A matrix identity and perturbation expressions

An identity expressing formally the diagonal and off-diagonal elements of an inverse of a matrix is deduced employing operator techniques. Several well-known perturbation expressions for the self-energy are deduced as special cases. A new approximation and other applications following from the above formalism are briefly indicated through illustrations from a perturbed harmonic oscillator, chemisorption approximations and Kelly's result in the problem of electron correlation.

On computing an equivalent symmetric matrix for a nonsymmetric matrix

A real or a complex symmetric matrix is defined here as an equivalent symmetric matrix for a real nonsymmetric matrix if both have the same eigenvalues. An equivalent symmetric matrix is useful in computing the eigenvalues of a real nonsymmetric matrix. A procedure to compute equivalent symmetric matrices and its mathematical foundation are presented.

Fabrication of device quality films of high loaded PPy/MWCNT nanocomposites using pulsed laser deposition

Polypyrrole (PPy) - multiwalled carbonnanotubes (MWCNT) nanocomposites with various MWCNT loading were prepared by in situ inversion emulsion polymerization technique. High loading of the nano filler were evaluated because of available inherent high interface area for charge separation in the nanocomposites. Solution processing of these conducting polymer nanocomposites is difficult because, most of them are insoluble in organic solvents. Device quality films of these composites were prepared by using pulsed laser deposition techniques (PLD). Comparative study of X-ray photoelectron spectroscopy (XPS) of bulk and film show that there is no chemical modification of polymer on ablation with laser. TEM images indicate PPy layer on MWCNT surface. SEM micrographs indicate that the MWCNT's are distributed throughout the film. It was observed that MWCNT in the composite held together by polymer matrix. Further more MWCNT diameter does not change from bulk to film indicating that the polymer layer remains intact during ablation. Even for very high loadings (80 wt.% of MWCNT's) of nanocomposites device quality films were fabricated, indicating laser ablation is a suitable technique for fabrication of device quality films. Conductivity of both bulk and films were measured using collinear four point probe setup. It was found that overall conductivity increases with increase in MWCNT loading. Comparative study of thickness with conductivity indicates that maximum conductivity was observed around 0.2 mu m. (C) 2010 Elsevier B.V. All rights reserved.

Free vibration of circular plates of arbitrary thickness

Free vibration of circular plates of arbitrary thickness is investigated using the method of initial functions. State-space approach is used to derive the governing equations of the above method. The formulation is such that theories of any desired order can be obtained by deleting higher terms in the infinite-order differential equations. Numerical results are obtained for flexural and extensional vibration of circular plates. Results are also computed using Mindlin's theory and they are in agreement with the present analysis.

An integer arithmetic method to compute generalized matrix inverse and solve linear equations exactly

An algorithm that uses integer arithmetic is suggested. It transforms anm ×n matrix to a diagonal form (of the structure of Smith Normal Form). Then it computes a reflexive generalized inverse of the matrix exactly and hence solves a system of linear equations error-free.

Thermal gap conductance at low contact pressures (<1 MPa): Effect of gold plating and plating thickness

Thermal contact conductance (TCC) measurements are made on bare and gold plated (<= 0.5 mu m) oxygen free high conductivity (OFHC) Cu and brass contacts in vacuum, nitrogen, and argon environments. It is observed that the TCC in gaseous environment is significantly higher than that in vacuum due to the enhanced thermal gap conductance. It is found that for a given contact load and gas pressure, the thermal gap conductance for bare OFHC Cu contacts is higher than that for gold plated contacts. It is due to the difference in the molecular weights of copper and gold, which influences the exchange of kinetic energy between the gas molecules and contact surfaces. Furthermore, the gap conductance is found to increase with increasing thickness of gold plating. Topography measurements and scanning electron microscopy (SEM) analysis of contact surfaces revealed that surfaces become smoother with increasing gold plating thickness, thus resulting in smaller gaps and consequently higher gap conductance. (C) 2010 Elsevier Ltd. All rights reserved.

