The Gaussian Toeplitz matrix

An analytical expression for the LL(T) decomposition for the Gaussian Toeplitz matrix with elements T(ij) = [1/(2-pi)1/2-sigma] exp[-(i - j)2/2-sigma-2] is derived. An exact expression for the determinant and bounds on the eigenvalues follows. An analytical expression for the inverse T-1 is also derived.

Symmetrizing a Hessenberg matrix: Designs for VLSI parallel processor arrays

A symmetrizer of a nonsymmetric matrix A is the symmetric matrix X that satisfies the equation XA = A(t)X, where t indicates the transpose. A symmetrizer is useful in converting a nonsymmetric eigenvalue problem into a symmetric one which is relatively easy to solve and finds applications in stability problems in control theory and in the study of general matrices. Three designs based on VLSI parallel processor arrays are presented to compute a symmetrizer of a lower Hessenberg matrix. Their scope is discussed. The first one is the Leiserson systolic design while the remaining two, viz., the double pipe design and the fitted diagonal design are the derived versions of the first design with improved performance.

Dry sliding wear of Al alloy 2024-Al203 particle metal matrix composites

In the present investigation, Al 2024-15vol.%Al2O3 particulate (average size, 18 mu m) composites were fabricated using the liquid metallurgy route. The wear and friction characteristics of Al alloy 2024 and Al 2024-15vol.%Al2O3p, composite in the as-extruded and peak-aged conditions were studied using a pin-on-disc machine (with a steel disc as the counterface material). The worn surfaces, subsurfaces and the debris were analysed in a scanning electron microscope.The performance of the composite in the as-extruded condition is slightly inferior to that of the unreinforced alloy. However, in the T6 condition, although the wear rates of two materials are initially comparable, the unreinforced alloy seizes while the composite does not within the tested range employed. In the as-extruded condition, the presence of Al2O3 particles is not particularly beneficial as they fracture and result in extensive localized cracking and removal of material from the surface. In the peak-aged condition, however, while the unreinforced alloy exhibits severe plastic deformation and undergoes seizure, there is no significant change in the mechanism in the case of the composite. Except in the case of the peak-aged unreinforced alloy, worn surfaces of all other materials show the presence of an iron-rich layer.

Heterogeneous nucleation of nanometre-sized Bi particles embedded in a Zn matrix

It is argued that the nanometric dispersion of Bi in a Zn matrix is an ideal model system for heterogeneous nucleation experiments. The classical theory of heterogeneous nucleation with a hemispherical cap model is applied to analyse the nucleation data. It is shown that, unlike the results of earlier experiments, the derived site density for catalytic nucleation and contact angle are realistic and strongly suggest the validity of the classical theory. The surface energy between the 0001 plane of Zn and the <10(1)over bar 2> plane of Bi, which constitute the epitaxial nucleation interface, is estimated to be 39 mJ m(-2).

Production and properties of carbon fibre/particle reinforced cast metal matrix composites

Carbon fibres/particles can be satisfactory reinforcing material in polymer, ceramic and metal matrices. Carbon fibres/particles reinforced polymer matrix composites and ceramic matrix composites are being used extensively in critical areas of application, but carbon fibre - metal matrix composites have not reached that stage yet. This paper discusses the salient aspects of production and specific properties of carbon fibre/particle reinforced cast metal matrix composites. It is envisaged that these materials will find extensive applications where cost, weight and thermal expansion are the key factors.

MIMO Precoding With X- and Y- Codes

We consider a slow fading multiple-input multiple-output (MIMO) system with channel state information at both the transmitter and receiver. A well-known precoding scheme is based upon the singular value decomposition (SVD) of the channel matrix, which transforms the MIMO channel into parallel subchannels. Despite having low maximum likelihood decoding (MLD) complexity, this SVD precoding scheme provides a diversity gain which is limited by the diversity gain of the weakest subchannel. We therefore propose X- and Y-Codes, which improve the diversity gain of the SVD precoding scheme but maintain the low MLD complexity, by jointly coding information across a pair of subchannels. In particular, subchannels with high diversity gain are paired with those having low diversity gain. A pair of subchannels is jointly encoded using a 2 2 real matrix, which is fixed a priori and does not change with each channel realization. For X-Codes, these rotation matrices are parameterized by a single angle, while for Y-Codes, these matrices are left triangular matrices. Moreover, we propose X-, Y-Precoders with the same structure as X-, Y-Codes, but with encoding matrices adapted to each channel realization. We observed that X-Codes/Precoders are good for well-conditioned channels, while Y-Codes/Precoders are good for ill-conditioned channels.

