The average hamiltonian view of low-energy scattering by a vibrating molecule

The average hamiltonian theory is used to examine the effect of molecular vibration on low-energy scattering. When the relative motion of the colliding molecules is slow on the timescale of molecular vibration, it is appropriate to transform the problem into an oscillating reference frame and to describe the collision in that frame by the average hamiltonian over one period of oscillation. The first-order result is identical to the distorted-wave Born approximation. High-order corrections introduce phase shifts for elastic scattering due to molecular vibration and provide transition amplitudes for inelastic scattering. The extent to which the higher-order corrections modify the distorted waves establishes criteria for the validity of the DWA. These criteria are used to examine recent distorted-wave calculations of V-V energy transfer rate constants.     

Rhenium complexes of tris(pyrazolyl)methanes and sulfonate derivative

The trioxo [ReO(3){SO(3)C(pz)(3)}] (1) (pz = pyrazolyl) and oxo [ReOCl{SO(3)C(pz)(3)}(PPh(3))]Cl (2) compounds with tris(pyrazolyl)methanesulfonate were obtained by treatment of Re(2)O(7) or [ReOCl(3)(PPh(3))(2)], respectively, with Li[SO(3)C(pz)(3)], whereas [ReCl(3){HC(pz)(3)}] (3), [ReCl(3){HC(3,5-Me(2)pz)(3)}] (4) and [ReCl(4){eta(2)-HC(pz)(3)}] (5) were prepared by reaction of [ReOCl(3)(PPh(3))(2)] (3,4) or [ReCl(4)(NCMe)(2)] (5) with hydrotris(pyrazolyl)methane HC(pz)(3) (3,5) or hydrotris(3,5-dimethyl-1-pyrazolyl)methane HC(3,5-Me(2)pz)(3) (4). [ReO{SO(3)C(pz)(3)}{OC(CH(3))(2)pz}][ReO(4)] 6, with a chelated pyrazolyl-alkoxide, was derived from an unprecedented ketone-pyrazolyl coupling on reaction of crude 1 with acetone. The compounds have been characterized by elemental analyses, IR and NMR spectroscopies, FAB-MS spectrometry and cyclic voltammetry and, in the case of 5 and 6, also by single-crystal X-ray diffraction. The electrochemical E(L) Lever parameter has been estimated, for the first time, for the SO(3)C(pz)(3)(-) and oxo ligands allowing the measurement of their electron-donor character and comparison with other ligands. Compounds 1, 2 and 6 appear to be the first tris(pyrazolyl)methanesulfonate complexes of rhenium to be reported.     

Inverse Problems for Differential Forms on Riemannian Manifolds with Boundary

Consider a real-analytic orientable connected complete Riemannian manifold M with boundary of dimension n ≥ 2 and let k be an integer 1 ≤ k ≤ n. In the case when M is compact of dimension n ≥ 3, we show that the manifold and the metric on it can be reconstructed, up to an isometry, from the set of the Cauchy data for harmonic k-forms, given on an open subset of the boundary. This extends a result of [14 Lassas , M. , Uhlmann , G. ( 2001 ). On determining a Riemannian manifold from the Dirichlet-to-Neumann map . Ann. Sci. École Norm. 34 : 771 – 787 .[Web of Science ®] , [Google Scholar]] when k = 0. In the two-dimensional case, the same conclusion is obtained when considering the set of the Cauchy data for harmonic 1-forms. Under additional assumptions on the curvature of the manifold, we carry out the same program when M is complete non-compact. In the case n ≥ 3, this generalizes the results of [13 Lassas , M. , Taylor , M. , Uhlmann , G. ( 2003 ). The Dirichlet-to-Neumann map for complete Riemannian manifolds with boundary . Comm. Anal. Geom. 11 : 207 – 221 .[Crossref], [Web of Science ®] , [Google Scholar]] when k = 0. In the two-dimensional case, we are able to reconstruct the manifold from the set of the Cauchy data for harmonic 1-forms.     

