A constant factor approximation algorithm for boxicity of circular arc graphs

Boxicity of a graph G(V, E) is the minimum integer k such that G can be represented as the intersection graph of k-dimensional axis parallel boxes in Rk. Equivalently, it is the minimum number of interval graphs on the vertex set V such that the intersection of their edge sets is E. It is known that boxicity cannot be approximated even for graph classes like bipartite, co-bipartite and split graphs below O(n0.5-ε)-factor, for any ε > 0 in polynomial time unless NP = ZPP. Till date, there is no well known graph class of unbounded boxicity for which even an nε-factor approximation algorithm for computing boxicity is known, for any ε < 1. In this paper, we study the boxicity problem on Circular Arc graphs - intersection graphs of arcs of a circle. We give a (2+ 1/k)-factor polynomial time approximation algorithm for computing the boxicity of any circular arc graph along with a corresponding box representation, where k ≥ 1 is its boxicity. For Normal Circular Arc(NCA) graphs, with an NCA model given, this can be improved to an additive 2-factor approximation algorithm. The time complexity of the algorithms to approximately compute the boxicity is O(mn+n2) in both these cases and in O(mn+kn2) which is at most O(n3) time we also get their corresponding box representations, where n is the number of vertices of the graph and m is its number of edges. The additive 2-factor algorithm directly works for any Proper Circular Arc graph, since computing an NCA model for it can be done in polynomial time.

Fabrication and characterization of micro-arc oxidized fluoride containing titania films on Cp Ti

The present study is focussed at establishing an appropriate electrolyte system for developing electrochemically stable and fluorine (F) containing titania (F-TiO2) films on Cp Ti by micro-arc oxidation (MAO) technique. To fabricate the F-TiO2 films on Cp Ti, different electrolyte solutions of chosen concentrations of tri-sodium orthophosphate (TSOP, Na3PO4 center dot I2H2O), potassium hydroxide (KOH) and various F-containing compounds such as ammonium fluoride (NH4F), potassium fluoride (KF), sodium fluoride (NaF) and potassium fluorotitanate (K2TiF6) are employed. The structural and morphological characteristics, thickness and elemental composition of the developed films have been assessed by X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS) techniques. The in-vitro electrochemical corrosion behavior of the films was studied under Kokubo simulated body fluid (SBF) environment by potentiodynamic polarization, long term potential measurement and electrochemical impedance spectroscopy (EIS) methods. The XRD and SEM-EDS results show that the rutile content in the films vary in the range of 15-37 wt% and the F and P contents in the films is found to be in the range of 2-3 at% and 2.9-4.7 at% respectively, suggesting that the anatase to rutile phase transformation and the incorporation of F and P into the films are significantly controlled by the respective electrolyte solution. The SEM elemental mapping results show that the electrolyte borne F and P elements are incorporated and distributed uniformly in all the films. Among all the films under study, the film developed with 5 g TSOP+2 g KOH+3 g K2TiF6 electrolyte system exhibits considerably improved in-vitro corrosion resistance and therefore best suited for biomedical applications. (C) 2012 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Friction Welding of Thixocast A356 Aluminium Alloy

In this paper, a numerical model for friction welding of thixo-cast materials is developed, which includes a coupling of thermal effect and plastic deformation using a finite element method (FEM). As the constitutive equations for flow behavior of materials for a thixo-cast material are expected to be different from those of conventionally cast material of the same alloy, the necessary material data are experimentally determined from isothermal hot compression tests of the A356 thixocast alloy. The Johnson-Cook model has been employed to represent the flow behavior of the thixocast A356 alloy. The purpose of this FEM analysis is to provide better understanding of the friction welding process of thixo-cast material, and to obtain optimized process parameters before an actual welding is carried out.

