Some general principles of dynamic instability of solid bodies

Résumé Ce travail représente une étude de l'équilibre des corps solides, avec un intérêt special accordé aux corps élastiques et à ceux de Voigt-Kelvin. Les efforts appliqués peuvent avoir des composants non conservatifs et gyroscopiques, quoique la dépendance explicite du temps soit exclue. Il est bien connu que, pour une catégorie de problèmes tellement large, l'établissement des conditions de la stabilité par les méthodes classiques de statique ou d'énergie n'est pas toujours applicable.Le traitement du problème essaie d'être assez compréhensif. En utilisant la méthode des vibrations modales on établie des critères généraux de stabilité sur la base d'une «énergie équivalente». Ces critères sont d'une telle généralité qu'ils contiennent, comme cas spéciaux, les critères publiés auparavant. En plus, de nouveaux principes ont été développés et démontrés à l'aide d'un exemple numérique.

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This work was supported by the National Science Foundation through Grant GK-368 to the University of Illinois at Chicago Circle.     

Discrete-continuous model conversion

This paper presents methods for model conversions of continuous-time state-space equations and discrete-time state-space equations. An improved geometric-series method is presented for converting continuous-time models to equivalent discrete-time models. Also, a direct truncation method, a matrix continued fraction method and a geometric-series method are presented for converting discrete models to equivalent continuous models. As a result, many well-developed theorems and methods in either continuous or discrete domains can be effectively applied to a suitable model in either domain.     

One-pot synthesis of hollow Au3Cu1 spherical-like and biomineral botallackite Cu2(OH)3Cl flowerlike architectures exhibiting antimicrobial activity

A new form of Au3Cu1 hollow nanostructure was prepared by the reaction of Cu nanoparticles with HAuCl4. Following a course of aging, the biomineral botallackite Cu2(OH)3Cl nanoflowers were developed with the aid of Au3Cu1 hollow nanostructures at room temperature. It was proposed that the hollow nanospheres could serve as active centers for heterogeneous nucleation and mediated a mineralization process. Scanning electron microscopy and high-resolution transmission electron microscopy indicated that the nanoflowers are three-dimensional in appearance with a range of 500 nm-- to 1 microm in size and made of several nanopetals with about 25 nm in thickness. In addition, we found that the shape separation could be achieved by using cationic cetyltrimethylammonium bromide to filter the different morphology spherical- and flowerlike structures due to the negative charge of hollow nanospheres. Both hollow nanospheres and nanoflowers presented antimicrobial activity toward Streptococcus aureus with MIC50 at 39.6 and 127.2 microg/mL, respectively.     

Recovering the Sturm-Liouville Operator with Singular Potential Using Nodal Data

The paper deals with the Sturm-Liouville operator with singular potential. We assume that the potential is a sum of an a priori known distribution from a certain class and an unknown sufficiently smooth function. The inverse problem is to recover the operator using zeros of eigenfunctions (nodes) as an input data. For this inverse problem we obtain a procedure for constructing the solution.     

Phase-transformation-induced microstructure in lead-free ferroelectric ceramics based on (Bi0.5Na0.5)TiO3–BaTiO3–(Bi0.5K0.5)TiO3

Lead-free ferroelectric ceramics with a morphotropic phase boundary (MPB) composition 85.4% (Bi_0.5Na_0.5)TiO₃–2.6%BaTiO₃–12.0% (Bi_0.5K_0.5)TiO₃ (BNT-BT-BKT at a molar ratio of 85.4: 2.6: 12.0) doped with 0.8?mol% Nb₂O₅ were studied for their crystalline phases and microstructure. The crystalline phases were identified using X-ray diffractometry (XRD) with the contents determined using the Rietveld refinement technique. The phase-transformation-induced microstructure was analyzed using transmission electron microscopy (TEM) and the crystal symmetries were determined using the convergent-beam electron diffraction (CBED) technique. Samples sintered at 1200°C contain a mixture of cubic (C-), tetragonal (T-) and rhombohedral (R-) phases at a ratio of C/T/R?=?56.6: 28.4: 15.0?wt%. Two types of grains are produced: one characterized by a featureless contrast consisting of nano-scale T-domains dispersed in a C-phase matrix; the other a core-shell structure with a shell containing twin and anti-phase-boundary (APB) domains coexisting with a (C?+?T)-phase mixture core. The T- and R-twin boundaries are determined to {111}_T and {110}_R, respectively, and the fault vector for T-APB to R?=?1/2?110]_T. The characteristic microstructure is discussed in terms of the reduction in the point group symmetry and changes in the unit cell volume or the Bravais lattice upon phase transformation among the C-, T- and R-phases. The twin and the APB domains are induced and explained.     

