High‐order stable interpolations for immersed boundary methods

The analysis and improvement of an immersed boundary method (IBM) for simulating turbulent flows over complex geometries are presented. Direct forcing is employed. It consists in interpolating boundary conditions from the solid body to the Cartesian mesh on which the computation is performed. Lagrange and least squares high‐order interpolations are considered. The direct forcing IBM is implemented in an incompressible finite volume Navier–Stokes solver for direct numerical simulations (DNS) and large eddy simulations (LES) on staggered grids. An algorithm to identify the body and construct the interpolation schemes for arbitrarily complex geometries consisting of triangular elements is presented. A matrix stability analysis of both interpolation schemes demonstrates the superiority of least squares interpolation over Lagrange interpolation in terms of stability. Preservation of time and space accuracy of the original solver is proven with the laminar two‐dimensional Taylor–Couette flow. Finally, practicability of the method for simulating complex flows is demonstrated with the computation of the fully turbulent three‐dimensional flow in an air‐conditioning exhaust pipe. Copyright © 2006 John Wiley & Sons, Ltd.     

Set covering with almost consecutive ones property

In this paper, we consider set covering problems with a coefficient matrix almost having the consecutive ones property, i.e., in most rows of the coefficient matrix, the ones appear consecutively and only a few blocks of consecutive ones appear in the remaining rows. If this property holds for all rows it is well known that the set covering problem can be solved efficiently. For our case of almost consecutive ones we present a reformulation exploiting the consecutive ones structure to develop bounds and a branching scheme. Our approach has been tested on real-world data as well as on theoretical problem instances.     

Tilivalline,a new pyrrolo[2, 1-c][1,4] benzodiazepine metabolite from klebsiella

From Klebsiella pneumoniae (+)(11S, 11aS) - 1,2,3,10,11,11a - hexahydro - 9 - hydroxy - 11 - (3′ - indolyl) - 5H - pyrrolo[2,1-c][1,4]benzodiazepin - 5 - one (1) has been isolated for which the name tilivalline is suggested. Structure elucidation and synthesis are reported.     

The Structure of [HSi9]3− in the Solid State and Its Unexpected Highly Dynamic Behavior in Solution

We report on the first unambiguous detection of the elusive [HSi₉]^3? anion in solutions of liquid ammonia by various ²⁹Si and ¹H NMR experiments including chemical exchange saturation transfer (CEST). The characteristic multiplicity patterns of both the ²⁹Si and ¹H resonances together with CEST and a partially reduced ¹H,²⁹Si coupling constant indicate the presence of a highly dynamic Si₈ entity and a Si?H moiety with slow proton hopping. Theoretical calculations corroborate both reorganization of Si₈ on the picosecond timescale via low vibrational modes and proton hopping. In addition, in a single‐crystal X‐ray study of (K(DB[18]crown‐6))(K([2.2.2]crypt))₂[ HSi₉ ]?8.5 NH₃, the H atom was unequivocally localized at one vertex of the basal square of the monocapped square‐antiprismatic cluster. Thus experimental studies and theoretical considerations provide unprecedented insight into both the structure and the dynamic behavior of these cluster anions, which hitherto had been considered to be rigid.     

The reaction of the group-13 alkyls ER3 (E = Al, Ga, In; R = CH2t-Bu, CH2 SiMe3) with the platinum-complex [(dcpe)Pt(H)(CH2t-Bu)]