Internal defect and process parameter analysis during friction stir welding of Al 6061 sheets

Welding parameters like welding speed, rotation speed, plunge depth, shoulder diameter etc., influence the weld zone properties, microstructure of friction stir welds, and forming behavior of welded sheets in a synergistic fashion. The main aims of the present work are to (1) analyze the effect of welding speed, rotation speed, plunge depth, and shoulder diameter on the formation of internal defects during friction stir welding (FSW), (2) study the effect on axial force and torque during welding, (c) optimize the welding parameters for producing internal defect-free welds, and (d) propose and validate a simple criterion to identify defect-free weld formation. The base material used for FSW throughout the work is Al 6061T6 having a thickness value of 2.1 mm. Only butt welding of sheets is aimed in the present work. It is observed from the present analysis that higher welding speed, higher rotation speed, and higher plunge depth are preferred for producing a weld without internal defects. All the shoulder diameters used for FSW in the present work produced defect-free welds. The axial force and torque are not constant and a large variation is seen with respect to FSW parameters that produced defective welds. In the case of defect-free weld formation, the axial force and torque are relatively constant. A simple criterion, (a,tau/a,p)(defective) > (a,tau/a,p)(defect free) and (a,F/a,p)(defective) > (a,F/a,p)(defect free), is proposed with this observation for identifying the onset of defect-free weld formation. Here F is axial force, tau is torque, and p is welding speed or tool rotation speed or plunge depth. The same criterion is validated with respect to Al 5xxx base material. Even in this case, the axial force and torque remained constant while producing defect-free welds.

Microwave Spectroscopic and Atoms in Molecules Theoretical Investigations on the ArPropargyl Alcohol Complex: ArHO, Ar, and ArC Interactions

The structure of the Arpropargyl alcohol (ArPA) complex is determined from the rotational spectra of the parent complex and its two deuterated isotopologues, namely ArPA-D(OD) and ArPA-D(CD). The spectra confirm a geometry in which PA exists in the gauche form with Ar located in between OH and CCH groups. All a, b and c types of transitions show small splitting due to some large-amplitude motion dominated by COH torsion, as in the monomer. Splittings in a- and b-type transitions are of the order of a few kilohertz, whereas splitting in the c-type transitions is relatively larger (0.92.6 MHz) and decreases in the order ArPA>ArPA-D(CD)>ArPA-D(OD). The assignments are well supported by ab initio calculations. Atoms in molecules (AIM) and electrostatic potential calculations are used to explore the nature of the interactions in this complex. AIM calculations not only reveal the expected OHAr and Ar interactions in the Argauche-PA complex, but also novel CAr (of CH2OH group) and OHAr interactions in the Artrans-PA complex. Similar interactions are also present in the Armethanol complex.

Chromite-silicate chemistry of the Neoarchean Sittampundi Complex, southern India: Implications for subduction-related arc magmatism

The Neoarchean layered anorthositic complex at Sittampundi in southern India is known for its chromitite layers that are mostly associated with anorthosite (An(90-100)). The chromitites contain FeAl-rich chromites concentrated in layers between amphibole-rich layers with a dominant mineralogy of amphibole-spinel-plagiocase+/-sapphirine. The chromite-rich layers contain only amphibole and plagioclase. Mineral compositions illustrated by X-ray composition maps and profiles show subtle chemical differences. The chrome spinels are of refractory grade with Cr2O3 and Al2O3 contents varying between 34-40 wt.% and 23-28 wt.%. The chromite compositions are noticeably different from those in layered igneous intrusions of the Bushveld-Stillwater type. The existence of original highly calcic plagioclase, FeAl-rich chromite, and magmatic amphibole is consistent with derivation from a parental magma of hydrous tholeiitic composition that was most likely generated in a supra-subduction zone arc setting. In terms of mineralogy and field relations, the Sittampundi chromitites are remarkably similar to anorthosite-hosted chromitites in the Neoarchean Fiskensset anorthositic complex, Greenland. We propose that the Sittampundi chromitites formed by partial melting of unusually aluminous harzburgite in a hydrated mantle wedge above a subduction zone. This melting process produced hydrous, aluminous basalt, which fractionated at depth to give rise to a variety of high-alumina basalt compositions from which the anorthositic complex with its cumulate chromite-rich and amphibole-rich layers formed within the magma chamber of a supra-subduction zone arc. (C) 2011 Elsevier B.V. All rights reserved.

