A multistep transversal linearization (MTL) method in non-linear dynamics through a Magnus characterization

A new form of a multi-step transversal linearization (MTL) method is developed and numerically explored in this study for a numeric-analytical integration of non-linear dynamical systems under deterministic excitations. As with other transversal linearization methods, the present version also requires that the linearized solution manifold transversally intersects the non-linear solution manifold at a chosen set of points or cross-section in the state space. However, a major point of departure of the present method is that it has the flexibility of treating non-linear damping and stiffness terms of the original system as damping and stiffness terms in the transversally linearized system, even though these linearized terms become explicit functions of time. From this perspective, the present development is closely related to the popular practice of tangent-space linearization adopted in finite element (FE) based solutions of non-linear problems in structural dynamics. The only difference is that the MTL method would require construction of transversal system matrices in lieu of the tangent system matrices needed within an FE framework. The resulting time-varying linearized system matrix is then treated as a Lie element using Magnus’ characterization [W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math., VII (1954) 649–673] and the associated fundamental solution matrix (FSM) is obtained through repeated Lie-bracket operations (or nested commutators). An advantage of this approach is that the underlying exponential transformation could preserve certain intrinsic structural properties of the solution of the non-linear problem. Yet another advantage of the transversal linearization lies in the non-unique representation of the linearized vector field – an aspect that has been specifically exploited in this study to enhance the spectral stability of the proposed family of methods and thus contain the temporal propagation of local errors. A simple analysis of the formal orders of accuracy is provided within a finite dimensional framework. Only a limited numerical exploration of the method is presently provided for a couple of popularly known non-linear oscillators, viz. a hardening Duffing oscillator, which has a non-linear stiffness term, and the van der Pol oscillator, which is self-excited and has a non-linear damping term.

Block Convolution Using Discrete Trigonometric Transforms and Discrete Fourier Transform

We derive expressions for convolution multiplication properties of discrete cosine transform II (DCT II) starting from equivalent discrete Fourier transform (DFT) representations. Using these expressions, a method for implementing linear filtering through block convolution in the DCT II domain is presented. For the case of nonsymmetric impulse response, additional discrete sine transform II (DST II) is required for implementing the filter in DCT II domain, where as for a symmetric impulse response, the additional transform is not required. Comparison with recently proposed circular convolution technique in DCT II domain shows that the proposed new method is computationally more efficient.

Synthesis, spectral characterization, in-vitro microbiological evaluation and cytotoxic activities of novel macrocyclic bis hydrazone

A macrocyclic hydrazone Schiff base was synthesized by reacting 1,4-dicarbonyl phenyl dihydrazide with 2,6-diformyl-4-methyl phenol and a series of metal complexes with this new Schiff base were synthesized by reaction with Co(II), Ni(II) and Cu(II) metal salts. The Schiff base and its complexes have been characterized by elemental analyses, IR, H-1 NMR, UV-vis, FAB mass, ESR spectra, fluorescence, thermal, magnetic and molar conductance data. The analytical data reveal that the Co(II), Ni(II) and Cu(II) complexes possess 2:1 metal-ligand ratios. All the complexes are non-electrolytes in DMF and DMSO due to their low molar conductance values. Infrared spectral data suggest that the hydrazone Schiff base behaves as a hexadentate ligand with NON NON donor sequence towards the metal ions. The ESR spectral data shows that the metal-ligand bond has considerable covalent character. The electrochemical behavior of the copper(II) complex was investigated by cyclic voltammetry. The Schiff base and its complexes have also been screened for their antibacterial (Escherichia coli, Staphylococcus aureus, Shigella dysentery, Micrococcus, Bacillus subtilis, Bacillus cereus and Pseudomonas aeruginosa) and antifungal activities (Aspergillus niger, Penicillium and Candida albicans) by MIC method. The brine shrimp bioassay was also carried out to study their in-vitro cytotoxic properties. (C) 2009 Elsevier Masson SAS. All rights reserved.

Synthesis of BaSO4 nanoparticles by precipitation method using sodium hexa metaphosphate as a stabilizer

We describe the synthesis and structure of Barium sulfate nanoparticles by precipitation method in the presence of water soluble inorganic stabilizing agent, sodium hexametaphosphate, (NaPO3)(6). The structural parameters were refined by the Rietveld refinement method using powder X-ray diffraction data. Barium sulfate nanoparticles were crystallized in the orthorhombic structure with space group Pbnm (No. 62) having the lattice parameters a = 7.215(1) (angstrom), b = 8.949(1) (angstrom) and c = 5.501 (1) (angstrom) respectively. Transmission electron microscopy study reveals that the nanoparticles are size range, 30-50 nm. Fourier transform infrared spectra showed distinct absorption due to the SO42- moiety at 1115 and 1084 cm(-1) indicating formation of barium sulfate nanoparticles free from the phosphate group from the stabilizer used in the synthesis. (C) 2009 Elsevier Ltd. All rights reserved.

