Synthesis and Structure of Bismuth(III)-Containing Noncentrosymmetric Phosphates, Cs(3)KBi(2)M(4)(PO(4))(6)Cl (M = Mn, Fe). Monoclinic (Cc) and Tetragonal (P4(3)) Polymorphs Templated by Chlorine-Centered Cl(Bi(2)Cs) Acentric Units

Single crystals of three new noncentrosymmetric (NCS) phosphates, α (1) and β (2) forms of Cs(3)KBi(2)Mn(4)(PO(4))(6)Cl and α-Cs(3)KBi(2)Fe(4)(PO(4))(6)Cl (3), were grown in a reactive CsCl/KCl molten-salt media. Their structures were determined by single-crystal X-ray diffraction methods showing that the α form crystallizes in the space group Cc (No. 9), which is in one of the 10 NCS polar crystal classes, m (2/m) while the β form crystallizes in P4(3) (No. 78) of another polar class, 4 (4/m). The unit cell parameters of the α form can be approximately correlated with that of the β form via the 3 × 3 orientation matrix [0.5, 0.5, 0; -0.5, 0.5, 0; 0, 0, 2 sin β]. The structures of these otherwise complicated phosphates exhibit two types of channels with circular and elliptical windows where the Cl-centered Cl(Bi(2)Cs) acentric unit is located. The neighboring acentric units are arranged in a parallel fashion in the α form, resulting in the monoclinic (Cc) lattice, but "antiparallel" in the β form, thus giving the tetragonal (P4(3)) unit cell. 1-3 feature the compatible M-O-P unit that contains four crystallographically independent MO(x) (x = 4, 5) polyhedra, which are connected to the Cl(Bi(2)Cs) acentric unit through one short and one long M(II)···Cl bond. The compositions of 1 and 2 consist of three Mn(2+) (d(5)) and one Mn(3+) (d(4)) per formula unit and that of 3 has three Fe(2+) (d(6)) and one Fe(3+) (d(5)). Bond valence sums reveal that, in the α phase, the trivalent site adopts distorted tetrahedral M(1)(3+)O(4) coordination and, in the β phase, distorted trigonal-bipyramidal M(4)(3+)O(5). Thus far, the iron phase has only been isolated in the α form presumably because of little extra stabilization energy gain if the Fe(2+) d(6) ion were to occupy the M(1)O(4) site. The possible origins pertaining to the structural differences in the α and β forms are discussed.     

Non-linear inverse scattering: high resolution quantitative breast tissue tomography

Recent published results in inverse scattering generally show the difficulty in dealing with moderate to high contrast inhomogeneities when employing linearized or iteratively linearized algorithms (e.g., distorted Born iterative method). This paper presents a fully nonlinear algorithm utilizing full wave field data, that results in ultrasound computed tomographic images from a laboratory breast scanner, and shows several such unique images from volunteer subjects. The forward problem, data collection process and inverse scattering algorithm used are discussed. A functional that represents the "best fit" between predicted and measured data is minimized, and therefore requires a very fast forward problem solver, Jacobian calculation, and gradient estimation, all of which are described. The data collection device is described. The algorithm and device yield quantitative estimates of human breast tissue in vivo. Several high resolution images, measuring ～150 by 150 wavelengths, obtained from the 2D inverse scattering algorithms, using data collected from a first prototype, are shown and discussed. The quantitative values are compared with previous published work.     

PIV measurements of the flow field inside an enclosed cubical cavity in natural convection

The natural convective velocity field in an enclosed air-filled cubical cavity with two opposing isothermal faces and the remaining four sides having a well-defined linear temperature rise from the cold to the hot face has been measured at different physical orientations and Rayleigh (Ra) numbers. In particular, two components of the velocity at the mid-plane have been measured by using particle image velocimetry (PIV) at Ra = 10⁶ and 6 × 10⁶ at each of two different physical orientations: heating-from-the-side (HFS), and heating-from-below (HFB). The 95% confidence limit uncertainties in the measured velocity vectors are about 2% for laminar flow. The accuracy and integrity of the experiments were validated by the comparison to some well-established CFD results at the HFS orientation at Ra = 10⁶. It was concluded that the experimental method is sound and so findings at other orientations and at other values of Ra should have an accuracy consistent with the findings of the uncertainty analysis. Therefore, the other results can be confidently used as benchmark data for testing CFD codes. The turbulence intensities at the mid-plane are also presented.     