Role of electrolyte chemistry on electronic and in vitro electrochemical properties of micro-arc oxidized titania films on Cp Ti

The primary objective of the present work was to study the electronic and in vitro electrochemical properties of micro-arc oxidized titania films on Cp Ti, fabricated independently in various electrolyte solutions consisting of anions such as phosphate (PO43-), borate (B4O72-), citrate (C6H5O73-) and silicate (SiO32-). Further the role of anions on the structural, morphological and compositional properties of the fabricated films was studied. All the titania films were developed by micro-arc oxidation (MAO) technique for a fixed treatment time of 8 min under constant current mode. The surface morphology, elemental distribution, composition and structural characteristics of the films were assessed by scanning electron microscope (SEM) equipped with energy dispersive spectroscopy (EDS) and X-ray diffraction (XRD) techniques. The thermodynamic and kinetic corrosion properties of the films were studied under simulated body fluid (SBF) conditions (pH 7.4 and 37 degrees C) by conducting chronopotentiometric and potentiodynamic polarization tests. Electrochemical impedance spectroscopy (EIS) coupled with equivalent circuit modelling was carried out to analyse the frequency response and Mott-Schottky analysis was performed to study the semiconducting (electronic) properties of the films. Salt spray fog accelerated corrosion test was conducted for 168h as per ASTM B117 standard to corroborate the corrosion and semiconducting properties of the samples based on the visual examination. The XRD results showed that the transformation from the metastable anatase phase to the thermodynamically stable rutile phase and the crystalline growth of the respective phases were strongly influenced by the addition of anions. The SEM-EDS results demonstrated that the phosphorous (P) content in the films varied from 2.4 at% to 5.0 at% indicating that the amount of P in the films could be modified by adding an appropriate electrolyte additive. The electrochemical corrosion test results showed that the film fabricated in citrate (C6H5O73-) containing electrolyte is thermodynamically and kinetically more stable compared to that of all the others. The results of the Mott-Schottky analysis indicated that all the fabricated films showed an n-type semiconducting behaviour and the film developed in citrate (C6H5O73-) containing electrolyte exhibited the lowest donor concentration and the most negative flat band potential that contributed to its highest corrosion resistance in SBF solution. The results of the salt spray accelerated corrosion tests were in agreement with those obtained from the electrochemical and Mott-Schottky analysis.

Neoarchean continental growth through arc magmatism in the Nilgiri Block, southern India

The formation and growth of continental crust in the Archean have been evaluated through models of subduction-accretion and mantle plume. The Nilgiri Block in southern India exposes exhumed Neoarchean lower crust, uplifted to heights of 2500 m above sea level along the north western margin of the Peninsula. Major lithologies in this block include charnockite with or without garnet, anorthosite-gabbro suite, pyroxenite, amphibolite and hornblende-biotite gneiss (TTG). All these rock types are closely associated as an arc magmatic suite, with diffuse boundaries and coeval nature. The charnockite and hornblende-biotite gneisses (TTG) show SiO2 content varying from 64 to 73 wt.%. The hornblende-biotite gneisses (TTG) are high-Al type with Al2O3 >15 wt.% whereas the charnockites show Al2O3 <15 wt.%. The composition of charnockite is mainly magnesian and calcic to calc-alkaline. The mafic-ultramafic rocks show composition close to that of tholeiitic series. The low values of K(2)o (<3 wt.%), (K/Rb)/K2O (<500), Zr/Ti, and trace element ratios like (La/Yb)n/(Sr/Y), (Y/Nb), (Y + Nb)/Rb, (Y+Ta)/Rb, Yb/Ta indicate a volcanic arc signature for these rocks. The geochemical signature is consistent with arc magmatic rocks generated through oceanic plate subduction. The primitive mantle normalized trace element patterns of these rocks display enrichment in large ion lithophile elements (LILE) and comparable high field strength elements (HFSE) in charnockite and hornblende-biotite gneisses (TTG) consistent with subduction-related origin. Primitive mantle normalized REE pattern displays an enrichment in LREE in the chamockite and hornblende-biotite gneisses (TTG) as compared to a flat pattern for the mafic rocks. The chondrite normalized REE patterns of zircons of all the rock types reveal cores with high HREE formed at ca. 2700 Ma and rims with low HREE formed at 2500-2450 Ma. Log-transformed La/Th-Nb/Th-Sm/Th-Yb/Th discrimination diagram for the mafic and ultramafic rocks from Nilgiri displays a transition from mid-oceanic ridge basalt (MORB) to island arc basalt (IAB) suggesting a MORB source. The U-Pb zircon data from the charnockites, mafic granulites and hornblende-biotite gneisses (TTG) presented in our study show that the magma generation during subduction and accretion events in this block occurred at 2700-2500 Ma. Together with the recent report on Neoarchean supra-subduction zone ophiolite suite at its southern margin, the Nilgiri Block provides one of the best examples for continental growth through vertical stacking and lateral accretion in a subduction environment during the Neoarchean. (c) 2014 Elsevier B.V. All rights reserved.

