Boxicity and Poset Dimension

Let G be a simple, undirected, finite graph with vertex set V (G) and edge set E(G). A k-dimensional box is a Cartesian product of closed intervals [a(1), b(1)] x [a(2), b(2)] x ... x [a(k), b(k)]. The boxicity of G, box(G), is the minimum integer k such that G can be represented as the intersection graph of k-dimensional boxes; i.e., each vertex is mapped to a k-dimensional box and two vertices are adjacent in G if and only if their corresponding boxes intersect. Let P = (S, P) be a poset, where S is the ground set and P is a reflexive, antisymmetric and transitive binary relation on S. The dimension of P, dim(P), is the minimum integer t such that P can be expressed as the intersection of t total orders. Let G(P) be the underlying comparability graph of P; i.e., S is the vertex set and two vertices are adjacent if and only if they are comparable in P. It is a well-known fact that posets with the same underlying comparability graph have the same dimension. The first result of this paper links the dimension of a poset to the boxicity of its underlying comparability graph. In particular, we show that for any poset P, box(G(P))/(chi(G(P)) - 1) <= dim(P) <= 2box(G(P)), where chi(G(P)) is the chromatic number of G(P) and chi(G(P)) not equal 1. It immediately follows that if P is a height-2 poset, then box(G(P)) <= dim(P) <= 2box(G(P)) since the underlying comparability graph of a height-2 poset is a bipartite graph. The second result of the paper relates the boxicity of a graph G with a natural partial order associated with the extended double cover of G, denoted as G(c): Note that G(c) is a bipartite graph with partite sets A and B which are copies of V (G) such that, corresponding to every u is an element of V (G), there are two vertices u(A) is an element of A and u(B) is an element of B and {u(A), v(B)} is an edge in G(c) if and only if either u = v or u is adjacent to v in G. Let P(c) be the natural height-2 poset associated with G(c) by making A the set of minimal elements and B the set of maximal elements. We show that box(G)/2 <= dim(P(c)) <= 2box(G) + 4. These results have some immediate and significant consequences. The upper bound dim(P) <= 2box(G(P)) allows us to derive hitherto unknown upper bounds for poset dimension such as dim(P) = 2 tree width (G(P)) + 4, since boxicity of any graph is known to be at most its tree width + 2. In the other direction, using the already known bounds for partial order dimension we get the following: (1) The boxicity of any graph with maximum degree Delta is O(Delta log(2) Delta), which is an improvement over the best-known upper bound of Delta(2) + 2. (2) There exist graphs with boxicity Omega(Delta log Delta). This disproves a conjecture that the boxicity of a graph is O(Delta). (3) There exists no polynomial-time algorithm to approximate the boxicity of a bipartite graph on n vertices with a factor of O(n(0.5-is an element of)) for any is an element of > 0 unless NP = ZPP.

Temperature dependent photoemission spectroscopy on lightly-doped sodium tungsten bronze

Temperature dependent photoemission studies on lightly doped (x = 0.025) sodium tungsten bronzes, NaxWO3 have been investigated by high-resolution photoemission spectroscopy. The experimental results show evidence for polaron formation at the valence band edge and the photoemission spectra taken in different modes of the electron analyzer suggest that the density of states at the valence band edge gradually moves to other k-points in the Brillouin zone with increasing temperature and explain the dynamics of polarons in the insulating disordered sodium tungsten bronzes. (C) 2012 Elsevier Ltd. All rights reserved.

Structural characterisation of reaction zone for friction stir welded aluminium-stainless steel joint

In the present investigation, commercially pure Al has been joined with 304 stainless steel (SS) by friction stir welding. The assembly finds widespread application in the field of cryogenics, nuclear, structural industries and domestic appliances. Microstructural characterisation was carried out using scanning and transmission electron microscopes. It has been found that diffusion of Fe, Cr and Ni is substantial within Al; however, diffusion of Al within 304SS is limited. Owing to interdiffusion of chemical species across the bondline, discrete islands of Fe3Al intermetallic form within the reaction zone. The rubbing action of tool over the butting edge of 304SS removed fine particles from 304SS, which were embedded in the stirring zone of Al matrix. Subsequently, austenite underwent phase transformation to ferrite due to large strain within this grain. Fracture path mainly moves through stirring zone of Al alloy under tensile loading; however, in some places, presence of Fe3Al compound has been also found.

