An optimal parallel algorithm for sparse matrix bandwidth reduction on a linear array

A simple and efficient algorithm for the bandwidth reduction of sparse symmetric matrices is proposed. It involves column-row permutations and is well-suited to map onto the linear array topology of the SIMD architectures. The efficiency of the algorithm is compared with the other existing algorithms. The interconnectivity and the memory requirement of the linear array are discussed and the complexity of its layout area is derived. The parallel version of the algorithm mapped onto the linear array is then introduced and is explained with the help of an example. The optimality of the parallel algorithm is proved by deriving the time complexities of the algorithm on a single processor and the linear array.

Error-free matrix symmetrizers and equivalent symmetric matrices

A symmetrizer of the matrix A is a symmetric solution X that satisfies the matrix equation XA=AprimeX. An exact matrix symmetrizer is computed by obtaining a general algorithm and superimposing a modified multiple modulus residue arithmetic on this algorithm. A procedure based on computing a symmetrizer to obtain a symmetric matrix, called here an equivalent symmetric matrix, whose eigenvalues are the same as those of a given real nonsymmetric matrix is presented.

Dry sliding wear of A356-Al-SiCp composites

Aluminium alloy (A356)-SiC composites containing 15 and 25 wt.% silicon carbide particles (average size 43 μm) were tested for sliding wear at different loads using a pin on disc machine. Composites exhibited better wear resistance compared with unreinforced alloy up to a pressure of 26 MPa. Scanning electron microscopy examination of worn surfaces and subsurfaces show that the presence of dispersed SiC particles help in reducing the propensity of material flow at the surface, at the same time leading to the formation of an iron-rich layer on the surface.

Effect of morphology and particle size on the ionic conductivities of composite solid electrolytes

A model incorporating the surface conductivity and morphology of the composite solid electrolytes is envisaged to explain their conduction behaviour. The conductivity data on LinX−50 m/o Al2O3 (X = F−, Cl−, Br−, CO32−, SO42−, PO43−) composites prepared by thermal decomposition of LinX·2nAl(OH)3·mH2O salts and Li2SO4−A (A=Al2O3, CeO2, Y2O3, Yb2O3, Zr2O3, ZrO2 and BaTiO3) composites prepared by mechanical mixing of the components are examined in the light of this model. It is surmised that the particle size of both the dispersoids and the hosts not only influence the ionic conductivity of the host matrix but also affect its bulk properties.

Processing maps for hot-working of powder metallurgy 1100 Al-10 vol % SiC-particulate metal-matrix composite

The hot-working characteristics of the metal-matrix composite (MMC) Al-10 vol % SiC-particulate (SiCp) powder metallurgy compacts in as-sintered and in hot-extruded conditions were studied using hot compression testing. On the basis of the stress-strain data as a function of temperature and strain rate, processing maps depicting the variation in the efficiency of power dissipation, given by eegr = 2m/(m+1), where m is the strain rate sensitivity of flow stress, have been established and are interpreted on the basis of the dynamic materials model. The as-sintered MMC exhibited a domain of dynamic recrystallization (DRX) with a peak efficiency of about 30% at a temperature of about 500°C and a strain rate of 0.01 s�1. At temperatures below 350°C and in the strain rate range 0.001�0.01 s�1 the MMC exhibited dynamic recovery. The as-sintered MMC was extruded at 500°C using a ram speed of 3 mm s�1 and an extrusion ratio of 10ratio1. A processing map was established on the extruded product, and this map showed that the DRX domain had shifted to lower temperature (450°C) and higher strain rate (1 s�1). The optimum temperature and strain rate combination for powder metallurgy billet conditioning are 500°C and 0.01 s�1, and the secondary metal-working on the extruded product may be done at a higher strain rate of 1 s�1 and a lower temperature of 425°C.

