heart show a highly complementary localization between Na⁺, K⁺, and two ions at m/z 145 and 667. Principal component analysis of the MSI data clearly identified different morphology of the heart by their distinct correlated molecular signatures. The results reported here represent the first 3D molecular reconstruction of rat heart by SIMS imaging.

Size characterization of green fluorescent protein inclusion bodies in E. coli using asymmetrical flow field-flow fractionation-multi-angle light scattering

The goal of this study was to investigate the applicability of asymmetrical flow field-flow fractionation-multi-angle light scattering (AsFlFFF-MALS) for size analysis of green fluorescent protein inclusion bodies (GFPIBs). The size distributions of GFPIBs prepared by various culture conditions were determined. For GFPIBs prepared at 37 degrees C the peak maximum hydrodynamic diameter (d(H)) first increased and then decreased with the increase of the induction times in the presence of 0.1 and 2 mM isopropyl-beta-D-thiogalactoside (IPTG). For GFPIBs prepared at 30 degrees C the peak maximum d(H) was constant at about 700 nm irrespectively of the induction times and IPTG concentrations.     

Modular synthesis of heterocyclic carbene precursors

A series of N-heterocyclic carbene precursors, containing an imidazoline or tetrahydropyrimidine framework, were prepared from omega-chloroalkanoyl chlorides. The sequential attachment of nitrogen nucleophiles and subsequent ring closure gave, depending on the reagents used, either the desired dihydroimidazolium and tetrahydropyrimidinium salts or their parent heterocycles. In this latter case, the second substituent was introduced in an alkylation step. The preparation of carbene precursors bearing chiral or bulky substituents was acieved with comparable efficiency.