Experimental and numerical studies on friction welding of thixocast A356 aluminum alloy

This paper highlights the role of globular microstructure on the weldability of semi-solid processed aluminum alloys via high temperature flow behavior. The investigation was carried out on the joining of thixocast A356 aluminum alloy components by friction welding. A thermomechanical model was developed to predict the temperature and stress distributions, as well as to identify the suitable and safe range of parameters. Good comparisons between numerical and experimental results were observed. In addition, metallographic examinations and hardness and tensile tests of the welded samples were carried out. It was found that the tensile strength of the joint is higher than the tensile strength of the parent material for the optimum set of parameters. (C) 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

A constant factor approximation algorithm for boxicity of circular arc graphs

The boxicity (resp. cubicity) of a graph G(V, E) is the minimum integer k such that G can be represented as the intersection graph of axis parallel boxes (resp. cubes) in R-k. Equivalently, it is the minimum number of interval graphs (resp. unit interval graphs) on the vertex set V, such that the intersection of their edge sets is E. The problem of computing boxicity (resp. cubicity) is known to be inapproximable, even for restricted graph classes like bipartite, co-bipartite and split graphs, within an O(n(1-epsilon))-factor for any epsilon > 0 in polynomial time, unless NP = ZPP. For any well known graph class of unbounded boxicity, there is no known approximation algorithm that gives n(1-epsilon)-factor approximation algorithm for computing boxicity in polynomial time, for any epsilon > 0. In this paper, we consider the problem of approximating the boxicity (cubicity) of circular arc graphs intersection graphs of arcs of a circle. Circular arc graphs are known to have unbounded boxicity, which could be as large as Omega(n). We give a (2 + 1/k) -factor (resp. (2 + log n]/k)-factor) polynomial time approximation algorithm for computing the boxicity (resp. cubicity) of any circular arc graph, where k >= 1 is the value of the optimum solution. For normal circular arc (NCA) graphs, with an NCA model given, this can be improved to an additive two approximation algorithm. The time complexity of the algorithms to approximately compute the boxicity (resp. cubicity) is O(mn + n(2)) in both these cases, and in O(mn + kn(2)) = O(n(3)) time we also get their corresponding box (resp. cube) representations, where n is the number of vertices of the graph and m is its number of edges. Our additive two approximation algorithm directly works for any proper circular arc graph, since their NCA models can be computed in polynomial time. (C) 2014 Elsevier B.V. All rights reserved.

Dissimilar friction stir welding between aluminum alloy and magnesium alloy at a low rotational speed

A sound weld was obtained between 2024-T3 Al alloy and AZ31B-O Mg alloy dissimilar metal plates of 5 mm thickness, at a rotational speed of 300 rev min(-1) and at a welding speed of 50 mm min(-1). One of the parameter studied was, the effect of interface offset variation, on the quality and properties of the welded samples and on the thickness of intermetallic layer formed in the welded samples. The intermetallic layer at the midst of the weld volume contains intermetallic compounds Al12Mg17 and Al3Mg2. Highest tensile strength of 106.86 MPa, corresponding tensile joint efficiency of 44.52% and corresponding elongation 1.33% were obtained for the tensile sample, with interface offset of 0.66 mm from zero interface offset in retreating side and with approximate least intermetallic thickness of 1.2 mu m. Dissimilar friction stir welded joint samples had failed completely in brittle fracture mode; the position of tensile fracture was located at the midst of intermetallic layer, which had maximum hardness and minimum ductility. The nano hardness values fluctuate in the weld nugget owing to dynamic recrystallization of alloy materials and formation of brittle intermetallic compounds of alloy materials in the weld nugget; maximum hardness of 10.74 GPa occurred for the sample with least intermetallic thickness of 1.2 mu m. (C) 2014 Elsevier B.V. All rights reserved.