The partition of unity finite element method for elastic wave propagation in Reissner-Mindlin plates

This paper reports a numerical method for modelling the elastic wave propagation in plates. The method is based on the partition of unity approach, in which the approximate spectral properties of the infinite dimensional system are embedded within the space of a conventional finite element method through a consistent technique of waveform enrichment. The technique is general, such that it can be applied to the Lagrangian family of finite elements with specific waveform enrichment schemes, depending on the dominant modes of wave propagation in the physical system. A four-noded element for the Reissner-indlin plate is derived in this paper, which is free of shear locking. Such a locking-free property is achieved by removing the transverse displacement degrees of freedom from the element nodal variables and by recovering the same through a line integral and a weak constraint in the frequency domain. As a result, the frequency-dependent stiffness matrix and the mass matrix are obtained, which capture the higher frequency response with even coarse meshes, accurately. The steps involved in the numerical implementation of such element are discussed in details. Numerical studies on the performance of the proposed element are reported by considering a number of cases, which show very good accuracy and low computational cost. Copyright (C)006 John Wiley & Sons, Ltd.

Automatic Road Extraction using High Resolution Satellite Image Based on Texture Progressive Analysis and Normalized Cut Method

In this paper the approach for automatic road extraction for an urban region using structural, spectral and geometric characteristics of roads has been presented. Roads have been extracted based on two levels: Pre-processing and road extraction methods. Initially, the image is pre-processed to improve the tolerance by reducing the clutter (that mostly represents the buildings, parking lots, vegetation regions and other open spaces). The road segments are then extracted using Texture Progressive Analysis (TPA) and Normalized cut algorithm. The TPA technique uses binary segmentation based on three levels of texture statistical evaluation to extract road segments where as, Normalizedcut method for road extraction is a graph based method that generates optimal partition of road segments. The performance evaluation (quality measures) for road extraction using TPA and normalized cut method is compared. Thus the experimental result show that normalized cut method is efficient in extracting road segments in urban region from high resolution satellite image.

Wave propagation analysis in carbon nanotube embedded composite using wavelet based spectral finite elements

In this paper, elastic wave propagation is studied in a nanocomposite reinforced with multiwall carbon nanotubes (CNTs). Analysis is performed on a representative volume element of square cross section. The frequency content of the exciting signal is at the terahertz level. Here, the composite is modeled as a higher order shear deformable beam using layerwise theory, to account for partial shear stress transfer between the CNTs and the matrix. The walls of the multiwall CNTs are considered to be connected throughout their length by distributed springs, whose stiffness is governed by the van der Waals force acting between the walls of nanotubes. The analyses in both the frequency and time domains are done using the wavelet-based spectral finite element method (WSFEM). The method uses the Daubechies wavelet basis approximation in time to reduce the governing PDE to a set of ODEs. These transformed ODEs are solved using a finite element (FE) technique by deriving an exact interpolating function in the transformed domain to obtain the exact dynamic stiffness matrix. Numerical analyses are performed to study the spectrum and dispersion relations for different matrix materials and also for different beam models. The effects of partial shear stress transfer between CNTs and matrix on the frequency response function (FRF) and the time response due to broadband impulse loading are investigated for different matrix materials. The simultaneous existence of four coupled propagating modes in a double-walled CNT-composite is also captured using modulated sinusoidal excitation.

Synthesis, characterization and photoluminescence properties of Gd2O3:Eu3+ nanophosphors prepared by solution combustion method

Gd2O3:Eu3+ (0.5-8.0 mol%) nanophosphors have been prepared by low temperature solution combustion method using metal nitrates as oxidizers and oxalyl dihydrazide (ODH) as a fuel. The phosphors are well characterized by powder X-ray diffraction (PXRD), scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FT-IR) and photoluminescence (PL) techniques. PXRD patterns of as-formed and calcined (800 degrees C, 3 h) Gd2O3 powders exhibit monoclinic phase with mean crystallite sizes ranging from 20 to 50 nm. Eu3+ doping changes the structure from monoclinic to mixed phase of monoclinic and cubic. SEM micrographs shows the products are foamy, agglomerated and fluffy in nature due to the large amount of gases liberated during combustion reaction. Upon 254 nm excitation the photoluminescence of the Gd2O3:Eu3+ particles show red emission at 611 nm corresponding to D-5(0)-> F-7(2) transition. It is observed that PL intensity increases with calcination temperature. This might be attributed to better crystallization and eliminates the defects, which serve as centers of non-radiative relaxation for nanomaterials. It is observed that the optical energy gap (E-g) is widened with increase Eu3+ content. (C) 2010 Elsevier B.V. All rights reserved.