Chopped nonlinear magneto-optic rotation: A technique for precision measurements

We have developed a technique for precise measurement of small magnetic fields using nonlinear magneto-optic rotation (NMOR). The technique relies on the resonant laser beam being chopped. During the on time, the atoms are optically pumped into an aligned ground state (Delta m=2 coherence). During the off time, they freely precess around the magnetic field at the Larmor frequency. If the on-off modulation frequency matches (twice) the Larmor precession frequency, the rotation is resonantly enhanced in every cycle, thereby making the process like a repeated Ramsey measurement of the Larmor frequency. We study chopped-NMOR in a paraffin-coated Cs vapor cell. The out-of-phase demodulated rotation shows a Lorentzian peak of linewidth 85 mu G, corresponding to a sensitivity of 0.15nG/root Hz. We discuss the potential of this technique for the measurement of an atomic electric-dipole moment. Copyright (C) EPLA, 2011

Lopsidedness in WHISP galaxies I. Rotation curves and kinematic lopsidedness

The frequently observed lopsidedness of the distribution of stars and gas in disc galaxies is still considered as a major problem in galaxy dynamics. It is even discussed as an imprint of the formation history of discs and the evolution of baryons in dark matter haloes. Here, we analyse a selected sample of 70 galaxies from the Westerbork Hi Survey of Spiral and Irregular Galaxies. The Hi data allow us to follow the morphology and the kinematics out to very large radii. In the present paper, we present the rotation curves and study the kinematic asymmetry. We extract the rotation curves of the receding and approaching sides separately and show that the kinematic behaviour of disc galaxies can be classified into five different types: symmetric velocity fields where the rotation curves of the receding and approaching sides are almost identical; global distortions where the rotation velocities of the receding and approaching sides have an offset that is constant with radius; local distortions leading to large deviations in the inner and negligible deviations in the outer parts (and vice versa); and distortions that divide the galaxies into two kinematic systems that are visible in terms of the different behaviour of the rotation curves of the receding and approaching sides, which leads to a crossing and a change in side. The kinematic lopsidedness is measured from the maximum rotation velocities, averaged over the plateau of the rotation curves. This gives a good estimate of the global lopsidedness in the outer parts of the sample galaxies. We find that the mean value of the perturbation parameter denoting the lopsided potential as obtained from the kinematic data is 0.056. Altogether, 36% of the sample galaxies are globally lopsided, which can be interpreted as the disc responding to a halo that was distorted by a tidal encounter. In Paper II, we study the morphological lopsidedness of the same sample of galaxies.

Microstructure evolution during solidification of DRMMCs (discontinuously reinforced metal matrix composites): State of art

Distribution of particle reinforcements in cast composites is determined by the morphology of the solidification front. Interestingly, during solidification, the morphology of the interface is intrinsically affected by the presence of dispersed reinforcements. Thus the dispersoid distribution and length scale of matrix microstructure is a result of the interplay between these two. A proper combination of material and process parameters can be used to obtain composites with tailored microstructures. This requires the generation of a broad data base and optimization of the complete solidification process. The length scale of soldification microtructure has a large influence on the mechanical properties of the composites. This presentation addresses the concept of a particle distribution map which can help in predicting particle distribution under different solidification conditions Future research directions have also been indicated.