Relationship Between The Impedance Matrix And The Transfer Matrix With Specific Reference To Symmetrical, Reciprocal And Conservative Systems

Impedance matrix and transfer matrix methods are often used in the analysis of linear dynamical systems. In this paper, general relationships between these matrices are derived. The properties of the impedance matrix and the transfer matrix of symmetrical systems, reciprocal systems and conservative systems are investigated. In the process, the following observations are made: (a) symmetrical systems are not a subset of reciprocal systems, as is often misunderstood; (b) the cascading of reciprocal systems again results in a reciprocal system, whereas cascading of symmetrical systems does not necessarily result in a symmetrical system; (c) the determinant of the transfer matrix, being ±1, is a property of both symmetrical systems and reciprocal systems, but this condition, however, is not sufficient to establish either the reciprocity or the symmetry of the system; (d) the impedance matrix of a conservative system is skew-Hermitian.

Structural, mechanical and biocompatibility studies of hydroxyapatite-derived composites toughened by zirconia addition

Hydroxyapatite(OHAp)-based ceramic composites with added ZrO2 have been prepared both by sintering at 1400 °C and by hot isostatic pressing (HIP) at 1450 °C and 140 MPa pressure (argon atmosphere). The development of the crystalline phases and the microstructure of the composites have been examined using X-ray diffraction, electron microscopy, infrared and magic-angle spinning nuclear magnetic resonance (MASNMR) spectroscopic techniques. The fracture toughness and biocompatibility of the composites have also been studied. The effect of the addition of CeO2- and Y2O3-stabilized ZrO2 and of simple monoclinic ZrO2 to the initial physical mixture, on the structure and properties of the resulting composites has been investigated. In most of the sintered or HIP samples, the OHAp decomposes into tricalcium phosphate (β-TCP). CaO, which forms as a product of decomposition, dissolves completely in ZrO2 and stabilizes the latter in its cubic/tetragonal phase. Presence of the β-TCP phase in the product seems to be the result of a structural synergistic effect of hexagonal OHAp. Two structurally distinct orthophosphate groups have been identified in the composites by MASNMR of 31P and attributed to decomposition products of OHAp at higher temperatures. The composites possess high KIC values (2–3 times higher than that of pure OHAp). Decomposition of hydroxyapatite gives rise to differences in microstructure between HIP and simply sintered composites although fracture toughness values are similar in magnitude indicating the presence of several toughening mechanisms. The in vitro SP2-O cell test suggests that these composites possess good biocompatibility. The combination of good biocompatibility, desirable microstructure and easy availability of initial reactants indicates that the simply sintered composite of OHAp and monoclinic ZrO2(ZAP-30) appears to be the most suitable for prosthetic applications.

Non-linearity in piezo-fiber reinforced composites: an asymptotic approach

An asymptotically correct analysis is developed for Macro Fiber Composite unit cell using Variational Asymptotic Method (VAM). VAM splits the 3D nonlinear problem into two parts: A 1D nonlinear problem along the length of the fiber and a linear 2D cross-sectional problem. Closed form solutions are obtained for the 2D problem which are in terms of 1D parameters.

The superheating of Pb embedded in a Zn matrix the role of interface melting

Evidence of a shape-dependent superheating of entrained nanosized Pb particles in a Zn matrix has been presented. It is shown that size dependence and pressure effects cannot explain the observed differences in melting points. The importance of crystallography and morphology at the microlevel at the interphase interface in controlling interfacial melting has been emphasized in order to explain the melting of entrained particles.

Large negative magnetoresistance and metal-insulator transition observed in MnO/C composite coatings grown on ceramic alumina by metalorganic chemical vapor deposition

MnO/C composite coatings were grown by the metalorganic chemical vapor deposition process on ceramic alumina in argon ambient. Characterization by various techniques confirms that these coatings are homogeneous composites comprising nanometer-sized MnO particles embedded in a matrix of nanometer-sized graphite. Components of the MnO/C composite coating crystalline disordered, but are electrically quite conductive. Resistance vs. temperature measurements show that coating resistance increases exponentially from a few hundred ohms at room temperature to a few megaohms at 30 K. Logarithmic plots of reduced activation energy vs. temperature show that the coating material undergoes a metal-insulator transition. The reduced activation energy exponent for the film under zero magnetic field was 2.1, which is unusually high, implying that conduction is suppressed at much faster rate than the Mott or the Efros-Shklovskii hopping mechanism. Magnetoconductance us. magnetic field plots obtained at various temperatures show a high magnetoconductance (similar to 28.8%) at 100 K, which is unusually large for a disordered system, wherein magnetoresistance is attributed typically to weak localization. A plausible explanation for the unusual behavior observed in the carbonaceous disordered composite material is proposed. (C) 2010 Elsevier Ltd. All rights reserved.