The Modulational Instability for a Generalized Korteweg–de Vries Equation

We study the spectral stability of a family of periodic standing wave solutions to the generalized Korteweg–de Vries in a neighborhood of the origin in the spectral plane using what amounts to a rigorous Whitham modulation theory calculation. In particular we are interested in understanding the role played by the null directions of the linearized operator in the stability of the traveling wave to perturbations of long wavelength. A study of the normal form of the characteristic polynomial of the monodromy map (the periodic Evans function) in a neighborhood of the origin in the spectral plane leads to two different instability indices. The first, an orientation index, counts modulo 2 the total number of periodic eigenvalues on the real axis. This index is a generalization of the one which governs the stability of the solitary wave. The second, a modulational instability index, provides a necessary and sufficient condition for the existence of a long-wavelength instability. This index is essentially the quantity calculated by Hǎrǎguş and Kapitula in the small amplitude limit. Both of these quantities can be expressed in terms of the map between the constants of integration for the ordinary differential equation defining the traveling waves and the conserved quantities of the partial differential equation. These two indices together provide a good deal of information about the spectrum of the linearized operator. We sketch the connection of this calculation to a study of the linearized operator—in particular we perform a perturbation calculation in terms of the Floquet parameter. This suggests a geometric interpretation attached to the vanishing of the orientation index previously mentioned.     

Solving Large Airline Crew Scheduling Problems: Random Pairing Generation and Strong Branching

The airline crew scheduling problem is the problem of assigning crew itineraries to flights. We develop a new approach for solving the problem that is based on enumerating hundreds of millions random pairings. The linear programming relaxation is solved first and then millions of columns with best reduced cost are selected for the integer program. The number of columns is further reduced by a linear programming based heuristic. Finally an integer solution is obtained with a commercial integer programming solver. The branching rule of the solver is enhanced with a combination of strong branching and a specialized branching rule. The algorithm produces solutions that are significantly better than ones found by current practice.     

The role of layer-thickness deviation in dispersion and structure of plasmons in finite superlattices

We study the effects of layer thickness variations on the collective plasmon excitation modes of finite superlattices. Unlike other symmetry lowering mechanisms, thickness variation does not strongly localize the surface modes. We find that the reason for this insensitivity lies in the fact that the collective modes of a given finite structure must evolve continuously from the single-finite-superlattice at zero thickness deviation into modes of a pair of uncoupled finite structures at large thickness variation. We also show that this behavior is analogous to the evolution of molecular orbitals from atomic orbitals as the internuclear separation is reduced, in contrast to the analogy of the superlattice modes as a stack of coupled quantum wells. This emphasizes the difference between the electromagnetic symmetry of the finite superlattice and the structural symmetry. Received 16 April 2001 and Received in final form 6 July 2001     

First observation by mass spectrometry of a 3+ oxidation state for a [4Fe-4S] metalloprotein: An ESI-FTICR mass spectrometry study of the high potential iron-sulfur protein from Chromatium vinosum

Electrospray ionization (ESI) Fourier transform ion cyclotron resonance mass spectrometry (FTICR) is used to measure the molecular weight of the high potential iron-sulfur protein (HiPIP) from Chromatium vinosum (C. vinosum) and its corresponding apoprotein. By accurate mass measurement of the metalloprotein, the oxidation state of the [4Fe-4S] metal center is assigned as 3+. This is the highest oxidation state yet observed by mass spectrometry for a [4Fe-4S] cluster, which usually appears in the 2+ oxidation state. In order to make this assignment correctly, the mass spectrum of the apoprotein was acquired, and a 1 Da difference was found between the molecular mass of the apoprotein and its published amino acid sequence. The mass spectra of the trypsin and cyanogen bromide digests of the alkylated apoprotein were obtained, and the data suggests that the C-terminal glycine residue is amidated.     

Synthesis of lariat ether carboxylic acids based on dibenzo‐16‐crown‐5

Synthetic routes to forty‐seven dibenzo‐16‐crown‐5 compounds with pendant carboxylic acid groups are reported. When taken together with previously described lariat ether carboxylic acids, these new compounds provide several series with systematic structural variations including changes in the identity and attachment site(s) of one or more lipophilic groups and the length of the spacer that connects the carboxylic acid group to the polyether framework.     

Composition dependence of the nucleation energy of iron antimonides from modulated elemental reactants.

Modulated elemental reactants containing iron and antimony were found to react at low temperature (T < 200 degrees C) forming either FeSb(2) or FeSb(3) depending on both the layer thicknesses and the overall composition of the initial reactant. For films containing 75% antimony and 25% iron, the metastable compound FeSb(3) was observed to nucleate and grow if the layer thickness was below approximately 35 A. Above this critical thickness for the modulation, annealing led to the formation of FeSb(2). This, combined with low-angle diffraction data, suggests that the initial interdiffusion between iron and antimony layers in an elementally modulated reactant results in the formation of an amorphous reaction intermediate if the layering thickness is less than 35 A. For modulated reactants with composition between 70 and 90 atomic % antimony and below this critical layer thickness, the metastable compound FeSb(3) formed. In more iron-rich modulated reactants FeSb(2) nucleates. The nucleation temperature and the nucleation energy of FeSb(3) were found to be a function of the composition of the amorphous intermediate, while those of FeSb(2) were found to be relatively independent of composition.