Boxicity of Circular Arc Graphs

A k-dimensional box is a Cartesian product R(1)x...xR(k) where each R(i) is a closed interval on the real line. The boxicity of a graph G, denoted as box(G), is the minimum integer k such that G can be represented as the intersection graph of a collection of k-dimensional boxes. That is, two vertices are adjacent if and only if their corresponding boxes intersect. A circular arc graph is a graph that can be represented as the intersection graph of arcs on a circle. We show that if G is a circular arc graph which admits a circular arc representation in which no arc has length at least pi(alpha-1/alpha) for some alpha is an element of N(>= 2), then box(G) <= alpha (Here the arcs are considered with respect to a unit circle). From this result we show that if G has maximum degree Delta < [n(alpha-1)/2 alpha] for some alpha is an element of N(>= 2), then box(G) <= alpha. We also demonstrate a graph having box(G) > alpha but with Delta = n (alpha-1)/2 alpha + n/2 alpha(alpha+1) + (alpha+2). For a proper circular arc graph G, we show that if Delta < [n(alpha-1)/alpha] for some alpha is an element of N(>= 2), then box(G) <= alpha. Let r be the cardinality of the minimum overlap set, i.e. the minimum number of arcs passing through any point on the circle, with respect to some circular arc representation of G. We show that for any circular arc graph G, box(G) <= r + 1 and this bound is tight. We show that if G admits a circular arc representation in which no family of k <= 3 arcs covers the circle, then box(G) <= 3 and if G admits a circular arc representation in which no family of k <= 4 arcs covers the circle, then box(G) <= 2. We also show that both these bounds are tight.

Ground-fault-arc suppression on series-and shunt-compensated lines

An extension of Rizk's analysis to cover any type of switching is presented for calculating the residual current and recovery voltage in a singlephase switched transmission system. Equations for the determination of the current and voltage are shown, and the method has been used for the analysis of a series- and shunt-compensated line.Three possible switching methods for the effective control of the recovery voltage and residual current are discussed: normal switching, switching at the ends of the line and switching of the series capacitors.

An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems

A finite element method for solving multidimensional population balance systems is proposed where the balance of fluid velocity, temperature and solute partial density is considered as a two-dimensional system and the balance of particle size distribution as a three-dimensional one. The method is based on a dimensional splitting into physical space and internal property variables. In addition, the operator splitting allows to decouple the equations for temperature, solute partial density and particle size distribution. Further, a nodal point based parallel finite element algorithm for multi-dimensional population balance systems is presented. The method is applied to study a crystallization process assuming, for simplicity, a size independent growth rate and neglecting agglomeration and breakage of particles. Simulations for different wall temperatures are performed to show the effect of cooling on the crystal growth. Although the method is described in detail only for the case of d=2 space and s=1 internal property variables it has the potential to be extendable to d+s variables, d=2, 3 and s >= 1. (C) 2011 Elsevier Ltd. All rights reserved.

A k-epsilon model for turbulent weld pool convection in gas metal arc welding process

In this paper, we present a modified k - epsilon model capable of addressing turbulent weld-pool convection in a GMAW process, taking into account the morphology of the phase change interface during a Gas Metal Arc Welding (GMAW) process. A three-dimensional turbulence mathematical model has been developed to study the heat transfer and fluid flow within the weld pool by considering the combined effect of three driving forces, viz., buoyancy, Lorentz force and surface tension (Marangoni convection). Mass and energy transports by the droplets are considered through the thermal analysis of the electrode. The falling droplet's heat addition to the molten pool is considered to be a volumetric heat source distributed in an imaginary cylindrical cavity ("cavity model") within the weld pool. This nature of heat source distribution takes into account the momentum and the thermal, energy of the falling droplets. The numerically predicted weld pool dimensions both from turbulence and laminar models are then compared with the experimental post-weld results sectioned across the weld axis. The above comparison enables us to analyze the overall effects of turbulent convection on the nature of heat and fluid flow and hence on the weld pool shape/size during the arc welding processes.

Minimization of the effects of harmonics and voltage dip caused by electric arc furnace

This study examines the thermal efficiency of the operation of arc furnace and the effects of harmonics and voltage dips of a factory located near Bangkok. It also attempts to find ways to improve the performance of the arc furnace operation and minimize the effects of both harmonics and voltage dips. A dynamic model of the arc furnace has been developed incorporating both electrical and thermal characteristics. The model can be used to identify potential areas for improvement of the furnace and its operation. Snapshots of waveforms and measurement of RMS values of voltage, current and power at the furnace, at other feeders and at the point of common coupling were recorded. Harmonic simulation program and electromagnetic transient simulation program were used in the study to model the effects of harmonics and voltage dips and to identify appropriate static and dynamic filters to minimize their effects within the factory. The effects of harmonics and voltage dips were identified in records taken at the point of common coupling of another factory supplied by another feeder of the same substation. Simulation studies were made to examine the results on the second feeder when dynamic filters were used in the factory which operated the arc furnace. The methodology used and the mitigation strategy identified in the study are applicable to general situation in a power distribution system where an arc furnace is a part of the load of a customer