A hybrid electrochemical-thermal method for the preparation of large ZnO nanoparticles

A simple and efficient two-step hybrid electrochemical-thermal route was developed for the synthesis of large quantity of ZnO nanoparticles using aqueous sodium bicarbonate electrolyte and sacrificial Zn anode and cathode in an undivided cell under galvanostatic mode at room temperature. The bath concentration and current density were varied from 30 to 120 mmol and 0.05 to 1.5 A/dm(2). The electrochemically generated precursor was calcined for an hour at different range of temperature from 140 to 600 A degrees C. The calcined samples were characterized by XRD, SEM/EDX, TEM, TG-DTA, FT-IR, and UV-Vis spectral methods. Rietveld refinement of X-ray data indicates that the calcined compound exhibits hexagonal (Wurtzite) structure with space group of P63mc (No. 186). The crystallite sizes were in the range of 22-75 nm based on Debye-Scherrer equation. The TEM results reveal that the particle sizes were in the order of 30-40 nm. The blue shift was noticed in UV-Vis absorption spectra, the band gaps were found to be 5.40-5.11 eV. Scanning electron micrographs suggest that all the samples were randomly oriented granular morphology.

Spectral assignments based on the 13C NMR spectra of mixed liquid crystals of opposite diamagnetic anisotropies

The proton-decoupled 13C NMR spectra of mixtures of liquid crystals with opposite diamagnetic anisotropies have been studied in the natural abundance of 13C. A new method to assign the spectral lines to specific carbons in the liquid crystalline phase has been developed. For this purpose, the assignments of lines in the isotropic media are required, and they were obtained from two-dimensional hetero-COSY experiments. From the spectra in the �critical� mixtures where both the orientations of the liquid crystal directors, with the alignments along and perpendicular to the direction of the magnetic field, �coexist,� the 13C chemical-shift anisotropies have been determined, assuming uniaxial symmetry.

Rapid synthesis of room temperature ferromagnetic Ag-doped LaMnO3 perovskite phases by the solution combustion method

We report the rapid solution combustion synthesis and characterization of Ag-substituted LaMnO3 phases at relatively low temperature using oxalyl dihydrazide, as fuel. Structural parameters were refined by the Rietveld method using powder X-ray diffraction data. While the parent LaMnO3 crystallizes in the orthorhombic structure, the Ag-substituted compounds crystallize in the rhombohedral symmetry. On increasing Ag-content, unit cell volume and Mn-O-Mn bond angle decreases. The Fourier transform infra red spectrum shows two absorption bands corresponding to Mn-O stretching vibration (v(s) mode) and Mn-O-Mn deformation vibration (v(b) mode) around 600 cm(-1) and 400 cm(-1) for the compositions x = 0.0, 0.05 and 0.10, respectively. Electrical resistivity measurements reveal that composition-controlled metal to insulator transition, with the maximum metal to insulator being 280 K for the composition La0.75Ag0.25MnO3. Increase in magnetic moment was observed with increase in Ag-content. The maximum magnetic moment of 35 emu/g was observed for the composition La0.80Ag0.20MnO3. (C) 2010 Elsevier Ltd. All rights reserved.

Spectral element approach to wave propagation in uncertain beam structures

This paper presents a study on the uncertainty in material parameters of wave propagation responses in metallic beam structures. Special effort is made to quantify the effect of uncertainty in the wave propagation responses at high frequencies. Both the modulus of elasticity and the density are considered uncertain. The analysis is performed using a Monte Carlo simulation (MCS) under the spectral finite element method (SEM). The randomness in the material properties is characterized by three different distributions, the normal, Weibull and extreme value distributions. Their effect on wave propagation in beams is investigated. The numerical study shows that the CPU time taken for MCS under SEM is about 48 times less than for MCS under a conventional one-dimensional finite element environment for 50 kHz loading. The numerical results presented investigate effects of material uncertainties on high frequency modes. A study is performed on the usage of different beam theories and their uncertain responses due to dynamic impulse load. These studies show that even for a small coefficient of variation, significant changes in the above parameters are noticed. A number of interesting results are presented, showing the true effects of uncertainty response due to dynamic impulse load.

