Stereochemical leakage mechanisms for tricarbonyl(dienyl)iron cations

ψ-Endo to ψ-exo leakage during solvolysis of a ψ-endo-dienol—Fe(CO)₃ dinitrobenzoate ester does not proceed via a syn, syn-cis-dienyl—Fe(CO)₃ cation. The most probable leakage mechanism involves non-stereospecific ionization of the dinitrobenzoate ester. syn,syn-cis-Dienyl—Fe(CO)₃ cations are formed from ψ-exo-dienol—Fe(CO)₃ complex during chromatography on grade I neutral alumina.     

Synthesis and Characterization of Photoactive Methyl 4-Bromo-3-((2,6-Difluorophenyl)diazenyl) Benzoate

Journal of Chemical Crystallography - The synthesis and structure of a novel ortho-fluoroazobenzene, methyl 4-bromo-3-((2,6-difluorophenyl)diazenyl) benzoate is described. The title molecule...     

Algebraic modular forms

In this paper, we develop an algebraic theory of modular forms, for connected, reductive groupsG overQ with the property that every arithmetic subgroup Γ ofG(Q) is finite. This theory includes our previous work [15] on semi-simple groupsG withG(R) compact, as well as the theory of algebraic Hecke characters for Serre tori [20]. The theory of algebraic modular forms leads to a workable theory of modular forms (modp), which we hope can be used to parameterize odd modular Galois representations. The theory developed here was inspired by a letter of Serre to Tate in 1987, which has appeared recently [21]. I want to thank Serre for sending me a copy of this letter, and for many helpful discussions on the topic.     

Ab initio calculations of the equation of state of hydrogen in a regime relevant for inertial fusion applications

We describe ab initio electronic structure calculations (density functional theory molecular dynamics and coupled electron-ion quantum Monte Carlo) of the equation of state (EOS) of hydrogen in a pressure-temperature regime relevant for simulating the initial phase of an inertial confinement fusion capsule implosion. We find the computed EOS to be quite close to that of the most recent SESAME table (constructed by G. Kerley, 2003). A simple density-dependent but temperature-independent correction brings the 2003-Kerley EOS into excellent agreement with ours in the chosen region of the hydrogen phase diagram. Simulations of fusion ignition experiments on the National Ignition Facility (NIF) with this modified 2003-Kerley table are shown to produce results nearly indistinguishable from those of the 2003-Kerley EOS, which was used to design the capsule. In this sense, we do not expect that further improvements to the hydrogen EOS in this particular regime will impact the capsule design.     

Less is more when simulating unsulfated glycosaminoglycan 3D‐structure: Comparison of GLYCAM06/TIP3P,PM3‐CARB1/TIP3P,and SCC‐DFTB‐D/TIP3P predictions with experiment

The 3D‐structure of extracellular matrix glycosaminoglycans is central to function, but is currently poorly understood. Resolving this will provide insight into their heterogeneous biological roles and help to realize their significant therapeutic potential. Glycosaminoglycan chemical isoforms are too numerous to study experimentally and simulation provides a tractable alternative. However, best practice for accurate calculation of glycosaminoglycan 3D‐structure within biologically relevant nanosecond timescales is uncertain. Here, we evaluate the ability of three potentials to reproduce experimentally observed glycosaminoglycan monosaccharide puckering, disaccharide 3D‐conformation, and characteristic solvent interactions. Temporal dynamics of unsulfated chondroitin, chondroitin‐4‐sulfate, and hyaluronan β(1→3) disaccharides were simulated within TIP3P explicit solvent unrestrained for 20 ns using the GLYCAM06 force‐field and two semi‐empirical quantum mechanics methods, PM3‐CARB1 and SCC‐DFTB‐D (both within a hybrid QM/MM formalism). Comparison of calculated and experimental properties (vicinal couplings, nuclear Overhauser enhancements, and glycosidic linkage geometries) showed that the carbohydrate‐specific parameterization of PM3‐CARB1 imparted quantifiable benefits on monosaccharide puckering and that the SCC‐DFTB‐D method (including an empirical correction for dispersion) best modeled the effects of hexosamine 4‐sulfation. However, paradoxically, the most approximate approach (GLYCAM06/TIP3P) was the best at predicting monosaccharide puckering, 3D‐conformation, and solvent interactions. Our data contribute to the debate and emerging consensus on the relative performance of these levels of theory for biological molecules. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Motives with Galois Group of type G2>: an Exceptional Theta-Correspondence