Antimicrobial activity of highly stable silver nano particles embedded in agar-agar matrix as a thin film

Highly stable silver nanoparticles (Ag NPs) in agar-agar (Ag/agar) as inorganic-organic hybrid were obtained as free-standing film by in situ reduction of silver nitrate by ethanol. The antimicrobial activity of Ag/agar film on Escherichia coli (E. coil), Staphylococcus aureus (S. aureus), and Candida albicans (C albicans) was evaluated in a nutrient broth and also in saline solution. In particular, films were repeatedly tested for antimicrobial activity after recycling. UV-vis absorption and TEM studies were carried out on films at different stages and morphological studies on microbes were carried out by SEM. Results showed spherical Ag NPs of size 15-25 nm, having sharp surface plasmon resonance (SPR) band. The antimicrobial activity of Ag/agar film was found to be in the order, C. albicans > E. coil > S. aureus, and antimicrobial activity against C. albicans was almost maintained even after the third cycle. Whereas, in case of E. coil and S. aureus there was a sharp decline in antimicrobial activity after the second cycle. Agglomeration of Ag NPs in Ag/agar film on exposure to microbes was observed by TEM studies. Cytotoxic experiments carried out on HeLa cells showed a threshold Ag NPs concentration of 60 mu g/mL, much higher than the minimum inhibition concentration of Ag NPs (25.8 mu g/mL) for E. coli. The mechanical strength of the film determined by nanoindentation technique showed almost retention of the strength even after repeated cycle. (C) 2010 Elsevier Ltd. All rights reserved.

Design of nonequivalent self-routing networks based on a matrix model

In earlier work, nonisomorphic graphs have been converted into networks to realize Multistage Interconnection networks, which are topologically nonequivalent to the Baseline network. The drawback of this technique is that these nonequivalent networks are not guaranteed to be self-routing, because each node in the graph model can be replaced by a (2 × 2) switch in any one of the four different configurations. Hence, the problem of routing in these networks remains unsolved. Moreover, nonisomorphic graphs were obtained by interconnecting bipartite loops in a heuristic manner; the heuristic nature of this procedure makes it difficult to guarantee full connectivity in large networks. We solve these problems through a direct approach, in which a matrix model for self-routing networks is developed. An example is given to show that this model encompases nonequivalent self-routing networks. This approach has the additional advantage in that the matrix model itself ensures full connectivity.

On the uniformity of film thickness on rotating spherical substrates on a planar work holder

Curves for the uniformity in film thickness on spherical substrates are drawn for various geometries. The optimum source-to-substrate height for maximum uniformity of the film thickness is determined. These data are approximated to achieve uniform thickness on a large number of small planar substrates loaded on a large spherical substrate holder, the appropriate geometry being selected on the basis of the radius of curvature of the substrate holder.

Heterogeneous nucleation of solidification of cadmium particles embedded in an aluminium matrix

