Models for spin-state transitions in solids

The model for spin-state transitions described by Bari and Sivardiere (1972) is static and can be solved exactly even when the dynamics of the lattice are included; the dynamic model does not, however, show any phase transition. A coupling between the octahedra, on the other hand, leads to a phase transition in the dynamical two-sublattice displacement model. A coupling of the spin states to the cube of the sublattice displacement leads to a first-order phase transition. The most reasonable model appears to be a two-phonon model in which an ion-cage mode mixes the spin states, while a breathing mode couples to the spin states without mixing. This model explains the non-zero population of high-spin states at low temperatures, temperature-dependent variations in the inverse susceptibility and the spin-state population ratio, as well as the structural phase transitions accompanying spin-state transitions found in some systems.

Cubicity of Interval Graphs and the Claw Number

Let G(V, E) be a simple, undirected graph where V is the set of vertices and E is the set of edges. A b-dimensional cube is a Cartesian product l(1) x l(2) x ... x l(b), where each l(i) is a closed interval of unit length on the real line. The cub/city of G, denoted by cub(G), is the minimum positive integer b such that the vertices in G can be mapped to axis parallel b-dimensional cubes in such a way that two vertices are adjacent in G if and only if their assigned cubes intersect. An interval graph is a graph that can be represented as the intersection of intervals on the real line-i.e. the vertices of an interval graph can be mapped to intervals on the real line such that two vertices are adjacent if and only if their corresponding intervals overlap. Suppose S(m) denotes a star graph on m+1 nodes. We define claw number psi(G) of the graph to be the largest positive integer m such that S(m) is an induced subgraph of G. It can be easily shown that the cubicity of any graph is at least log(2) psi(G)]. In this article, we show that for an interval graph G log(2) psi(G)-]<= cub(G)<=log(2) psi(G)]+2. It is not clear whether the upper bound of log(2) psi(G)]+2 is tight: till now we are unable to find any interval graph with cub(G)> (log(2)psi(G)]. We also show that for an interval graph G, cub(G) <= log(2) alpha], where alpha is the independence number of G. Therefore, in the special case of psi(G)=alpha, cub(G) is exactly log(2) alpha(2)]. The concept of cubicity can be generalized by considering boxes instead of cubes. A b-dimensional box is a Cartesian product l(1) x l(2) x ... x l(b), where each I is a closed interval on the real line. The boxicity of a graph, denoted box(G), is the minimum k such that G is the intersection graph of k-dimensional boxes. It is clear that box(G)<= cub(G). From the above result, it follows that for any graph G, cub(G) <= box(G)log(2) alpha]. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 65: 323-333, 2010

A heuristic clustering algorithm using union of overlapping pattern-cells

Relative geometric arrangements of the sample points, with reference to the structure of the imbedding space, produce clusters. Hence, if each sample point is imagined to acquire a volume of a small M-cube (called pattern-cell), depending on the ranges of its (M) features and number (N) of samples; then overlapping pattern-cells would indicate naturally closer sample-points. A chain or blob of such overlapping cells would mean a cluster and separate clusters would not share a common pattern-cell between them. The conditions and an analytic method to find such an overlap are developed. A simple, intuitive, nonparametric clustering procedure, based on such overlapping pattern-cells is presented. It may be classified as an agglomerative, hierarchical, linkage-type clustering procedure. The algorithm is fast, requires low storage and can identify irregular clusters. Two extensions of the algorithm, to separate overlapping clusters and to estimate the nature of pattern distributions in the sample space, are also indicated.

Analytical and simulation studies of a multiprocessor system for high-speed numerical computations

This paper describes the architecture of a multiprocessor system which we call the Broadcast Cube System (BCS) for solving important computation intensive problems such as systems of linear algebraic equations and Partial Differential Equations (PDEs), and highlights its features. Further, this paper presents an analytical performance study of the BCS, and it describes the main details of the design and implementation of the simulator for the BCS.