Formation of nematic liquid crystals of sterically stabilized layered double hydroxide platelets

Colloidal platelets of hydrotalcite, a layered double hydroxide, have been prepared by coprecipitation at pH 11-12 of magnesium nitrate and aluminum nitrate at two different magnesium to aluminum ratios. Changing the temperature and ionic strength during hydrothermal treatment, the platelets were tailored to different sizes and aspect ratios. Amino-modified polyisobutylene molecules were grafted onto the platelets following a convenient new route involving freeze-drying. Organic dispersions in toluene were prepared of the particles with the largest size and highest aspect ratio. The colloidal dispersions prepared in this way showed isotropic-nematic phase transitions above a limiting concentration in a matter of days. The number density at the transition and the width of the biphasic region were determined and compared to theory. The orientation of the platelets in nematic droplets (tactoids) and at the isotropic-nematic interface were analyzed by polarization microscopy. It was observed that sedimentation induces a nematic layer in samples that are below the limiting concentration for isotropic-nematic phase separation. No nematic phase was observed in the initial aqueous suspensions of the ungrafted particles.     

SLE Boundary Visits

We study the probabilities with which chordal Schramm–Loewner evolutions (SLE) visit small neighborhoods of boundary points. We find formulas for general chordal SLE boundary visiting probability amplitudes, also known as SLE boundary zig-zags or order refined SLE multi-point Green’s functions on the boundary. Remarkably, an exact answer can be found to this important SLE question for an arbitrarily large number of marked points. The main technique employed is a spin chain–Coulomb gas correspondence between tensor product representations of a quantum group and functions given by Dotsenko–Fateev type integrals. We show how to express these integral formulas in terms of regularized real integrals, and we discuss their numerical evaluation. The results are universal in the sense that apart from an overall multiplicative constant the same formula gives the amplitude for many different formulations of the SLE boundary visit problem. The formula also applies to renormalized boundary visit probabilities for interfaces in critical lattice models of statistical mechanics: we compare the results with numerical simulations of percolation, loop-erased random walk, and Fortuin–Kasteleyn random cluster models at Q = 2 and Q = 3, and find good agreement.     

Coating of open tubular capillaries with discoidal and spherical high-density lipoprotein particles in electrochromatography

A new method was developed for the coating of fused-silica capillaries with human high-density lipoproteins (HDLs) for use in electrochromatography. The HDL particles used for the coating differed in particle shape and composition. Both discoidal and spherical particles formed a monolayer on the inner silica wall as confirmed by atomic force microscopy. The effect of coating conditions, such as HDL concentration and coating time, was investigated with spherical HDL particles. Examination of the influence of pH on the coating stability also allowed the determination of pI values for the HDL particles attached to the capillary wall. The pI values for spherical and discoidal HDL particles were close to 5.0. The repeatabilities of the EOF mobility and the retention factors of the uncharged steroid hormones used as model compounds were exploited in the evaluation of the coating stability. The optimal coating was achieved with 0.1 mg/mL HDL protein and 50 min flushing with coating solution followed by 15 min standing time. Electrochromatography with HDL-coated open tubular capillaries offers a new tool for the study of HDL particle structure and transformations.     

Pt(II)-mediated nitrile-tetramethylguanidine coupling as a key step for a novel synthesis of 1,6-dihydro-1,3,5-dihydrotriazines