Thermal instability and the feedback regulation of hot haloes in clusters, groups and galaxies

We present global multidimensional numerical simulations of the plasma that pervades the dark matter haloes of clusters, groups and massive galaxies (the intracluster medium; ICM). Observations of clusters and groups imply that such haloes are roughly in global thermal equilibrium, with heating balancing cooling when averaged over sufficiently long time- and length-scales; the ICM is, however, very likely to be locally thermally unstable. Using simple observationally motivated heating prescriptions, we show that local thermal instability (TI) can produce a multiphase medium with similar to 104 K cold filaments condensing out of the hot ICM only when the ratio of the TI time-scale in the hot plasma (tTI) to the free-fall time-scale (tff) satisfies tTI/tff? 10. This criterion quantitatively explains why cold gas and star formation are preferentially observed in low-entropy clusters and groups. In addition, the interplay among heating, cooling and TI reduces the net cooling rate and the mass accretion rate at small radii by factors of similar to 100 relative to cooling-flow models. This dramatic reduction is in line with observations. The feedback efficiency required to prevent a cooling flow is similar to 10-3 for clusters and decreases for lower mass haloes; supernova heating may be energetically sufficient to balance cooling in galactic haloes. We further argue that the ICM self-adjusts so that tTI/tff? 10 at all radii. When this criterion is not satisfied, cold filaments condense out of the hot phase and reduce the density of the ICM. These cold filaments can power the black hole and/or stellar feedback required for global thermal balance, which drives tTI/tff? 10. In comparison to clusters, groups have central cores with lower densities and larger radii. This can account for the deviations from self-similarity in the X-ray luminositytemperature () relation. The high-velocity clouds observed in the Galactic halo can be due to local TI producing multiphase gas close to the virial radius if the density of the hot plasma in the Galactic halo is >rsim 10-5 cm-3 at large radii.

Microstructure and texture evolution during beta extrusion of boron modified Ti-6A1-4V alloy

Boron addition to conventional titanium alloys below the eutectic limit refines the cast microstructure and improves mechanical properties. The present work explores the influence of hypoeutectic boron addition on the microstructure and texture evolution in Ti-6Al-4V alloy under beta extrusion. The beta extruded microstructure of Ti-6Al-4V is characterized by shear bands parallel to the extrusion direction. In contrast, the extruded Ti-6Al-4V-0.1B alloy shows a regular beta worked microstructure consisting of fine prior beta grains and acicular alpha-lamellae with no signs of the microstructural instability. Crystallographic texture after extrusion was almost identical for the two alloys indicating the similarity in their transformation behavior, which is attributed to complete dynamic recrystallization during beta processing. Microstructural features as well as crystallographic texture indicate dominant grain boundary related deformation processes for the boron modified alloy that leads to homogeneous deformation without instability formation. The absence of shear bands has significant technological importance as far as the secondary processing of boron added alloys in (alpha + beta)-phase field are concerned. (C) 2012 Elsevier B.V. All rights reserved.

Synthesis and characterization of carbon-covered alumina (CCA) supported TiO2 nanocatalysts with enhanced visible light photodegradation of Rhodamine B

The anatase phase of titania (TiO2) nano-photocatalysts was prepared using a modified sol gel process and thereafter embedded on carbon-covered alumina supports. The carbon-covered alumina (CCA) supports were prepared via the adsorption of toluene 2,4-diisocyanate (TDI) on the surface of the alumina. TDI was used as the carbon source for the first time for the carbon-covered alumina support system. The adsorption of TDI on alumina is irreversible; hence, the resulting organic moiety can undergo pyrolysis at high temperatures resulting in the formation of a carbon coating on the surface of the alumina. The TiO2 catalysts were impregnated on the CCA supports. X-ray diffraction analysis indicated that the carbon deposited on the alumina was not crystalline and also showed the successful impregnation of TiO2 on the CCA supports. In the Raman spectra, it could be deduced that the carbon was rather a conjugated olefinic or polycyclic hydrocarbons which can be considered as molecular units of a graphitic plane. The Raman analysis of the catalysed CCAs showed the presence of both the anatase titania and D and G band associated with the carbon of the CCAs. The scanning electron microscope micrographs indicated that the alumina was coated by a carbon layer and the energy dispersive X-ray spectra showed the presence of Al, O and C in the CCA samples, with the addition of Ti for the catalyst impregnated supports. The Brunauer Emmet and Teller surface area analysis showed that the incorporating of carbon on the alumina surface resulted in an increase in surface area, while the impregnation with TiO2 resulted in a further increase in surface area. However, a decrease in the pore volume and diameter was observed. The photocatalytic activity of the nanocatalysts was studied for the degradation of Rhodamine B dye. The CCA-TiO2 nanocatalysts were found to be more photocatalytically active under both visible and UV light irradiation compared to the free TIO2 nanocatalysts.

