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.

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.

Closed-form solutions for non-uniform Euler-Bernoulli free-free beams

In this paper, the free vibration of a non-uniform free-free Euler-Bernoulli beam is studied using an inverse problem approach. It is found that the fourth-order governing differential equation for such beams possess a fundamental closed-form solution for certain polynomial variations of the mass and stiffness. An infinite number of non-uniform free-free beams exist, with different mass and stiffness variations, but sharing the same fundamental frequency. A detailed study is conducted for linear, quadratic and cubic variations of mass, and on how to pre-select the internal nodes such that the closed-form solutions exist for the three cases. A special case is also considered where, at the internal nodes, external elastic constraints are present. The derived results are provided as benchmark solutions for the validation of non-uniform free-free beam numerical codes. (C) 2013 Elsevier Ltd. All rights reserved.

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.

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.

Modal tailoring and closed-form solutions for rotating non-uniform Euler-Bernoulli beams

In this paper, the free vibration of a rotating Euler-Bernoulli beam is studied using an inverse problem approach. We assume a polynomial mode shape function for a particular mode, which satisfies all the four boundary conditions of a rotating beam, along with the internal nodes. Using this assumed mode shape function, we determine the linear mass and fifth order stiffness variations of the beam which are typical of helicopter blades. Thus, it is found that an infinite number of such beams exist whose fourth order governing differential equation possess a closed form solution for certain polynomial variations of the mass and stiffness, for both cantilever and pinned-free boundary conditions corresponding to hingeless and articulated rotors, respectively. A detailed study is conducted for the first, second and third modes of a rotating cantilever beam and the first and second elastic modes of a rotating pinned-free beam, and on how to pre-select the internal nodes such that the closed-form solutions exist for these cases. The derived results can be used as benchmark solutions for the validation of rotating beam numerical methods and may also guide nodal tailoring. (C) 2014 Elsevier Ltd. All rights reserved.

Tailoring the second mode of Euler-Bernoulli beams: an analytical approach

In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analytical approach. The mass and stiffness variations are determined for a beam, having various boundary conditions, which has a prescribed polynomial second mode shape with an internal node. It is found that physically feasible rectangular cross-section beams which satisfy the inverse problem exist for a variety of boundary conditions. The effect of the location of the internal node on the mass and stiffness variations and on the deflection of the beam is studied. The derived functions are used to verify the p-version finite element code, for the cantilever boundary condition. The paper also presents the bounds on the location of the internal node, for a valid mass and stiffness variation, for any given boundary condition. The derived property variations, corresponding to a given mode shape and boundary condition, also provides a simple closed-form solution for a class of non-uniform Euler-Bernoulli beams. These closed-form solutions can also be used to check optimization algorithms proposed for modal tailoring.

B-Spline potential function for maximum a-posteriori image reconstruction in fluorescence microscopy

An iterative image reconstruction technique employing B-Spline potential function in a Bayesian framework is proposed for fluorescence microscopy images. B-splines are piecewise polynomials with smooth transition, compact support and are the shortest polynomial splines. Incorporation of the B-spline potential function in the maximum-a-posteriori reconstruction technique resulted in improved contrast, enhanced resolution and substantial background reduction. The proposed technique is validated on simulated data as well as on the images acquired from fluorescence microscopes (widefield, confocal laser scanning fluorescence and super-resolution 4Pi microscopy). A comparative study of the proposed technique with the state-of-art maximum likelihood (ML) and maximum-a-posteriori (MAP) with quadratic potential function shows its superiority over the others. B-Spline MAP technique can find applications in several imaging modalities of fluorescence microscopy like selective plane illumination microscopy, localization microscopy and STED. (C) 2015 Author(s).

Implicit scheme for meshless compressible Euler solver

In this paper, an implicit scheme is presented for a meshless compressible Euler solver based on the Least Square Kinetic Upwind Method (LSKUM). The Jameson and Yoon's split flux Jacobians formulation is very popular in finite volume methodology, which leads to a scalar diagonal dominant matrix for an efficient implicit procedure (Jameson & Yoon, 1987). However, this approach leads to a block diagonal matrix when applied to the LSKUM meshless method. The above split flux Jacobian formulation, along with a matrix-free approach, has been adopted to obtain a diagonally dominant, robust and cheap implicit time integration scheme. The efficacy of the scheme is demonstrated by computing 2D flow past a NACA 0012 airfoil under subsonic, transonic and supersonic flow conditions. The results obtained are compared with available experiments and other reliable computational fluid dynamics (CFD) results. The present implicit formulation shows good convergence acceleration over the RK4 explicit procedure. Further, the accuracy and robustness of the scheme in 3D is demonstrated by computing the flow past an ONERA M6 wing and a clipped delta wing with aileron deflection. The computed results show good agreement with wind tunnel experiments and other CFD computations.

Meshless Local Petrov-Galerkin Method for Rotating Euler-Bernoulli Beam

Free vibration problem of a rotating Euler-Bernoulli beam is solved with a truly meshless local Petrov-Galerkin method. Radial basis function and summation of two radial basis functions are used for interpolation. Radial basis function satisfies the Kronecker delta property and makes it simpler to apply the essential boundary conditions. Interpolation with summation of two radial basis functions increases the node carrying capacity within the sub-domain of the trial function and higher natural frequencies can be computed by selecting the complete domain as a sub-domain of the trial function. The mass and stiffness matrices are derived and numerical results for frequencies are obtained for a fixed-free beam and hinged-free beam simulating hingeless and articulated helicopter blades. Stiffness and mass distribution suitable for wind turbine blades are also considered. Results show an accurate match with existing literature.

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.

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.