Time-Dependent Dynamics of a Planar Galaxy Model

Time-dependent models of collisionless stellar systems with harmonic potentials allowing for an essentially exact analytic description have recently been described. These include oscillating spheres and spheroids. This paper extends the analysis to time-dependent elliptic discs. Although restricted to two space dimensions, the systems are richer in that their parameters form a 10-dimensional phase space (in contrast to six for the earlier models). Apart from total energy and angular momentum, two additional conserved quantities emerge naturally. These can be chosen as the areas of extremal sections of the ellipsoidal region of phase space occupied by the system (their product gives the conserved volume). The present paper describes the construction of these models. An application to a tidal encounter is given which allows one to go beyond the impulse approximation and demonstrates the effects of rotation of the perturbed system on energy and angular-momentum transfer. The angular-momentum transfer is shown to scale inversely as the cube of the encounter velocity for an initial configuration of the perturbed galaxy with zero quadrupole moment.

Formation of a single, rotated-Brass (1 1 0)< 5 5 6 > texture by hot cross-rolling of an Al-Zn-Mg-Cu-Zr alloy

The present work describes the evolution of a strong, single-component rotated-Brass ((1 1 0) < 5 5 6 >) texture in an Al-Zn-Mg-Cu-Zr alloy by an uneven hot cross-rolling with frequent interpass annealing. This texture development is unique because hot rolling of aluminum alloys results in orientation distribution along the ``beta-fibre''. It has been demonstrated that the deformation by cross-rolling of a partially recrystallized grain structure having rotated-Cube and Goss orientations, and the recrystallization resistance of near-Brass-oriented elongated grains play a critical role in development of this texture. (C) 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Symmetry adaptation of correlated states in the valence bond basis

Symmetry?adapted linear combinations of valence?bond (VB) diagrams are constructed for arbitrary point groups and total spin S using diagrammatic VB methods. VB diagrams are related uniquely to invariant subspaces whose size reflects the number of group elements; their nonorthogonality leads to sparser matrices and is fully incorporated into a binary integer representation. Symmetry?adapated linear combinations of VB diagrams are constructed for the 1764 singlets of a half?filled cube of eight sites, the 2.8 million ??electron singlets of anthracene, and for illustrative S?0 systems.

Lossless and lossy image compression using Boolean function minimization

A novel approach for lossless as well as lossy compression of monochrome images using Boolean minimization is proposed. The image is split into bit planes. Each bit plane is divided into windows or blocks of variable size. Each block is transformed into a Boolean switching function in cubical form, treating the pixel values as output of the function. Compression is performed by minimizing these switching functions using ESPRESSO, a cube based two level function minimizer. The minimized cubes are encoded using a code set which satisfies the prefix property. Our technique of lossless compression involves linear prediction as a preprocessing step and has compression ratio comparable to that of JPEG lossless compression technique. Our lossy compression technique involves reducing the number of bit planes as a preprocessing step which incurs minimal loss in the information of the image. The bit planes that remain after preprocessing are compressed using our lossless compression technique based on Boolean minimization. Qualitatively one cannot visually distinguish between the original image and the lossy image and the value of mean square error is kept low. For mean square error value close to that of JPEG lossy compression technique, our method gives better compression ratio. The compression scheme is relatively slower while the decompression time is comparable to that of JPEG.

Comparative study on flexural response of full and partial depth fiber-reinforced high-strength concrete

This study presents the results of an experimental and analytical comparison of the flexural behavior of a high-strength concrete specimen (no conventional reinforcement) with an average plain concrete cube strength of nearly 65 MPa and containing trough shape steel fibers. Trough shape steel fibers with a volume fraction ranging from 0 to 1.5% and having a constant aspect ratio of 80 have been used in this study. Increased toughness and a more ductile stress-strain response were observed with an increase in fiber content, when the fibers were distributed over the full/partial depth of the beam cross section. Based on the tests, a robust analytical procedure has been proposed to establish the required partial depth to contain fiber-reinforced concrete (FRC) so as to obtain the flexural capacity of a member with FRC over the full depth. It is expected that this procedure will help designers in properly estimating the required partial depth of fibers in composite sections for specific structural applications. Empirical and mechanistic relations have also been proposed in this study to establish the load-deflection behavior of high-strength FRC.

