Synthesis, characterization, crystal structure and magnetic property of asymmetrical double Schiff base heterotrinuclear complex: Cu(II)-Co(II)-Cu(II)

An asymmetrical double Schiff-base Cu(II) mononuclear complex, HCuLp (H(3)Lp is N-3-carboxylsalicylidene-N'-5-chlorosalicylaldehyde-1,3-diaminopropane) and a heterometal trinuclear complex with double molecular structure (CuLp)(2)Co center dot 5H(2)O have been synthesized and characterized by means of elemental analyses, IR and electronic spectra. The crystal structure of the heterotrinucler complex was determined by X-ray analysis. Each asymmetric unit within the unit cell of the complex contains two heterotrinuclear neutral molecules (a) [CuLpCoCuLp], (b) [(CuLpH(2)O) CoCuLp] and four uncoordinated water molecules. In the two neutral molecules, the central Co2+ ions are located at the site of O-6 with a distorted octahedral geometry, one terminal Cu2+ ion (Cu(3)) at the square-pyramidal environment of N2O3, and the other three at the square planar coordination geometry with N2O2 donor atoms. Magnetic properties of the heterotrinucler complex have been determined in the temperature range 5-300 K, indicating that the interaction between the central Co2+ ion and the outer Co2+ ions is antiferromagnetic.

From dissymmetrical mononuclear entities to centrosymmetrical heterotrinuclear complex with 2D supramolecular structure: synthesis, characterization, crystal structure, and magnetic properties

A new centrosymmetrical heterotrinuclear complex, {[Cu(oxbe)](2)Co(H2O)(2)}.2DMF.DMA with 2D supramolecular structure, has been obtained by the self-assembly of a dissymmetrical building block [Cu(oxbe)](-) with bivalent metal ion Co2+, where H(3)oxbe is dissymmetrical ligand N-benzoato-N'-(2-aminoethyl)oxamido, DMF = dimethylformamide, DMA = dimethylamine. Its structure was determined by single crystal X-ray analysis. The molecular structure is centrosymmetrical with the cobalt atom lying on an inversion center. Through the hydrogen bonds and d-pi stacking interactions, a 2D supramolecular structure is formed. This study exemplifies a new method for the assembly of supramolecular structure using a dissymmetrical brick. Magnetic susceptibility measurements (5-300 K) indicate that the central cobalt and terminal copper metal ions are antiferromagnetically coupled with J = -23.1 cm(-1).

The Synthesis and Characterization of a Novel (E,E)-Dioxime and its Mono- and Heterotrinuclear Complexes Containing an 18-Membered Dioxadithiadiazamacrocycle

The novel (E,E)-dioxime, 5,6:17,18-dibenzo-11,12-(4-nitrobenzo)-2,3-bis(hydroxyimino)-7,16-dithia-10,13-dioxa-1,4-diazacyclooctadecane) (H2L), has been synthesized from reaction of (E,E)-dichloroglyoxime (1) with 2,3:14,15-dibenzo 8,9-(4-nitrobenzo)-4,13-dithia-7,10-dioxa-1,16-diazahegzadecane (2). The mononuclear Co(III) complex (4) of this dioxime was prepared by oxidation of the cobalt (II) complex. The -capped Co(III) complex (5) was synthesized by using a precursor Co(III) complex and boron trifluoride dietherate. The heterotrinuclear complexes (6) and (7) were prepared by reaction of (5) with NiCl2·6H2O and CdCl2·H2O, respectively. In addition, the homotrinuclear Cu(II) complex (8), has also been prepared by the reaction of this dioxime with CuCl2·H2O. The structures of the dioxime and its complexes were identified by using elemental analysis, 1H- and 13C-NMR, IR, and mass spectral data.

