Simulation of potential and electric field across faulty ceramic disc insulator string

Ceramic/Porcelain insulators are widely used in power transmission lines to provide mechanical support for High voltage conductors in addition to withstand electrical stresses. As a result of lightning, switching or temporary over voltages that could initiate flashover under worst weather conditions, and to operate within interference limits. Given that the useful life in service of the individual insulator elements making up the insulator strings is hard to predict, they must be verified periodically to ensure that adequate line reliability is maintained at all times. Over the years utilities have adopted few methods to detect defective discs in a string, subsequently replacement of the faulty discs are being carried out for smooth operation. But, if the insulator is found to be defective in a string at some location that may not create any changes in the field configuration, there is no need to replace to avoid manpower and cost of replacement. Due to deficiency of electric field data for the existing string configuration, utilities are forced to replace the discs which may not be essentially required. Hence, effort is made in the present work to simulate the potential and electric field along the normal and with faults induced discs in a string up to 765 kV system voltages using Surface Charge Simulation Method (SCSM). A comparison is made between simulated results, experimental and field data and it was found that the computed results are quite acceptable and useful.

Superbubble breakout and galactic winds from disc galaxies

We study the conditions for disc galaxies to produce superbubbles that can break out of the disc and produce a galactic wind. We argue that the threshold surface density of supernovae rate for seeding a wind depends on the ability of superbubble energetics to compensate for radiative cooling. We first adapt Kompaneets formalism for expanding bubbles in a stratified medium to the case of continuous energy injection and include the effects of radiative cooling in the shell. With the help of hydrodynamic simulations, we then study the evolution of superbubbles evolving in stratified discs with typical disc parameters. We identify two crucial energy injection rates that differ in their effects, the corresponding breakout ranging from being gentle to a vigorous one. (a) Superbubbles that break out of the disc with a Mach number of the order of 2-3 correspond to an energy injection rate of the order of 10(-4) erg cm(-2) s(-1), which is relevant for disc galaxies with synchrotron emitting gas in the extra-planar regions. (b) A larger energy injection threshold, of the order of 10(-3) erg cm(-2) s(-1), or equivalently, a star formation surface density of similar to 0.1 M-circle dot yr(-1) kpc(-2), corresponds to superbubbles with a Mach number similar to 5-10. While the milder superbubbles can be produced by large OB associations, the latter kind requires super-starclusters. These derived conditions compare well with observations of disc galaxies with winds and the existence of multiphase halo gas. Furthermore, we find that contrary to the general belief that superbubbles fragment through Rayleigh-Taylor (RT) instability when they reach a vertical height of the order of the scaleheight, the superbubbles are first affected by thermal instability for typical disc parameters and that RT instability takes over when the shells reach a distance of approximately twice the scaleheight.

Narrow escape: how ionizing photons escape from disc galaxies

In this paper we calculate the escape fraction (f(esc)) of ionizing photons from starburst galaxies. Using 2D axisymmetric hydrodynamic simulations, we study superbubbles created by overlapping supernovae in OB associations. We calculate the escape fraction of ionizing photons from the centre of the disc along different angles through the superbubble and the gas disc. After convolving with the luminosity function of OB associations, we show that the ionizing photons escape within a cone of similar to 40 degrees, consistent with observations of nearby galaxies. The evolution of the escape fraction with time shows that it falls initially as cold gas is accumulated in a dense shell. After the shell crosses a few scaleheights and fragments, the escape fraction through the polar regions rises again. The angle-averaged escape fraction cannot exceed similar to1 - cos (1 rad)] = 0.5 from geometrical considerations (using the emission cone opening angle). We calculate the dependence of the time-and angle-averaged escape fraction on the mid-plane disc gas density (in the range n(0) = 0.15-50 cm(-3)) and the disc scaleheight (between z(0) = 10 and 600 pc). We find that the escape fraction is related to the disc parameters (the mid-plane disc density and scaleheight) roughly so that f(esc)(alpha)n(0)(2)z(0)(3) (with alpha approximate to 2.2) is a constant. For discs with a given warm neutral medium temperature, massive discs have lower escape fraction than low-mass galaxies. For Milky Way ISM parameters, we find f(esc) similar to 5 per cent, and it increases to approximate to 10 per cent for a galaxy 10 times less massive. We discuss the possible effects of clumpiness of the ISM on the estimate of the escape fraction and the implications of our results for the reionization of the Universe.

Performance analysis of 1200 kV ceramic disc insulator string under normal and faulted conditions

In the recent years there has been a considerable increase in demand for the electrical power requirement in our country. Presently the transmission system voltages has increased to 765 kV ac and 800kV dc, keeping in view of the future demand experimentation and simulation studies for 1200 kV ac and 1100kV dc transmission are under progress. In the present study an attempt is made to compute the surface potential, electric field across the string of ceramic disc insulators used for 1200kV ac systems. The studies are carried out under normal, polluted conditions and for the case of insulator string containing faulty discs. A computer code using surface charge simulation method (SCSM) is developed for the present analysis. Also a new technique which enhances the surface potential and electric field strength for the existing ceramic disc insulators is presented.