Studies on age-hardening characteristics of ceramic particle/matrix interfaces in Al-Cu-SiCp composites using ultra low-load-dynamic microhardness measurements

Ultra low-load-dynamic microhardness testing facilitates the hardness measurements in a very low volume of the material and thus is suited for characterization of the interfaces in MMC's. This paper details the studies on age-hardening behavior of the interfaces in Al-Cu-5SiC(p) composites characterized using this technique. Results of hardness studies have been further substantiated by TEM observations. In the solution-treated condition, hardness is maximum at the particle/matrix interface and decreases with increasing distance from the interface. This could be attributed to the presence of maximum dislocation density at the interface which decreases with increasing distance from the interface. In the case of composites subjected to high temperature aging, hardening at the interface is found to be faster than the bulk matrix and the aging kinetics becomes progressively slower with increasing distance from the interface. This is attributed to the dislocation density gradient at the interface, leading to enhanced nucleation and growth of precipitates at the interface compared to the bulk matrix. TEM observations reveal that the sizes of the precipitates decrease with increasing distance from the interface and thus confirms the retardation in aging kinetics with increasing distance from the interface.

Regarding the effect of aging heat treatment on the failure behaviour of a SiC reinforced Al based metal matrix composite

In the present study, 6061 Al metallic matrix was reinforced by 12.2 wt% df SiC particulates using liquid metallurgy route. The composite material thus obtained was extruded and characterized in the as-solutionized and peak aged conditions in order to delineate the effect of aging associated precipitation of secondary phases on the tensile fracture behavior of the composite samples. The results' of microstructural characterization studies carried out using scanning electron microscope revealed the increased presence of precipitated secondary phases in the metallic matrix and a more pronounced interfacial segregation of alloying elements in case of peak aged samples when compared to the as-solutionized samples. The results of the fractographic studies conducted on the as-solutionized samples revealed that the failure was dominated by the SiC particulates cracking while for the peak aged samples the fracture surface revealed a comparatively more pronounced SiC/6061 Al debonding and reduced SiC particulates cracking. This change in the failure behavior was rationalized in terms of embrittlement of the interfacial region brought about by the aging heat treatment and is correlated, in addition, with the mechanical properties of the composite samples in as-solutionized and peak aged conditions.

Microstructure and properties of squeeze cast Cu-carbon fibre metal matrix composite

There have been reported attempts of producing Cu based MMCs employing solid phase routes. In this work, copper was reinforced with short carbon fibres by pressure infiltration (squeeze casting) of molten metal through dry-separated carbon fibres. The resulting MMC's microstructure revealed uniform distribution of fibres with minimum amount of clustering. Hardness values are considerably higher than that for the unreinforced matrix. Addition of carbon fibres has brought in strain in the crystal lattice of the matrix, resulting in higher microhardness of MMCs and improved wear resistance. Tensile strength values of MMCs at elevated temperatures are considerably higher than that of the unreinforced matrix processed under identical conditions. (C) 1999 Kluwer Academic Publishers.

Muon-spin rotation spectra in the mixed phase of high-T-c superconductors: Thermal fluctuations and disorder effects

We study muon-spin rotation (mu SR) spectra in the mixed phase of highly anisotropic layered superconductors, specifically Bi2+xSr2-xCaCu2O8+delta (BSCCO), by modeling the fluid and solid phases of pancake Vortices using liquid-state and density functional methods. The role of thermal fluctuations in causing motional narrowing of mu SR line shapes is quantified in terms of a first-principles theory of the flux-lattice melting transition. The effects of random point pinning are investigated using a replica treatment of liquid-state correlations and a replicated density functional theory. Our results indicate that motional narrowing in the pure system, although substantial, cannot account for the remarkably small linewidths obtained experimentally at relatively high fields and low temperatures. We find that satisfactory agreement with the mu SR data for BSCCO in this regime can be obtained through the ansatz that this ''phase'' is characterized by frozen short-range positional correlations reflecting the structure of the liquid just above the melting transition. This proposal is consistent with recent suggestions of a ''pinned liquid'' or ''glassy'' state of pancake Vortices in the presence of pinning disorder. Our results for the high-temperature liquid phase indicate that measurable linewidths may be obtained in this phase as a consequence of density inhomogeneities induced by the pinning disorder. The results presented here comprise a unified, first-principles theoretical treatment of mu SR spectra in highly anisotropic layered superconductors in terms of a controlled set of approximations. [S0163-1829(99)08033-9].