A hypomonotectic alloy of Al-4.5wt%Cd has been manufactured by melt spinning and the resulting microstructure examined by transmission electron microscopy. As-melt spun hypomonotectic Al-4.5wt%Cd consists of a homogeneous distribution of faceted 5 to 120 nm diameter cadmium particles embedded in a matrix of aluminium, formed during the monotectic solidification reaction. The cadmium particles exhibit an orientation relationship with the aluminium matrix of {111}Al//{0001}Cd and lang110rangAlAl//lang11¯20> Cd, with four cadmium particle variants depending upon which of the four {111}Al planes is parallel to {0001}Cd. The cadmium particles exibit a distorted cuboctahedral shape, bounded by six curved {100}Al//{20¯23}Cd facets, six curved {111}Al/{40¯43}Cd facets and two flat {111}Al//{0001}Cd facets. The as-melt spun cadmium particle shape is metastable and the cadmium particles equilibrate during heat treatment below the cadmium melting point, becoming elongated to increase the surface area and decrease the separation of the {111}Al//{0001}Cd facets. The equilibrium cadmium particle shape and, therefore, the anisotropy of solid aluminium-solid cadmium and solid aluminium -liquid cadmium surface energies have been monitored by in situ heating in the transmission electron microscope over the temperature range between room temperature and 420 °C. The anisotropy of solid aluminium-solid cadmium surface energy is constant between room temperature and the cadmium melting point, with the {100}Al//{20¯23}Cd surface energy on average 40% greater than the {111}Al//{0001}Cd surface energy, and 10% greater than the {111}Al//{40¯43Cd surface energy. When the cadmium particles melt at temperatures above 321 °C, the {100}Al//{20¯23}Cd facets disappear and the {111}Al//{40¯43}Cd and {111}A1//{0001}Cd surface energies become equal. The {111}Al facets do not disappear when the cadmium particles melt, and the anisotropy of solid aluminium-liquid cadmium surface energy decreases gradually with increasing temperature above the cadmium melting point. The kinetics of cadmium solidification have been examined by heating and cooling experiments in a differential scanning calorimeter over a range of heating and cooling rates. Cadmium particle solidification is nucleated catalytically by the surrounding aluminium matrix on the {111}Al faceted surfaces, with an undercooling of 56 K and a contact angle of 42 °. The nucleation kinetics of cadmium particle solidification are in good agreement with the hemispherical cap model of heterogeneous nucleation.

Structure and representation of correlation functions and the density matrix for a statistical wave field in optics

A systematic structure analysis of the correlation functions of statistical quantum optics is carried out. From a suitably defined auxiliary two‐point function we are able to identify the excited modes in the wave field. The relative simplicity of the higher order correlation functions emerge as a byproduct and the conditions under which these are made pure are derived. These results depend in a crucial manner on the notion of coherence indices and of unimodular coherence indices. A new class of approximate expressions for the density operator of a statistical wave field is worked out based on discrete characteristic sets. These are even more economical than the diagonal coherent state representations. An appreciation of the subtleties of quantum theory obtains. Certain implications for the physics of light beams are cited.

Magnetic, electric, and dielectric properties of FeCo alloy nanoparticles dispersed in amorphous matrix

Nanocrystalline Fe53Co47 alloy was synthesized by a single-step transmetallation chemical method at room temperature. The Fe53Co47 alloy nanoparticles of 77 and 47 wt% were dispersed in silica matrix by the sol-gel process using tetraethyl orthosilcate. Structural studies reveal that the as-prepared alloy powders are in bcc phase and silica is in an amorphous state. The phase-transition temperature and Mossbauer spectra analysis of the Fe-Co alloy establishes the homogeneous alloy formation. A saturation magnetization of 218 emu/g was obtained for pure FeCo alloy at room temperature. Scanning electron microscopic analysis demonstrates the hollow-sphere morphology for FeCo alloy particles. Magnetic nanocomposite consisting of 47 wt% FeCo-silica shows enhanced thermal stability over the native FeCo alloy. Electrical and dielectric properties of 47 wt% FeCo-silica nanocomposites were investigated as a function of frequency and temperature. It was found that the dielectric constants and dielectric loss were stable throughout the measured temperature (310-373 K). Our results indicate that FeCo-silica nanocomposite is a promising candidate for high-frequency applications. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

S-matrix for magnons in the D1-D5 system

We show that integrability and symmetries of the near horizon geometry of the D1-D5 system determine the S-matrix for the scattering of magnons with polarizations in AdS(3) x S-3 completely up to a phase. Using semi-classical methods we evaluate the phase to the leading and to the one-loop approximation in the strong coupling expansion. We then show that the phase obeys the unitarity constraint implied by the crossing relations to the one-loop order. We also verify that the dispersion relation obeyed by these magnons is one-loop exact at strong coupling which is consistent with their BPS nature.