Complex potentials and singular integral equation for curve crack problem in antiplane elasticity

Four types of the fundamental complex potential in antiplane elasticity are introduced: (a) a point dislocation, (b) a concentrated force, (c) a dislocation doublet and (d) a concentrated force doublet. It is proven that if the axis of the concentrated force doublet is perpendicular to the direction of the dislocation doublet, the relevant complex potentials are equivalent. Using the obtained complex potentials, a singular integral equation for the curve crack problem is introduced. Some particular features of the obtained singular integral equation are discussed, and numerical solutions and examples are given.

Large Eddy Simulation of Complex Turbulent Flows: Physical Aspects and Research Trends

In the current paper, we have primarily addressed one powerful simulation tool developed during the last decades-Large Eddy Simulation (LES), which is most suitable for unsteady three-dimensional complex turbulent flows in industry and natural environment. The main point in LES is that the large-scale motion is resolved while the small-scale motion is modeled or, in geophysical terminology, parameterized. With a view to devising a subgrid-scale(SGS) model of high quality, we have highlighted analyzing physical aspects in scale interaction and-energy transfer such as dissipation, backscatter, local and non-local interaction, anisotropy and resolution requirement. They are the factors responsible for where the advantages and disadvantages in existing SGS models come from. A case study on LES of turbulence in vegetative canopy is presented to illustrate that LES model is more based on physical arguments. Then, varieties of challenging complex turbulent flows in both industry and geophysical fields in the near future-are presented. In conclusion; we may say with confidence that new century shall see the flourish in the research of turbulence with the aid of LES combined with other approaches.

Multiscale Coupling in Complex Mechanical Systems

Multiscale coupling attracts broad interests from mechanics, physics and chemistry to biology. The diversity and coupling of physics at different scales are two essential features of multiscale problems in far-from-equilibrium systems. The two features present fundamental difficulties and are great challenges to multiscale modeling and simulation. The theory of dynamical system and statistical mechanics provide fundamental tools for the multiscale coupling problems. The paper presents some closed multiscale formulations, e.g., the mapping closure approximation, multiscale large-eddy simulation and statistical mesoscopic damage mechanics, for two typical multiscale coupling problems in mechanics, that is, turbulence in fluids and failure in solids. It is pointed that developing a tractable, closed nonequilibrium statistical theory may be an effective approach to deal with the multiscale coupling problems. Some common characteristics of the statistical theory are discussed.

Pattern Recognition With Weighted Complex Networks

In this paper we introduce a weighted complex networks model to investigate and recognize structures of patterns. The regular treating in pattern recognition models is to describe each pattern as a high-dimensional vector which however is insufficient to express the structural information. Thus, a number of methods are developed to extract the structural information, such as different feature extraction algorithms used in pre-processing steps, or the local receptive fields in convolutional networks. In our model, each pattern is attributed to a weighted complex network, whose topology represents the structure of that pattern. Based upon the training samples, we get several prototypal complex networks which could stand for the general structural characteristics of patterns in different categories. We use these prototypal networks to recognize the unknown patterns. It is an attempt to use complex networks in pattern recognition, and our result shows the potential for real-world pattern recognition. A spatial parameter is introduced to get the optimal recognition accuracy, and it remains constant insensitive to the amount of training samples. We have discussed the interesting properties of the prototypal networks. An approximate linear relation is found between the strength and color of vertexes, in which we could compare the structural difference between each category. We have visualized these prototypal networks to show that their topology indeed represents the common characteristics of patterns. We have also shown that the asymmetric strength distribution in these prototypal networks brings high robustness for recognition. Our study may cast a light on understanding the mechanism of the biologic neuronal systems in object recognition as well.

A high order accurate difference scheme for complex flow fields

A high order accurate finite difference method for direct numerical simulation of coherent structure in the mixing layers is presented. The reason for oscillation production in numerical solutions is analyzed, It is caused by a nonuniform group velocity of wavepackets. A method of group velocity control for the improvement of the shock resolution is presented. In numerical simulation the fifth-order accurate upwind compact difference relation is used to approximate the derivatives in the convection terms of the compressible N-S equations, a sixth-order accurate symmetric compact difference relation is used to approximate the viscous terms, and a three-stage R-K method is used to advance in time. In order to improve the shock resolution the scheme is reconstructed with the method of diffusion analogy which is used to control the group velocity of wavepackets. (C) 1997 Academic Press.