Cubicity of threshold graphs

We show that the cubicity of a connected threshold graph is equal to inverted right perpendicularlog(2) alpha inverted left perpendicular, where alpha is its independence number.

Frictional response of fatty acids on steel

Self-assembled monolayers of fatty acids were formed on stainless steel by room-temperature solution deposition. The acids are covalently bound to the Surface as carboxylate in a bidentate manner. To explore the effect Of Saturation in the carbon backbone on friction in sliding tribology, we Study the response of saturated stearic acid (SA) and unsaturated linoleic acid (LA) as self-assembled monolayers using lateral force microscopy and nanotribometry and when the molecules are dispersed in hexadecane, using pin-on-disc tribometry. Over a very wide range (10 MPa-2.5 GPa) of contact pressures it is consistently demonstrated that the unsaturated linoleic acid molecules yield friction which is significantly lower than that of the saturated stearic acid. it is argued, using density functional theory predictions and XPS of slid track, that when the molecular backbone of unsaturated fatty acids are tilted and pressed strongly by a probe, in tribological contact, the high charge density of the double bond region of the backbone allows coupling with the steel Substrate. The interaction yields a low friction carboxylate soap film on the substrate. The saturated fatty acid does not show this effect.

A Classification of Homogeneous Operators in the Cowen-Douglas Class

A complete list of homogeneous operators in the Cowen-Douglas class B-n(D) is given. This classification is obtained from an explicit realization of all the homogeneous Hermitian holomorphic vector bundles on the unit disc under the action of the universal covering group of the bi-holomorphic automorphism group of the unit disc.

Bounds on isoperimetric values of trees

Let G = (V, E) be a finite, simple and undirected graph. For S subset of V, let delta(S, G) = {(u, v) is an element of E : u is an element of S and v is an element of V - S} be the edge boundary of S. Given an integer i, 1 <= i <= vertical bar V vertical bar, let the edge isoperimetric value of G at i be defined as b(e)(i, G) = min(S subset of V:vertical bar S vertical bar=i)vertical bar delta(S, G)vertical bar. The edge isoperimetric peak of G is defined as b(e)(G) = max(1 <= j <=vertical bar V vertical bar)b(e)(j, G). Let b(v)(G) denote the vertex isoperimetric peak defined in a corresponding way. The problem of determining a lower bound for the vertex isoperimetric peak in complete t-ary trees was recently considered in [Y. Otachi, K. Yamazaki, A lower bound for the vertex boundary-width of complete k-ary trees, Discrete Mathematics, in press (doi: 10.1016/j.disc.2007.05.014)]. In this paper we provide bounds which improve those in the above cited paper. Our results can be generalized to arbitrary (rooted) trees. The depth d of a tree is the number of nodes on the longest path starting from the root and ending at a leaf. In this paper we show that for a complete binary tree of depth d (denoted as T-d(2)), c(1)d <= b(e) (T-d(2)) <= d and c(2)d <= b(v)(T-d(2)) <= d where c(1), c(2) are constants. For a complete t-ary tree of depth d (denoted as T-d(t)) and d >= c log t where c is a constant, we show that c(1)root td <= b(e)(T-d(t)) <= td and c(2)d/root t <= b(v) (T-d(t)) <= d where c(1), c(2) are constants. At the heart of our proof we have the following theorem which works for an arbitrary rooted tree and not just for a complete t-ary tree. Let T = (V, E, r) be a finite, connected and rooted tree - the root being the vertex r. Define a weight function w : V -> N where the weight w(u) of a vertex u is the number of its successors (including itself) and let the weight index eta(T) be defined as the number of distinct weights in the tree, i.e eta(T) vertical bar{w(u) : u is an element of V}vertical bar. For a positive integer k, let l(k) = vertical bar{i is an element of N : 1 <= i <= vertical bar V vertical bar, b(e)(i, G) <= k}vertical bar. We show that l(k) <= 2(2 eta+k k)

Synergy between tribo-oxidation and strain rate response on governing the dry sliding wear behavior of titanium.