Direct Growth of Gold Nanorods on Gold and Indium Tin Oxide Surfaces: Spectral, Electrochemical, and Electrocatalytic Studies

The surfactant-assisted seed-mediated growth method was used for the formation of gold nanorods (GNRs) directly on gold (Au) and indium tin oxide (ITO) surfaces. Citrate-stabilized similar to 2.6 nm spherical gold nanoparticles (AuNPs) were first self-assembled on ITO or Au surfaces modified with (3-mercaptopropyl)-trimethoxysilane (MPTS) sol-gel film and then immersed in a cationic surfactant growth solution to form GNRs. The growth of GNRs on the MPTS sol gel film modified ITO surface was monitored by UV-visible spectroscopy. The ITO surface with the attached spherical AuNPs shows a surface plasmon resonance band at 550 nm. The intensity of this absorption band increases while increasing the immersion time of the AuNP-modified ITO surface into the growth solution, and after 5 h, an additional shoulder band around 680 nm was observed. The intensity of this shoulder band increases, and it was shifted to longer wavelength as the immersion time of the AuNP-modified ITO surface into the growth solution increases. After 20 h, a predominant wave at 720 nm was observed along with a band at 550 nm. Further immersion of the modified ITO surface into the growth solution did not change the absorption characteristics. The bands observed at 550 and 720 nm were characteristics of GNRs, corresponding to transverse and longitudinal waves, respectively. The AFM images showed the presence of GNRs on the surface of the MPTS sol gel modified ITO surface with a typical length of similar to 100-120 nm and a width of similar to 20-22 nm in addition to a few spherical AuNPs, indicating that seeded spherical AuNPs were not completely involved in the GNRs' formation. Finally, the electrocatalytic activity of the surface-grown GNRs on the MPTS sol gel film modified Au electrode toward the oxidation of ascorbic acid (AA) was studied. Unlike a polycrystalline Au electrode, the surface-grown GNR-modified electrode shows two well-defined voltammetric peaks for AA at 0.01 and 0.35 V in alkaline, neutral, and acidic pHs. The cause for the observed two oxidation peaks for AA was due to the presence of both nanorods and spherical nanoparticles on the electrode surface. The presence of spherical AuNPs on the MPTS sol gel film oxidized AA at more positive potential, whereas the GNRs oxidized AA at less positive potential. The observed 340 mV less positive potential shift in the oxidation of AA suggested that GNRs are better electrocatalysts for the oxidation of AA than the spherical AuNPs.

Data compression by linear prediction for storage and transmission of EEG signals

The EEG time series has been subjected to various formalisms of analysis to extract meaningful information regarding the underlying neural events. In this paper the linear prediction (LP) method has been used for analysis and presentation of spectral array data for the better visualisation of background EEG activity. It has also been used for signal generation, efficient data storage and transmission of EEG. The LP method is compared with the standard Fourier method of compressed spectral array (CSA) of the multichannel EEG data. The autocorrelation autoregressive (AR) technique is used for obtaining the LP coefficients with a model order of 15. While the Fourier method reduces the data only by half, the LP method just requires the storage of signal variance and LP coefficients. The signal generated using white Gaussian noise as the input to the LP filter has a high correlation coefficient of 0.97 with that of original signal, thus making LP as a useful tool for storage and transmission of EEG. The biological significance of Fourier method and the LP method in respect to the microstructure of neuronal events in the generation of EEG is discussed.

Synthesis, spectral characterization and in vitro microbiological evaluation of novel glyoxal, biacetyl and benzil bis-hydrazone macrocyclic Schiff bases and their Co(II), Ni(II) and Cu(II) complexes

A series of binuclear Co(II), Ni(II) and Cu(II) complexes were synthesized by the template condensation of glyoxal, biacetyl or benzil bis-hydrazide, 2,6-diformyl-4-methylphenol and Co(11), Ni(II) or Cu(II) chloride in a 2:2:2 M ratio in ethanol. These 22-membered macrocyclic complexes were characterized by elemental analyses, magnetic, molar conductance, spectral, thermal and fluorescence studies. Elemental analyses suggest the complexes have a 2:1 stoichiometry of the type (M2LX2]center dot nH(2)O and Ni(2)LX(2)2H(2)O]center dot nH(2)O (where M = Co(II) and Cu(II); L = H2L1, H2L2 and H2L3; X = Cl; n = 2). From the spectroscopic and magnetic studies, it has been concluded that the Co(11) and Cu(11) complexes display a five coordinated square pyramidal geometry and the Ni(II) complexes have a six coordinated octahedral geometry. The Schiff bases and their metal complexes have also been screened for their antibacterial and antifungal activities by the MIC method. (C) 2011 Elsevier Ltd. All rights reserved.