Effect of equal channel angular extrusion on wear and corrosion behavior of the orthopedic Ti-13Nb-13Zr alloy in simulated body fluid

We report investigations on the texture, corrosion and wear behavior of ultra-fine grained (UFG) Ti-13Nb-Zr alloy, processed by equal channel angular extrusion (ECAE) technique, for biomedical applications. The microstructure obtained was characterized by X-ray line profile analysis, scanning electron microscope (SEM) and electron back scattered diffraction (EBSD). We focus on the corrosion resistance and the fretting behavior, the main considerations for such biomaterials, in simulated body fluid. To this end. potentiodynamic polarization tests were carried out to evaluate the corrosion behavior of the UFG alloy in Hanks solution at 37 degrees C. The fretting wear behavior was carried out against bearing steel in the same conditions. The roughness of the samples was also measured to examine the effect of topography on the wear behavior of the samples. Our results showed that the ECAE process increases noticeably the performance of the alloy as orthopedic implant. Although no significant difference was observed in the fretting wear behavior, the corrosion resistance of the UFG alloy was found to be higher than the non-treated material. (c) 2012 Elsevier B.V. All rights reserved.

Hardness and Nitrogen Bonding Structure of A(x)Ti(1-x)N/CrN Multilayer Hard Coating

AlxTi1-xN/CrN multilayer coatings were fabricated by magnetron sputtering and those hardness variations were studied by observing the crack propagation and measuring the chemical bonding state of nitrides by Ti addition. While AlN/CrN multilayer shown stair-like crack propagation, AlxTi1-xN/CrN multilayer illustrated straight crack propagation. Most interestingly, Ti addition induced more broken nitrogen bonds in the nitride multilayers, leading to the reduction of hardness. However, the hardness of Al0.25Ti0.75N/CrN multilayer, having high Ti contents, increased by the formation of many Ti-N bond again instead of Al-N bond. From these results, we found that linear crack propagation behavior was dominated by broken nitrogen bonds in the AlxT1-xN/CrN multilayer coatings.

Structure and mechanical properties of Ti-C films deposited using combination of pulsed DC and normal DC magnetron co-sputtering

Titanium-carbon (Ti-C) thin films of different compositions were prepared by a combination of pulsed DC (for Ti target) and normal DC (for graphite target) magnetron co-sputtering on oxidized silicon and fused quartz substrates. At 33.7 at.% of C content, pure hcp Ti transforms into fcc-TiC with a preferential orientation of (2 2 0) along with (1 1 1) and (2 0 0). A clear transformation in the preferential orientation from (2 2 0) to (1 1 1) has been observed when the C content was increased to 56 at.%. At 62.5 at.% of C, TiC precipitates in an amorphous carbon matrix whereas further increase in C leads to X-ray amorphous films. The cross-sectional scanning electron microscope images reveal that the films with low carbon content consists of columnar grains, whereas, randomly oriented grains are in an amorphous carbon matrix at higher carbon content. A dramatic variation was observed in the mechanical properties such as hardness, H, from 30 to 1 GPa and in modulus, E, from 255 to 25 GPa with varying carbon content in the films. Resistance to plastic deformation parameter was observed as 0.417 for films containing 62.5 at.% of C. Nanoscratch test reveals that the films are highly scratch resistant with a coefficient of friction ranging from 0.15 to 0.04. (C) 2012 Elsevier B.V. All rights reserved.