The present work provides an insight into the dry sliding wear behavior of titanium based on synergy between tribo-oxidation and strain rate response. Pin-on-disc tribometer was used to characterize the friction and wear behavior of titanium pin in sliding contact with polycrystalline alumina disk under ambient and vacuum condition. The sliding speed was varied from 0.01 to 1.4 ms(-1), normal load was varied from 15.3 to 76 N and with a sliding distance of 1500 m. It was seen that dry sliding wear behavior of titanium was governed by combination of tribo-oxidation and strain rate response in near surface region of titanium. Strain rate response of titanium was recorded by conducting uni-axial compression tests at constant true strain rate of 100 s(-1) in the temperature range from 298 to 873 K. Coefficient of friction and wear rate were reduced with increased sliding speed from 0.01 to 1.0 ms(-1). This is attributed to the formation of in situ self lubricating oxide film (TiO) and reduction in the intensity of adiabatic shear band cracking in the near surface region. This trend was confirmed by performing series of dry sliding tests under vacuum condition of 2 x 10(-4) Torr. Characterization tools such as optical microscopy, scanning electron microscopy, and X-ray diffractometer provided evidence of such processes. These experimental findings can be applied to enhance the dry sliding wear behavior of titanium with proper choice of operating conditions such as sliding speed, normal load, and environment.

Fast matrix transposition computer implementation

Eklundh's (1972) algorithm to transpose a large matrix stored on an external device such as a disc has been programmed and tested. A simple description of computer implementation is given in this note.

A technique for steady-state polarisation of stationary solid electrodes and its applications

A new technique has been devised to achieve a steady-state polarisation of a stationary electrode with a helical shaft rotating coaxial to it. A simplified theory for the convective hydrodynamics prevalent under these conditions has been formulated. Experimental data are presented to verify the steady-state character of the current-potential curves and the predicted dependence of the limiting current on the rotation speed of the rotor, the bulk concentration of the depolariser and the viscosity of the solution. Promising features of the multiple-segment electrodes concentric to a central disc electrode are pointed out.

Characterization of dry sliding wear of Al---Si alloys

Controversy exists in the published literature as to the effect of silicon content and pressure on the dry sliding wear of Al---Si alloys. The present paper attempts to clarify the question by reporting a statistical analysis of data obtained from factorially designed experiments conducted on a pinon-disc machine in the pressure range 0.105–1.733 MPa and speed range 0.19–0.94 m s−1. Under these conditions it was found that, in the range 4–24 wt.% Si, wear of binary unmodified alloys does not significantly differ between the alloys. However, it is significantly less than that corresponding to an alloy containing no silicon. The effect of pressure on wear rate was found to be linear and monotonie and, over the narrow range of speeds used, the wear rate was found to be unaffected by speed. The coefficient of friction was found to be insensitive to variations in silicon content, pressure and speed.

Scanning electron microscopy study of worn Al-Si alloy surfaces

A pin-on-disc machine was used to wear Al-Si alloy pins under dry conditions. Unmodified and modified binary alloys and commercial multi-component alloys were tested. The surfaces of the worn alloys were examined by scanning electron microscopy to identify distinct topographical features to aid elucidation of the mechanisms of wear.

Dry sliding wear behaviour of magnesium alloy based hybrid composites in the longitudinal direction

In the present investigation, the wear behaviour of a creep-resistant AE42 magnesium alloy and its composites reinforced with Saffil short fibres and SiC particles in various combinations is examined in the longitudinal direction i.e., the plane containing random fibre orientation is perpendicular to the steel counter-face. Wear tests are conducted on a pin-on-disc set-up under dry sliding condition having a constant sliding velocity of 0.837 m/s for a constant sliding distance of 2.5 km in the load range of 10-40 N. It is observed that the wear rate increases with increase in load for the alloy and the composites, as expected. Wear rate of the composites is lower than the alloy and the hybrid composites exhibit a lower wear rate than the Saffil short fibres reinforced composite at all the loads. Therefore, the partial replacement of Saffil short fibres by an equal volume fraction of SiC particles not only reduces the cost but also improves the wear resistance of the composite. Microstructural investigation of the surface and subsurface of the worn pin and wear debris is carried out to explain the observed results and to understand the wear mechanisms. It is concluded that the presence of SiC particles in the hybrid composites improves the wear resistance because these particles remain intact and retain their load bearing capacity even at the highest load employed, they promote the formation of iron-rich transfer layer and they also delay the fracture of Saffil short fibres to higher loads. Under the experimental conditions used in the present investigation, the dominant wear mechanism is found to be abrasion for the AE42 alloy and its composites. It is accompanied by severe plastic deformation of surface layers in case of alloy and by the fracture of Saffil short fibres as well as the formation of iron-rich transfer layer in case of composites.

Wear lip formation during dry sliding

A pin-on-disc test configuration has been used to examine the formation of the strain-hardened projection, or wear lips, especially at the trailing edge of the pin during dry sliding of aluminium alloys against steel discs. The mechanism of formation of such wear lips is studied with the aid of optical and electron microscopes. The plastic deformation of the pin, growth and eventual removal of the wear lip as wear debris are elucidated. The size and shape of the wear lips in pins of different shapes, i.e. square, rectangular, triangular and circular cross-sections, are described.