The coupling between tetramethylguanidine, HN=C(NMe2)2, and coordinated organonitriles in the platinum(II) complexes cis/trans-[PtCl2(RCN)2] (R = Me, Et, Ph) proceeds rapidly under mild conditions to afford the diimino compounds containing two N-bound monodentate 1,3-diaza-1,3-diene ligands [PtCl2{NH=C(R)N=C(NMe2)2}2] (R = Et, trans-1; R = Ph, trans-2; R = Me, cis-3; R = Et, cis-4), and this reaction is the first observation of metal-mediated nucleophilic addition of a guanidine to ligated nitrile. Complexes 1-4 were characterized by elemental analyses (C, H, N), X-ray diffraction, FAB mass spectrometry, IR, and 1H and 13C{1H} NMR spectroscopies; assignment of signals from E/Z-forms of 1,3-diaza-1,3-diene ligands and verification of routes for their Z right harpoon over left harpoon E isomerization in solution were performed using 2D 1H,1H-COSY, 1H,13C-HETCOR, and 1D NOE NMR experiments. The newly formed and previously unknown 1,3-diaza-1,3-dienes NH=C(R)N=C(NMe2)2 were liberated from the platinum(II) complexes [PtCl2{NH=C(R)N=C(NMe2)2}2] (1-3) by substitution with 2 equiv of 1,2-bis-(diphenylphosphino)ethane (dppe) to give the uncomplexed HN=C(R)N=C(NMe2)2 species (5-7) in solution and the solid [Pt(dppe)2](Cl)2. The former were utilized in situ, after filtration of the latter, in the reaction with 1,3-di-p-tolylcarbodiimide, (p-tol)N=C=N(tol-p), in CDCl3 to generate (6E)-N,N-dimethyl-1-(4-methylphenyl)-6-[(4-methylphenyl)imino]-1,6-dihydro-1,3,5-triazin-2-amines) (8-10) due to the [4 + 2]-cycloaddition accompanying elimination of HNMe2. The formulation of 8-10 is based on ESI-MS, 1H, 13C{1H} NMR, and X-ray crystal structures determined for 9 and 10. The reaction of 1,3-diaza-1,3-dienes with 1,3-di-p-tolylcarbodiimide, described in this article, constitutes a novel synthetic approach to a useful class of heterocyclic species like 1,6-dihydro-1,3,5-triazines.     

Exploiting the Chiral Ligands of Bis(imidazolinyl)- and Bis(oxazolinyl)thiophenes—Synthesis and Application in Cu-Catalyzed Friedel–Crafts Asymmetric Alkylation

Five new C₂-symmetric chiral ligands of 2,5-bis(imidazolinyl)thiophene (L1–L3) and 2,5-bis(oxazolinyl)thiophene (L4 and L5) were synthesized from thiophene-2,5-dicarboxylic acid (1) with enantiopure amino alcohols (4a–c) in excellent optical purity and chemical yield. The utility of these new chiral ligands for Friedel–Crafts asymmetric alkylation was explored. Subsequently, the optimized tridentate ligand L5 and Cu(OTf)₂ catalyst (15 mol%) in toluene for 48 h promoted Friedel–Crafts asymmetric alkylation in moderate to good yields (up to 76%) and with good enantioselectivity (up to 81% ee). The bis(oxazolinyl)thiophene ligands were more potent than bis(imidazolinyl)thiophene analogues for the asymmetric induction of the Friedel–Crafts asymmetric alkylation.     

Models for the modern power grid

This article reviews different kinds of models for the electric power grid that can be used to understand the modern power system, the smart grid. From the physical network to abstract energy markets, we identify in the literature different aspects that co-determine the spatio-temporal multilayer dynamics of power system. We start our review by showing how the generation, transmission and distribution characteristics of the traditional power grids are already subject to complex behaviour appearing as a result of the the interplay between dynamics of the nodes and topology, namely synchronisation and cascade effects. When dealing with smart grids, the system complexity increases even more: on top of the physical network of power lines and controllable sources of electricity, the modernisation brings information networks, renewable intermittent generation, market liberalisation, prosumers, among other aspects. In this case, we forecast a dynamical co-evolution of the smart grid and other kind of networked systems that cannot be understood isolated. This review compiles recent results that model electric power grids as complex systems, going beyond pure technological aspects. From this perspective, we then indicate possible ways to incorporate the diverse co-evolving systems into the smart grid model using, for example, network theory and multi-agent simulation.