The reactions of the sterically demanding group-13 alkyls ER₃ (E = Al, Ga, In; R = CH₂t-Bu, CH₂SiMe₃) with the platinum-complex [(dcpe)Pt(H)(CH₂t-Bu)] were re-investigated. The bimetallic compounds [(dcpe)Pt(ER₂)(R)] (3: E = Ga, R = CH₂SiMe₃; 5: E = In, R = CH₂t-Bu; dcpe = bis(dicyclohexylphosphino)ethane) with direct σ(Pt-E) bonds were obtained by oxidative addition of an E-C bond to the coordinatively unsaturated fragment [(dcpe)Pt] produced in situ by thermolysis of the starting complex [(dcpe)Pt(CH₂t-Bu)(H)]. The single crystal structure determination reveals a Pt-Ga bond length of 2.376(2) Å and a Pt-In bond length of 2.608(1) Å. All new compounds were characterised by elemental analysis, ³¹P and ¹⁹⁵Pt NMR spectroscopy. Interestingly, the Pt-Ga compound 3 slowly transforms into the platinum alkyl/hydride isomer {(dcpe)Pt(μ₂-H)[CH₂Si(CH₃)₂ CH₂Ga(CH₂SiMe₃)₂]} (4) during crystallization from solution at room temperature. The X-ray single crystal structure analysis revealed both complexes 3 and 4 coexisting in the unit cell in a 1:1 relation. The inaccessibility of analytically pure samples of the Pt-Al complex {(dcpe)Pt[Al(CH₂t-Bu)₂](CH₂t-Bu)} (6), postulated as intermediate of the reaction of [(dcpe)Pt(H)(CH₂t-Bu)] with Al(CH₂t-Bu) on the basis of ³¹P and ¹⁹⁵Pt NMR data, is attributed to an enhanced tendency to isomerisation into the alkyl/hydride Pt/Al congener of 4. A brief DFT analysis of the bonding situation of the model complex [(dhpe)Pt(GaMe₂)(Me)] (1M) revealed, that the contribution of π(Pt-Ga) back-bonding is negligible.     

Power-law solvation dynamics in DNA over six decades in time

Time-resolved Stokes shifts in a dye-containing oligonucleotide have been observed over the entire time range from 40 fs to 40 ns. The dynamics fit to a power law with a small exponent of 0.15. Similar relaxation has been seen in proteins but has not been anticipated in DNA. Distinct relaxation components due to specific subcomponents of the system, bulk water, bound water, counterions, backbone, bases, and so on, are not found. The various subcomponents may be so strongly coupled that their motions cannot be treated separately.     

An isolated cyclo-tetraarsendiide: low temperature synthesis and crystal structure of bis-pentaamminesodium tetraarsendiide-ammonia (1/3) [Na(NH3)5]2As(4).3NH3

Reduction of an excess of arsenic with a solution of sodium in liquid ammonia yields the thermally unstable title compound [Na(NH3)5]2As(4).3NH3, which contains isolated square-planar As4(2-) ions with a mean As-As bond length of 2,345 A.     

Solution-state dynamic nuclear polarization at high magnetic field

The goal of dynamic nuclear polarization (DNP) is to enhance NMR signals by transferring electron spin polarization to the nuclei. Although mechanisms such as the solid effect and thermal mixing can be used for DNP in the solid state, currently, the only practical mechanism in solutions is the Overhauser effect (OE), which usually arises due to dipolar relaxation between electrons and the nuclei. At magnetic fields greater than approximately 1 T, dipolar relaxation does not result in a useful enhancement and therefore the conventional wisdom is that DNP should not work in solutions at high magnetic fields. However, scalar relaxation due to time-dependent scalar couplings has a different magnetic field dependence and can lead to substantial OE enhancements. At room temperature and at a magnetic field of 5 T (211 MHz for protons, 140 GHz for electrons), we have observed that scalar relaxation between electrons and nuclei results in NMR signal enhancements of 180, 42, -36, and 8, for 31P, 13C, 15N, and 19F, respectively.     

Li(CH(Me)P(Ph)2(NCO2Me))2(THF)2]: crystal,solution, and calculated structure of a N-delocalized lithium phosphazene

The first crystal structure of the lithium complex of a P-alkyl-P,P-diphenyl(N-methoxycarbonyl)phosphazene has been characterized. It is dimeric, with the anion chelating the lithium in an unusual six-membered ring. A monomer-dimer equilibrium has been identified in THF solution. Ab initio calculations indicated that the six-membered ring is electronically favored over an alternative Li-C-P-N four-membered ring.     

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