Neoarchean arc magmatism followed by high-temperature, high-pressure metamorphism in the Nilgiri Block, southern India

The Nilgiri Block, southern India is an exhumed lower crust formed through arc magmatic processes in the Neoarchean. The main lithologies in this terrane include charnockites, gneisses, volcanic tuff, metasediments, banded iron formation and mafic-ultramafic bodies. Mafic-ultramafic rocks are present towards the northern and central part of the Nilgiri Block. We examine the evolution of these mafic granulites/metagabbros by phase diagram modeling and U-Pb sensitive high resolution ion microprobe (SHRIMP) dating. They consist of a garnet-clinopyroxene-plagioclase-hornblende-ilmenite +/- orthopyroxene +/- rutile assemblage. Garnet and clinopyroxene form major constituents with labradorite and orthopyroxene as the main mineral inclusions. Labradorite, identified using Raman analysis, shows typical peaks at 508 cm(-1), 479 cm(-1), 287 cm(-1) and 177 cm(-1). It is stable along with orthopyroxene towards the low-pressure high-temperature region of the granulite fades (M1 stage). Subsequently, orthopyroxene reacted with plagioclase to form the peak garnet + clinopyroxene + rutile assemblage (M2 stage). The final stage is represented by amphibolite facies-hornblende and plagioclase-rim around the garnet-clinopyroxene assemblage (M3 stage). Phase diagram modeling shows that these mafic granulites followed an anticlockwise P-T-t path during their evolution. The initial high-temperature metamorphism (M1 stage) was at 850-900 degrees C and similar to 9 kbar followed by high-pressure granulite fades metamorphism (M2 stage) at 850-900 degrees C and 14-15 kbar. U-Pb isotope studies of zircons using SHRIMP revealed late Neoarchean to early paleoproterozoic ages of crystallization and metamorphism respectively. The age data shows that these mafic granulites have undergone arc magmatism at ca. 25392 +/- 3 Ma and high-temperature, high-pressure metamorphism at ca. 2458.9 +/- 8.6 Ma. Thus our results suggests a late Neoarchean arc magmatism followed by early paleoproterozoic high-temperature, high-pressure granulite facies metamorphism due to the crustal thickening and suturing of the Nilgiri Block onto the Dharwar Craton. (C) 2015 Elsevier B.V. All rights reserved.

Microstructure Formation in Dissimilar Metal Welds: Electron Beam Welding of Ti/Ni

We present results for electron beam welding of a binary Ti/Ni dissimilar metal couple. The difference in physical properties of the base metals and metallurgical features (thermodynamics and kinetics) of the system influence both macroscopic transport and microstructure development in the weld. Microstructures near the fusion interfaces are markedly different from those inside the weld region. At the Ti side, Ti2Ni dendrites are observed to grow toward the fusion interface, while in the Ni side, layered growth of gamma-Ni, Ni3Ti, and Ni3Ti + NiTi eutectic is observed. Different morphologies of the latter eutectic constitute the predominant microstructure inside the weld metal region. These results are compared and contrasted with those from laser welding of the same binary couple, and a scheme of solidification is proposed to explain the observations. This highlights notable departures from welding of similar and other dissimilar metals such as a significant asymmetry in heat transport that governs progress of solidification from each side of the couple, and a lack of unique liquidus isotherm characterizing the liquid-solid front.

Arc Voltage Fluctuation in DC Laminar and Turbulent Plasma Jets Generat Ion

Arc voltage fluctuations in a direct current (DC) non-transferred arc plasma generator are experimentally studied, in generating a jet in the laminar, transitional and turbulent regimes. The study is with a view toward elucidating the mechanism of the fluctuations and their relationship with the generating parameters, arc root movement and flow regimes. Results indicate that the existence of a 300 Hz alternating current (AC) component in the power supply ripples does not cause the transition of the laminar plasma jet into a turbulent state. There exists a high frequency fluctuation at 4 kHz in the turbulent jet regime. It may be related to the rapid movement of the anode attachment point of the arc.