Complex stress functions and plastic zone sizes for notch cracks subjected to various loading conditions

In this paper, the conformal mapping method is used to solve the plane problem of an infinite plate containing a central lip-shaped notch subjected to biaxial loading at a remote boundary or a surface uniform pressure on the notch. The stress intensity factors KI and KII are obtained by the derived complex stress functions. The simple analytical expressions can be applied to the situation of cracks originating from a circular or an elliptical notch. The plastic zone sizes for such notch cracks are subsequently evaluated in light of the Dugdale strip yield concept. The results are consistent with available numerical data.

Complex Transition of Double-Diffusive Convection in a Rectangular Enclosure with Height-to-Length Ratio Equal to 4: Part I

This is the first part of direct numerical simulation (DNS) of double-diffusive convection in a slim rectangular enclosure with horizontal temperature and concentration gradients. We consider the case with the thermal Rayleigh number of 10^5, the Pradtle number of 1, the Lewis number of 2, the buoyancy ratio of composition to temperature being in the range of [0,1], and height-to-width aspect ration of 4. A new 7th order upwind compact scheme was developed for approximation of convective terms, and a three-stage third-order Runge-Kutta method was employed for time advancement. Our DNS suggests that with the buoyancy ratio increasing form 0 to 1, the flow of transition is a complex series changing fromthe steady to periodic, chaotic, periodic, quasi-periodic, and finally back to periodic. There are two types of periodic flow, one is simple periodic flow with single fundamental frequency (FF), and another is complex periodic flow with multiple FFs. This process is illustrated by using time-velocity histories, Fourier frequency spectrum analysis and the phase-space rajectories.

MODIFIED DIRECT TWOS-COMPLEMENT PARALLEL ARRAY MULTIPLICATION ALGORITHM FOR COMPLEX MATRIX OPERATION

A direct twos-complement parallel array multiplication algorithm is introduced and modified for digital optical numerical computation. The modified version overcomes the problems encountered in the conventional optical twos-complement algorithm. In the array, all the summands are generated in parallel, and the relevant summands having the same weights are added simultaneously without carries, resulting in the product expressed in a mixed twos-complement system. In a two-stage array, complex multiplication is possible with using four real subarrays. Furthermore, with a three-stage array architecture, complex matrix operation is straightforwardly accomplished. In the experiment, parallel two-stage array complex multiplication with liquid-crystal panels is demonstrated.

Three-dimensional superresolution by three-zone complex pupil filters

Complex pupil filters are introduced to improve the three-dimensional resolving power of an optical imaging system. Through the design of the essential parameters of such filters, the transmittance and radius of the first zone, three-dimensional superresolution is realized. The Strehl ratio and the transverse and axial gains of such filters are analyzed in detail. A series of simulation examples of such filters are also presented that prove that three-dimensional superresolution can be realized. The advantage of such filters is that it is easy to realize three-dimensional superresolution, and the disadvantage is that the sidelobes of the axial intensity distribution are too high. But this can be overcome by the application of a confocal system. (C) 2005 Optical Society of America.

One-shot parallel complex Fourier-domain optical coherence tomography using a spatial carrier frequency

We propose a novel method of one-shot parallel complex Fourier-domain optical coherence tomography using a spatial carrier frequency for full range imaging. The spatial carrier frequency is introduced into the 2-D spectral interferogram in the lateral direction by using a tilted reference wavefront. This spatial-carrier- contained 2-D spectral interferogram is recorded with one shot of a 2-D CCD camera, and is Fourier-transformed in the lateral direction to obtain a 2-D complex spectral interferogram by a spatial-carrier technique. A full-range tomogram is reconstructed from the 2-D complex spectral interferogram. The principle of this method is confirmed by cross-sectional imaging of a glass slip object. (c) 2008 Society of Photo-Optical Instrumentation Engineers.