Gibbs Energy of Formation of Ca3Ti8Al12O37 and Phase Relations and Chemical Potentials in the System Al2O3-TiO2-CaO

The quaternary oxide in the system Al2O3-CaO-TiO2 is found to have the composition Ca3Ti8Al12O37 rather than CaTi3Al8O19 as reported in the literature. The standard Gibbs energy of formation of Ca3Ti8Al12O37 from component binary oxides is measured in the temperature range from 900 to 1250 K using a solid-state electrochemical cell incorporating single crystal CaF2 as the solid electrolyte. The results can be represented by the equation: delta G(f(0x))(0) (+/- 70)/J mol(-1) = -248474 - 15.706(T/K). Combining this information with thermodynamic data on calcium aluminates and titanates available in the literature, subsolidus phase relations in the pseudo-ternary system Al2O3-CaO-TiO2 are computed and presented as isothermal sections. The evolution of phase relations with temperature is highlighted. Chemical potential diagrams are computed at 1200 K, showing the stability domains of the various phases in the chemical potential-composition space. In each chemical potential diagram, chemical potential of one component is plotted against the cationic fraction of the other two components. The diagrams are valid at relatively high oxygen potentials where Ti is present in its four-valent state in all the oxide phases.

The irradiation of 1:1 mixture of ammonia:carbon dioxide ice at 30 K using 1 kev electrons

In this Letter the results of an experimental investigation of 1 keV electron irradiation of a 1:1 ice mixture of NH3:CO2 at 30 K was made under ultrahigh vacuum (10(-9) mbar) conditions. Molecular products formed within the ice were detected and monitored using FTIR spectroscopy. The formation of ammonium ions (NH4+), cyanate ions (OCN-), CO was observed leading to the synthesis of ammonium carbamate (NH4NH2CO2). The consequences of these results for prebiotic chemistry in the interstellar medium and star forming regions are discussed. Crown Copyright (C) 2012 Published by Elsevier B.V. All rights reserved.

The Kπ form factors from analyticity and unitarity

Analyticity and unitarity techniques are employed to obtain bounds on the shape parameters of the scalar and vector form factors of semileptonic K l3 decays. For this purpose we use vector and scalar correlators evaluated in pQCD, a low energy theorem for scalar form factor, lattice results for the ratio of kaon and pion decay constants, chiral perturbation theory calculations for the scalar form factor at the Callan-Treiman point and experimental information on the phase and modulus of Kπ form factors up to an energy t in = 1GeV 2. We further derive regions on the real axis and in the complex-energy plane where the form factors cannot have zeros.

Nucleation-Growth Mode of Cubic-Tetragonal Transition with Coexistence of Phases over a Wide Temperature Interval in the High Temperature Ferroelectric Systems PbTiO3-BiMeO3:Me = Sc , and Zn1/2Ti1/2

Temperature dependent X-ray powder diffraction and dielectric studies have been carried out on tetragonal compositions of (1-x) PbTiO 3(x) BiMeO 3; Me similar to Sc and Zn 1/2 Ti 1/2. The cubic and the tetragonal phases coexist over more than 100 degrees C for 0.70 PbTiO 30.3 Bi ( Zn 1/2 Ti 1/2) O 3 and 0.66 PbTiO 30.34 BiScO 3. The wide temperature range of phase coexistence is shown to be an intrinsic feature of the system, and is attributed to the increase in the degree of the covalent character of the ( Pb +Bi ) O bond with increasing concentration of Bi at the Pb -site. The d-values of the {111} planes of the coexisting phases are nearly identical, suggesting this plane to be the invariant plane for the martensitic type cubic-tetragonal transformation occurring in these systems.

Continuum theory of edge states of topological insulators: variational principle and boundary conditions

We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us to derive natural boundary conditions valid for such systems. Our formulation is particularly suited for developing a continuum theory of the protected edge/surface excitations of topological insulators both in two and three dimensions. By a detailed comparison of our analytical formulation with tight binding calculations of ribbons of topological insulators modelled by the Bernevig-Hughes-Zhang (BHZ) Hamiltonian, we show that the continuum theory with a natural boundary condition provides an appropriate description of the low energy physics.

The 27-plet contributions to the CP-conserving K -> pi l(+)l(-) decays

We revisit the rare kaon decays K -> pi l(+)l(-) which are of special interest due to the recent measurements of the charged kaon decay spectra. We compute the contribution of the 27-plet to the decay amplitudes in one loop SU(3) chiral perturbation theory. We estimate the resulting impact to be similar to 10% to the branching ratios of the charged kaon decays, and also noticeably influence the shape of the spectra. With current values of the constants G(8) associated with the octet and G(27) associated with the 27-plet, the contribution of the latter pushes the spectrum in the correct direction, towards the charged lepton spectra. We also discuss the impact for neutral decay rates and spectra.