Dilations of Gamma-contractions by solving operator equations

For a contraction P and a bounded commutant S of P. we seek a solution X of the operator equation S - S*P = (1 - P* P)(1/2) X (1 - P* P)(1/2) where X is a bounded operator on (Ran) over bar (1 - P* P)(1/2) with numerical radius of X being not greater than 1. A pair of bounded operators (S, P) which has the domain Gamma = {(z(1) + z(2), z(2)): vertical bar z(1)vertical bar < 1, vertical bar z(2)vertical bar <= 1} subset of C-2 as a spectral set, is called a P-contraction in the literature. We show the existence and uniqueness of solution to the operator equation above for a Gamma-contraction (S, P). This allows us to construct an explicit Gamma-isometric dilation of a Gamma-contraction (S, P). We prove the other way too, i.e., for a commuting pair (S, P) with parallel to P parallel to <= 1 and the spectral radius of S being not greater than 2, the existence of a solution to the above equation implies that (S, P) is a Gamma-contraction. We show that for a pure F-contraction (S, P), there is a bounded operator C with numerical radius not greater than 1, such that S = C + C* P. Any Gamma-isometry can be written in this form where P now is an isometry commuting with C and C. Any Gamma-unitary is of this form as well with P and C being commuting unitaries. Examples of Gamma-contractions on reproducing kernel Hilbert spaces and their Gamma-isometric dilations are discussed. (C) 2012 Elsevier Inc. All rights reserved.

Role of electrolyte additives on in-vitro electrochemical behavior of micro arc oxidized titania films on Cp Ti

The present work is aimed at studying the influence of electrolyte chemistry on the voltage-time (V-T) response characteristics, phase structure, surface morphology, film growth rate and corrosion properties of titania films fabricated by micro arc oxidation (MAO) on Cp Ti. The titania films were developed with a sodium phosphate based reference electrolyte comprising the additives such as sodium carbonate (Na2CO3), sodium nitrite (NaNO2) and urea (CO(NH2)(2)). The phase composition, surface morphology, elemental composition and thickness of the films were assessed by X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS) techniques. The corrosion characteristics of the fabricated films were studied under Kokubo simulated body fluid (SBF) condition by potentiodynamic polarization, long term potential and linear polarization resistance (LPR) measurements and electrochemical impedance spectroscopy (EIS) methods. In addition, the corrosion characteristics of the grown films were analyzed by EIS curve fitting and equivalent circuit modeling. Salt spray test (SST) as per ASTM B 117 standard was also conducted to verify the corrosion resistance of the grown films. The XRD results showed that the titania films were composed of both anatase and rutile phases at different proportions. Besides, the films grown in carbonate and nitrite containing electrolyte systems showed an enhanced growth of their rutile phase in the 1 0 1] direction which could be attributed to the modifications introduced in the growth process by the abundant oxygen available during the process. The SEM-EDX and elemental mapping results showed that the respective electrolyte borne elements were incorporated and distributed uniformly in all the films. Among all the grown films under study, the film developed in carbonate containing electrolyte system exhibited considerably improved corrosion resistance due to suitable modifications in its structural and morphological characteristics. The rate of anatase to rutile phase transformation and the rutile growth direction were strongly influenced by the abundant oxidizing species available during the film growth process. (C) 2012 Elsevier B. V. All rights reserved.

An operator-splitting Galerkin/SUPG finite element method for population balance equations : stability and convergence

We present a heterogeneous finite element method for the solution of a high-dimensional population balance equation, which depends both the physical and the internal property coordinates. The proposed scheme tackles the two main difficulties in the finite element solution of population balance equation: (i) spatial discretization with the standard finite elements, when the dimension of the equation is more than three, (ii) spurious oscillations in the solution induced by standard Galerkin approximation due to pure advection in the internal property coordinates. The key idea is to split the high-dimensional population balance equation into two low-dimensional equations, and discretize the low-dimensional equations separately. In the proposed splitting scheme, the shape of the physical domain can be arbitrary, and different discretizations can be applied to the low-dimensional equations. In particular, we discretize the physical and internal spaces with the standard Galerkin and Streamline Upwind Petrov Galerkin (SUPG) finite elements, respectively. The stability and error estimates of the Galerkin/SUPG finite element discretization of the population balance equation are derived. It is shown that a slightly more regularity, i.e. the mixed partial derivatives of the solution has to be bounded, is necessary for the optimal order of convergence. Numerical results are presented to support the analysis.

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.

Operator-splitting finite element algorithms for computations of high-dimensional parabolic problems

An operator-splitting finite element method for solving high-dimensional parabolic equations is presented. The stability and the error estimates are derived for the proposed numerical scheme. Furthermore, two variants of fully-practical operator-splitting finite element algorithms based on the quadrature points and the nodal points, respectively, are presented. Both the quadrature and the nodal point based operator-splitting algorithms are validated using a three-dimensional (3D) test problem. The numerical results obtained with the full 3D computations and the operator-split 2D + 1D computations are found to be in a good agreement with the analytical solution. Further, the optimal order of convergence is obtained in both variants of the operator-splitting algorithms. (C) 2012 Elsevier Inc. All rights reserved.

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.

Riesz transforms and multipliers for the Grushin operator

We show that Riesz transforms associated to the Grushin operator G = -Delta - |x|(2 similar to) (t) (2) are bounded on L (p) (a''e (n+1)). We also establish an analogue of the Hormander-Mihlin Multiplier Theorem and study Bochner-Riesz means associated to the Grushin operator. The main tools used are Littlewood-Paley theory and an operator-valued Fourier multiplier theorem due to L. Weis.