Shape-Aware Matching of Implicit Surfaces Based on Thin Shell Energies

A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane energy measuring the rate of tangential distortion when deforming the reference shell into the template shell, and a bending energy measuring the bending under the deformation in terms of the change of the shape operators from the undeformed into the deformed configuration. The variational method applies to surfaces described as level sets. It is mathematically well-posed, and an existence proof of an optimal matching deformation is given. The variational model is implemented using a finite element discretization combined with a narrow band approach on an efficient hierarchical grid structure. For the optimization, a regularized nonlinear conjugate gradient scheme and a cascadic multilevel strategy are used. The features of the proposed approach are studied for synthetic test cases and a collection of geometry processing examples.     

The slowly reacting mode of combustion of gaseous mixtures in spherical vessels. Part 1: Transient analysis and explosion limits

Frank-Kamenetskii's analysis of thermal explosions is revisited, using also a single-reaction model with an Arrhenius rate having a large activation energy, to describe the transient combustion of initially cold gaseous mixtures enclosed in a spherical vessel with a constant wall temperature. The analysis shows two modes of combustion. There is a flameless slowly reacting mode for low wall temperatures or small vessel sizes, when the temperature rise resulting from the heat released by the reaction is kept small by the heat-conduction losses to the wall, so as not to change significantly the order of magnitude of the reaction rate. In the other mode, the slow reaction rates occur only in an initial ignition stage, which ends abruptly when very large reaction rates cause a temperature runaway, or thermal explosion, at a well-defined ignition time and location, thereby triggering a flame that propagates across the vessel to consume the reactant rapidly. Explosion limits are defined, in agreement with Frank-Kamenetskii's analysis, by the limiting conditions for existence of the slowly reacting mode of combustion. In this mode, a quasi-steady temperature distribution is established after a transient reaction stage with small reactant consumption. Most of the reactant is burnt, with nearly uniform mass fraction, in a subsequent long stage during which the temperature follows a quasi-steady balance between the rates of heat conduction to the wall and of chemical heat release. The changes in the explosion limits caused by the enhanced heat-transfer rates associated with buoyant motion are described in an accompanying paper.     

Magnetic and structural properties of FeCr alloys

Synergistic synchrotron x-ray absorption experiments using imaging magnetic microspectroscopy, x-ray magnetic circular dichroism, and ab initio calculations on FeCr alloys reveal that the Cr content strongly influences the ferromagnetic microstructure and the Fe magnetic moments. The Cr local structure resolved by extended x-ray absorption fine structure (EXAFS) is also found to be affected by the alloy's composition. Both EXAFS and ab initio calculations show a change in the Cr local atomic structure above 10 at.% Cr content from the distance contraction of the first two coordination shells around the Cr absorbing atom. These results indicate the strong dependence of magnetic and structural properties of these alloys on Cr concentration.     

A Bis(pyridine N‐oxide) Analogue of DOTA: Relaxometric Properties of the GdIII Complex and Efficient Sensitization of Visible and NIR‐Emitting Lanthanide(III) Cations Including PrIII and HoIII

We report the synthesis of a cyclen‐based ligand (4,10‐bis[(1‐oxidopyridin‐2‐yl)methyl]‐1,4,7,10‐tetraazacyclododecane‐1,7‐diacetic acid= L1 ) containing two acetate and two 2‐methylpyridine N‐oxide arms anchored on the nitrogen atoms of the cyclen platform, which has been designed for stable complexation of lanthanide(III) ions in aqueous solution. Relaxometric studies suggest that the thermodynamic stability and kinetic inertness of the Gd^III complex may be sufficient for biological applications. A detailed structural study of the complexes by ¹H NMR spectroscopy and DFT calculations indicates that they adopt an anti‐Δ(λλλλ) conformation in aqueous solution, that is, an anti‐square antiprismatic (anti‐SAP) isomeric form, as demonstrated by analysis of the ¹H NMR paramagnetic shifts induced by Yb^III. The water‐exchange rate of the Gd^III complex is ${k{{298\hfill \atop {\rm ex}\hfill}}}$ =6.7×10⁶ s^?1, about a quarter of that for the mono‐oxidopyridine analogue, but still about 50 % higher than the ${k{{298\hfill \atop {\rm ex}\hfill}}}$ of GdDOTA (DOTA=1,4,7,10‐tetraazacyclododecane‐1,4,7,10‐tetraacetic acid). The 2‐methylpyridine N‐oxide chromophores can be used to sensitize a wide range of Ln^III ions emitting in both the visible (Eu^III and Tb^III) and NIR (Pr^III, Nd^III, Ho^III, Yb^III) spectral regions. The emission quantum yield determined for the Yb^III complex (${Q{{{\rm L}\hfill \atop {\rm Yb}\hfill}}}$ =7.3(1)×10^?3) is among the highest ever reported for complexes of this metal ion in aqueous solution. The sensitization ability of the ligand, together with the spectroscopic and relaxometric properties of its complexes, constitute a useful step forward on the way to efficient dual probes for optical imaging (OI) and MRI.     