A scalable synthesis of an azabicyclooctanyl derivative, a novel DPP-4 inhibitor

A practical synthetic strategy to a chiral azabicycclooctanyl derivative (1), a potent DPP-4 inhibitor, starting from a commercially available nortropine is described. The stereogenic center of 1 was established employing a modified protocol of Ellman's diastereoselective addition of a benzylic nucleophile to tert-butanesulfinimine. Other key steps include Corey-Chaykovsky reaction, Meinwald rearrangement, and CDMT-promoted amide bond formation involving a sterically hindered amine 2.     

Copper halide-bridged ruthenium telluride carbonyl complexes: discovery of the semiconducting cluster chain polymer {[PPh4]2[Te2Ru4(CO)10Cu4Br2Cl2].THF}infinity

A new series of Te-Ru-Cu carbonyl complexes was prepared by the reaction of K(2)TeO(3) with [Ru(3)(CO)(12)] in MeOH followed by treatment with PPh(4)X (X=Br, Cl) and [Cu(MeCN)(4)]BF(4) or CuX (X=Br, Cl) in MeCN. When the reaction mixture of K(2)TeO(3) and [Ru(3)(CO)(12)] was first treated with PPh(4)X followed by the addition of [Cu(MeCN)(4)]BF(4), doubly CuX-bridged Te(2)Ru(4)-based octahedral clusters [PPh(4)](2)[Te(2)Ru(4)(CO)(10)Cu(2)X(2)] (X=Br, [PPh(4)](2)[1]; X=Cl, [PPh(4)](2)[2]) were obtained. When the reaction mixture of K(2)TeO(3) and [Ru(3)(CO)(12)] was treated with PPh(4)X (X=Br, Cl) followed by the addition of CuX (X=Br, Cl), three different types of CuX-bridged Te-Ru carbonyl clusters were obtained. While the addition of PPh(4)Br or PPh(4)Cl followed by CuBr produced the doubly CuBr-bridged cluster 1, the addition of PPh(4)Cl followed by CuCl led to the formation of the Cu(4)Cl(2)-bridged bis-TeRu(5)-based octahedral cluster compound [PPh(4)](2)[{TeRu(5)(CO)(14)}(2)Cu(4)Cl(2)] ([PPh(4)](2)[3]). On the other hand, when the reaction mixture of K(2)TeO(3) and [Ru(3)(CO)(12)] was treated with PPh(4)Br followed by the addition of CuCl, the Cu(Br)CuCl-bridged Te(2)Ru(4)-based octahedral cluster chain polymer {[PPh(4)](2)(Te(2)Ru(4)(CO)(10)Cu(4)Br(2)Cl(2)).THF}(infinity) ({[PPh(4)](2)[4].THF}(infinity)) was produced. The chain polymer {[PPh(4)](2)[4].THF}(infinity) is the first ternary Te-Ru-Cu cluster and shows semiconducting behavior with a small energy gap of about 0.37 eV. It can be rationalized as resulting from aggregation of doubly CuX-bridged clusters 1 and 2 with two equivalents of CuCl or CuBr, respectively. The nature of clusters 1-4 and the formation and semiconducting properties of the polymer of 4 were further examined by molecular orbital calculations at the B3LYP level of density functional theory.     

IMPLEMENTATION OF VORTEX FILAMENT METHODS ON PARALLEL MACHINES WITH DISTRIBUTED ADAPTIVE DATA STRUCTURE

This paper addressed the implementation of vortex filament methods on parallel machines with distributed memory to simulate a three-dimensionally evolving jet. Vortical structure developments due to Kelvin–Helmholtz instability of the axially perturbed jet are also examined. The implementation is conducted in a single-programme multiple-data (SPMD) environment and the parallelism is focused on issues of data distribution, efficient support of parallel I/O and overlapping of communications with computations. In addition, since the number of segment markers in a filament is dynamically growing according to the requirement of numerical accuracy, a novel packet-oriented data structure is proposed not only to partition filament segment markers among distributed processors but also to support dynamical load balancing at run time. This work is the first to apply packet-oriented structures to implement a parallel vortex filament method. Experimental results indicate performance improvement from 1·5 to 2·6 times over static schemes on nCUBE2, DEC Alpha and IBM SP2 by incorporating the proposed scheme with packet-oriented structures. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 939–951, 1997.