Morphology and thermal characteristics of nano-sized Pb-Sn inclusions in Al

Nanoembedded aluminum alloys with bimetallic dispersoids of Sn and Pb of compositions Sn-82-Pb-18,Pb- Sn-64-Pb-36, and Sn-54-Pb-46 were synthesized by rapid solidification. The two phases, face-centered-cubic Pb and tetragonal Sn solid-solution, coexist in all the particles. The crystallographic relation between the two phases and the matrix depends upon the solidification pathways adopted by the particles. For Al-(Sn-82-Pb-18), we report a new orientation relation given by [011]Al//[010]Sn and (011)Al//(101)Sn. Pb exhibits a cube-on-cube orientation with Al in few particles, while in others no orientation relationship could be observed. In contrast, Pb in Sn-64-Pb-36 and Sn-54-Pb-46 particles always exhibits cube-on-cube orientation with the matrix. Sn does not show any orientation relationship with Al or Pb in these cases. Differential scanning calorimetry studies revealed melting at eutectic temperature for all compositions, although solidification pathways are different. Attempts were made to correlate these with the melting and heterogeneous nucleation. characteristics.

Morphology and thermal characteristics of nano-sized Pb–Sn inclusions in Al

Nanoembedded aluminum alloys with bimetallic dispersoids of Sn and Pb of compositions Sn82–Pb18, Sn64–Pb36, and Sn54–Pb46 were synthesized by rapid solidification. The two phases, face-centered-cubic Pb and tetragonal Sn solid-solution, coexist in all the particles. The crystallographic relation between the two phases and the matrix depends upon the solidification pathways adopted by the particles. For Al–(Sn82–Pb18), we report a new orientation relation given by [011]Al//[010]Sn and (o11)A1//(101)Sn. Pb exhibits a cube-on-cube orientation with Al in few particles, while in others no orientation relationship could be observed. In contrast, Pb in Sn64–Pb36 and Sn54–Pb46 particles always exhibits cube-on-cube orientation with the matrix. Sn does not show any orientation relationship with Al or Pb in these cases. Differential scanning calorimetry studies revealed melting at eutectic temperature for all compositions, although solidification pathways are different. Attempts were made to correlate these with the melting and heterogeneous nucleation characteristics.

Epitaxial Growth of Co3O4 Films by Low Temperature, Low Pressure Chemical Vapor Deposition

The growth of strongly oriented or epitaxial thin films of metal oxides generally requires relatively high growth temperatures or infusion of energy to the growth surface through means such as ion bombardment. We have grown high quality epitaxial thin films of Co3O4 on different substrates at a temperature as low as 450°C by low-pressure metal-organic chemical vapor deposition (MOCVD) using cobalt(II) acetylacetonate as the precursor. With oxygen as the reactant gas, polycrystalline Co3O4 films are formed on glass and Si(100) in the temperature range 350-550°C. Under similar conditions of growth, highly oriented films of Co3O4 are formed on SrTiO3(100) and LaAlO3(100). The film on LaAlO3(100) grown at 450°C show a rocking curve FWHM of 1.61°, which reduces to 1.32° when it is annealed in oxygen at 725°C. The film on SrTiO3(100) has a FWHM of 0.330 (as deposited) and 0.29° (after annealing at 725°C). The ø-scan analysis shows cube-on-cube epitaxy on both these substrates. The quality of epitaxy on SrTiO3(100) is comparable to the best of the pervoskite-based oxide thin films grown at significantly higher temperatures.