In this paper, we study an exceptional theta correspondence, obtained by restricting the minimal automorphic representation of the adjoint group of type E₇ and rank 3 over Q to the dual pair GxPGSp₆. Here G is the anisotropic form of G₂ over Q; using the correspondence, we lift certain automorphic forms on G to holomorphic cusp forms on PGSp₆. This lifting provides the first step in a project to construct motives of rank 7 and weight O over Q with Galois group of type G₂.     

Dynamically tessellating algorithm for analysis of pore size distribution in particle agglomerates

We describe a novel physical application of the OctTree data structure [P. Meagher, Comput. Graphics Image Process 19(2) (1982) 129–147] in a dynamically tessellating algorithm, in conjunction with an object-oriented, constructive solid geometry library (DOC), to efficiently determine pore size distributions in large multi-particle systems. We apply the DOC library to investigate the evolving dynamics of pore formation in multi-particle systems, such as a mixture of smooth hard cubes and spheres and a collection of frictional soft spheres. We demonstrate that the algorithm is able to provide insight into the effect of structural changes on the porosity network; for example, during the uniaxial compaction of soft spheres, we find the number density of pores increases while the mean volume of the pores decreases. This trend is responsible for a shift in the distribution of the pore volumes to favour smaller volumes. We anticipate that the DOC method will have wider applications in the area of granular materials for studying the changes in pore structure in both experimental and numerical systems as a complement to the analysis of particle packing.     

Risk averse elastic shape optimization with parametrized fine scale geometry

Shape optimization of the fine scale geometry of elastic objects is investigated under stochastic loading. Thus, the object geometry is described via parametrized geometric details placed on a regular lattice. Here, in a two dimensional set up we focus on ellipsoidal holes as the fine scale geometric details described by the semiaxes and their orientation. Optimization of a deterministic cost functional as well as stochastic loading with risk neutral and risk averse stochastic cost functionals are discussed. Under the assumption of linear elasticity and quadratic objective functions the computational cost scales linearly in the number of basis loads spanning the possibly large set of all realizations of the stochastic loading. The resulting shape optimization algorithm consists of a finite dimensional, constraint optimization scheme where the cost functional and its gradient are evaluated applying a boundary element method on the fine scale geometry. Various numerical results show the spatial variation of the geometric domain structures and the appearance of strongly anisotropic patterns.     

Inspection of periodically poled waveguide devices by confocal luminescence microscopy

Using confocal defect-luminescence microscopy, we investigated Er³⁺-doped periodically-poled LiNbO₃ waveguide devices and found that the Er³⁺ ion and vibrational Raman modes can be used effectively as probes to inspect and characterize the devices with high spatial resolution, non-destructively, and free of topographical artifacts. The technique is based on scanning over the sample, while simultaneously measuring and evaluating the emission or Raman spectra in terms of their moments (i.e., area, average emission wavelength, and spectral width). The contrast is observed even in tempered samples because of differences in intrinsic electric (strain) fields and defect arrangements that occur in regions inside and outside the waveguide as well as in regions in which domains have been inverted, or which are as grown. Evaluating different parts of the Er³⁺ spectra and/or using different moments, different aspects of the device can be highlighted and regions inside and outside the waveguide, in which domains have been inverted or not inverted, as well as domain walls, can be identified. Raman spectroscopy is less sensitive, but it still can identify the domain wall regions. PACS 42.64.Wi; 42.65.Yj; 77.84.Dy