Heterogeneous nucleation of pb particles embedded in a Zn matrix

Zinc-10 and 20 wt pct Pb alloys have been rapidly solidified by melt spinning to obtain a very fine scale dispersion of nanometer-sized Pb particles embedded in Zn matrix. The microstructure and crystallography of the Pb particles have been studied using transmission electron microscopy (TEM). Each embedded Pb particle is a single crystal, with a truncated hexagonal biprism shape with the 6/mmm Zn matrix point group symmetry surrounded by and { 0001 á },\text { \text10[`\text1] \text0 },\text and { \text10[`\text1] \text1 }0001 1010 and 1011 facets. The Pb particles solidify with a well-defined orientation relationship with the Zn matrix of ( 0001 )Zn ||(111)Pb\text and\text [ \text11[`\text2] \text0 ]Zn| ||[ 1[`1] 0 ]Pb 0001Zn(111)Pb and 1120Zn110Pb . The melting and solidification behavior of the Pb particle have been studied using differential scanning calorimetry (DSC). The Pb particles solidify with an undercooling of approximately 30 K, by heterogeneous nucleation on the {0001} facets of the surrounding Zn matrix, with an apparent contact angle of 23 deg.

Characteristics of superplasticity domain in the processing map for hot working of an Al alloy 2014---20vol.%Al2O3 metal matrix composite

The processing map for hot working of Al alloy 2014-20vol.%Al2O3 particulate-reinforced cast-plus-extruded composite material has been generated covering the temperature range 300-500 degrees C and the strain rate range 0.001-10 s(-1) based on the dynamic materials model. The efficiency eta of power dissipation given by 2m/(m + 1), where m is the strain rate sensitivity, is plotted as a function of temperature and strain rate to obtain a processing map. A domain of superplasticity has been identified, with a peak efficiency of 62% occurring at 500 degrees C and 0.001 s(-1). The characteristics of this domain have been studied with the help of microstructural evaluation and hot-ductility measurements. Microstructural instability is predicted at higher strain rates above (ls(-1)) and lower temperatures (less than 350 degrees C).

Concise row-pruning algorithm to invert a matrix

Presented here, in a vector formulation, is an O(mn2) direct concise algorithm that prunes/identifies the linearly dependent (ld) rows of an arbitrary m X n matrix A and computes its reflexive type minimum norm inverse A(mr)-, which will be the true inverse A-1 if A is nonsingular and the Moore-Penrose inverse A+ if A is full row-rank. The algorithm, without any additional computation, produces the projection operator P = (I - A(mr)- A) that provides a means to compute any of the solutions of the consistent linear equation Ax = b since the general solution may be expressed as x = A(mr)+b + Pz, where z is an arbitrary vector. The rank r of A will also be produced in the process. Some of the salient features of this algorithm are that (i) the algorithm is concise, (ii) the minimum norm least squares solution for consistent/inconsistent equations is readily computable when A is full row-rank (else, a minimum norm solution for consistent equations is obtainable), (iii) the algorithm identifies ld rows, if any, and reduces concerned computation and improves accuracy of the result, (iv) error-bounds for the inverse as well as the solution x for Ax = b are readily computable, (v) error-free computation of the inverse, solution vector, rank, and projection operator and its inherent parallel implementation are straightforward, (vi) it is suitable for vector (pipeline) machines, and (vii) the inverse produced by the algorithm can be used to solve under-/overdetermined linear systems.

Influence of Circular Defects on the Flexural Strength of Kevlar/Epoxy Composites

The flexural strength of the Kevlar/epoxy composite laminates, in the pres ence of unfilled and filled circular defects, was studied. Circular drillings of two different diameters extending up to the neutral axis from the compression face as well as through holes, at three different positions from the midspan, have been considered as simplified cases of dents and defects. Bonded buttons of aluminium metal have been tested and shown to yield a strength-wise compensation for test samples with depressions. Macrography of the failed specimens is also discussed.