Percolation and Connectivity in AB Random Geometric Graphs

Given two independent Poisson point processes ©(1);©(2) in Rd, the AB Poisson Boolean model is the graph with points of ©(1) as vertices and with edges between any pair of points for which the intersection of balls of radius 2r centred at these points contains at least one point of ©(2). This is a generalization of the AB percolation model on discrete lattices. We show the existence of percolation for all d ¸ 2 and derive bounds for a critical intensity. We also provide a characterization for this critical intensity when d = 2. To study the connectivity problem, we consider independent Poisson point processes of intensities n and cn in the unit cube. The AB random geometric graph is de¯ned as above but with balls of radius r. We derive a weak law result for the largest nearest neighbour distance and almost sure asymptotic bounds for the connectivity threshold.

On a Novel Geometric Representation of Rotation

This paper presents a novel method of representing rotation and its application to representing the ranges of motion of coupled joints in the human body, using planar maps. The present work focuses on the viability of this representation for situations that relied on maps on a unit sphere. Maps on a unit sphere have been used in diverse applications such as Gauss map, visibility maps, axis-angle and Euler-angle representations of rotation etc. Computations on a spherical surface are difficult and computationally expensive; all the above applications suffer from problems associated with singularities at the poles. There are methods to represent the ranges of motion of such joints using two-dimensional spherical polygons. The present work proposes to use multiple planar domain “cube” instead of a single spherical domain, to achieve the above objective. The parameterization on the planar domains is easy to obtain and convert to spherical coordinates. Further, there is no localized and extreme distortion of the parameter space and it gives robustness to the computations. The representation has been compared with the spherical representation in terms of computational ease and issues related to singularities. Methods have been proposed to represent joint range of motion and coupled degrees of freedom for various joints in digital human models (such as shoulder, wrist and fingers). A novel method has been proposed to represent twist in addition to the existing swing-swivel representation.

WEPA: Wind energy potential assessment-spatial decision support system

Spatial Decision Support System (SDSS) assist in strategic decision-making activities considering spatial and temporal variables, which help in Regional planning. WEPA is a SDSS designed for assessment of wind potential spatially. A wind energy system transforms the kinetic energy of the wind into mechanical or electrical energy that can be harnessed for practical use. Wind energy can diversify the economies of rural communities, adding to the tax base and providing new types of income. Wind turbines can add a new source of property value in rural areas that have a hard time attracting new industry. Wind speed is extremely important parameter for assessing the amount of energy a wind turbine can convert to electricity: The energy content of the wind varies with the cube (the third power) of the average wind speed. Estimation of the wind power potential for a site is the most important requirement for selecting a site for the installation of a wind electric generator and evaluating projects in economic terms. It is based on data of the wind frequency distribution at the site, which are collected from a meteorological mast consisting of wind anemometer and a wind vane and spatial parameters (like area available for setting up wind farm, landscape, etc.). The wind resource is governed by the climatology of the region concerned and has large variability with reference to space (spatial expanse) and time (season) at any fixed location. Hence the need to conduct wind resource surveys and spatial analysis constitute vital components in programs for exploiting wind energy. SDSS for assessing wind potential of a region / location is designed with user friendly GUI’s (Graphic User Interface) using VB as front end with MS Access database (backend). Validation and pilot testing of WEPA SDSS has been done with the data collected for 45 locations in Karnataka based on primary data at selected locations and data collected from the meteorological observatories of the India Meteorological Department (IMD). Wind energy and its characteristics have been analysed for these locations to generate user-friendly reports and spatial maps. Energy Pattern Factor (EPF) and Power Densities are computed for sites with hourly wind data. With the knowledge of EPF and mean wind speed, mean power density is computed for the locations with only monthly data. Wind energy conversion systems would be most effective in these locations during May to August. The analyses show that coastal and dry arid zones in Karnataka have good wind potential, which if exploited would help local industries, coconut and areca plantations, and agriculture. Pre-monsoon availability of wind energy would help in irrigating these orchards, making wind energy a desirable alternative.