Understanding Stability Trends along the Lanthanide Series

The stability trends across the lanthanide series of complexes with the polyaminocarboxylate ligands TETA^4? (H₄TETA=2,2′,2′′,2′′′‐(1,4,8,11‐tetraazacyclotetradecane‐1,4,8,11‐tetrayl)tetraacetic acid), BCAED^4? (H₄BCAED=2,2′,2′′,2′′′‐{[(1,4‐diazepane‐1,4‐diyl)bis(ethane‐2,1‐diyl)]bis(azanetriyl)}tetraacetic acid), and BP18C6^2? (H₂BP18C6=6,6′‐[(1,4,10,13‐tetraoxa‐7,16‐diazacyclooctadecane‐7,16‐diyl)bis(methylene)]dipicolinic acid) were investigated using DFT calculations. Geometry optimizations performed at the TPSSh/6‐31G(d,p) level, and using a 46+4fⁿ ECP for lanthanides, provide bond lengths of the metal coordination environments in good agreement with the experimental values observed in the X‐ray structures. The contractions of the Ln³⁺ coordination spheres follow quadratic trends, as observed previously for different isostructural series of complexes. We show here that the parameters obtained from the quantitative analysis of these data can be used to rationalize the observed stability trends across the 4f period. The stability trends along the lanthanide series were also evaluated by calculating the free energy for the reaction [La( L )]^n+/?_(sol)+Ln³⁺_(sol)→[Ln( L )]^n+/?_(sol)+La³⁺_(sol). A parameterization of the Ln³⁺ radii was performed by minimizing the differences between experimental and calculated standard hydration free energies. The calculated stability trends are in good agreement with the experimental stability constants, which increase markedly across the series for BCAED^4? complexes, increase smoothly for the TETA^4? analogues, and decrease in the case of BP18C6^2? complexes. The resulting stability trend is the result of a subtle balance between the increased binding energies of the ligand across the lanthanide series, which contribute to an increasing complex stability, and the increase in the absolute values of hydration energies along the 4f period.     

Supramolecular Luminescent Lanthanide Dimers for Fluoride Sequestering and Sensing

Lanthanide complexes (Ln=Eu, Tb, and Yb) that are based on a C₂‐symmetric cyclen scaffold were prepared and characterized. The addition of fluoride anions to aqueous solutions of the complexes resulted in the formation of dinuclear supramolecular compounds in which the anion is confined into the cavity that is formed by the two complexes. The supramolecular assembly process was monitored by UV/Vis absorption, luminescence, and NMR spectroscopy and high‐resolution mass spectrometry. The X‐ray crystal structure of the europium dimer revealed that the architecture of the scaffold is stabilized by synergistic effects of the Eu? F? Eu bridging motive, π stacking interactions, and a four‐component hydrogen‐bonding network, which control the assembly of the two [EuL] entities around the fluoride ion. The strong association in water allowed for the luminescence sensing of fluoride down to a detection limit of 24 nM .     

The Coordination Behaviour of CuI Photosensitizers Bearing Multidentate Ligands Investigated by X-ray Absorption Spectroscopy

A systematic series of four novel homo- and heteroleptic Cu^I photosensitizers based on tetradentate 1,10-phenanthroline ligands of the type X^N^N^X containing two additional donor moieties in the 2,9-position (X=SMe or OMe) were designed. Their solid-state structures were assessed by X-ray diffraction. Cyclic voltammetry, UV-vis absorption, emission and X-ray absorption spectroscopy were then used to determine their electrochemical, photophysical and structural features in solution. Following, time-resolved X-ray absorption spectroscopy in the picosecond time scale, coupled with time-dependent density functional theory calculations, provided in-depth information on the excited state electron configurations. For the first time, a significant shortening of the Cu−X distance and a change in the coordination mode to a pentacoordinated geometry is shown in the excited states of the two homoleptic complexes. These findings are important with respect to a precise understanding of the excited state structures and a further stabilization of this type of photosensitizers.     

Directed ortho-lithiation of unprotected diphenylphosphinic acids

Directed ortho lithiation of diphenylphosphinic acid and subsequent electrophilic trapping provides mono ortho-functionalized derivatives including enantiopure γ-aminophosphinic acids in moderate yields. Copper catalyzed coupling of the ortho anion leads to biphenyl-2,2′-diylbis(phenylphosphinic acid), a phosphorus analogue of biphenyl-2,2′-dicarboxylic acid. Preliminary studies of the metal-binding abilities of this O,O-chelating ligand towards a series of metal cations are included.     

The reaction of benzotriazoles with 3,4-dihydro-4H-pyrane and 2-acetoxymethyl-3,4-dihydro-2H-pyrane

From the reaction of benzotriazoles with 2,3-dihydro-4H-pyrane and 2-acetoxymethyl-3,4-dihydro-2H-pyrane the corresponding 1-(2-tetrahydropyranyl)benzotriazole and cis-and trans-1-(6-acetoxymethyl-2-tetrahydropyranyl)benzotriazole derivatives were obtained. The structures and conformations of these compounds were confirmed by UV and NMR spectra.