Boxicity of line graphs

The boxicity of a graph H, denoted by box(H), is the minimum integer k such that H is an intersection graph of axis-parallel k-dimensional boxes in R(k). In this paper we show that for a line graph G of a multigraph, box(G) <= 2 Delta (G)(inverted right perpendicularlog(2) log(2) Delta(G)inverted left perpendicular + 3) + 1, where Delta(G) denotes the maximum degree of G. Since G is a line graph, Delta(G) <= 2(chi (G) - 1), where chi (G) denotes the chromatic number of G, and therefore, box(G) = 0(chi (G) log(2) log(2) (chi (G))). For the d-dimensional hypercube Q(d), we prove that box(Q(d)) >= 1/2 (inverted right perpendicularlog(2) log(2) dinverted left perpendicular + 1). The question of finding a nontrivial lower bound for box(Q(d)) was left open by Chandran and Sivadasan in [L. Sunil Chandran, Naveen Sivadasan, The cubicity of Hypercube Graphs. Discrete Mathematics 308 (23) (2008) 5795-5800]. The above results are consequences of bounds that we obtain for the boxicity of a fully subdivided graph (a graph that can be obtained by subdividing every edge of a graph exactly once). (C) 2011 Elsevier B.V. All rights reserved.

Coupling of High Voltage AC Power Line Fields to Metallic Pipelines

In the recent years, there has been a trend to run metallic pipelines carrying petroleum products and high voltage AC power lines parallel to each other in a relatively narrow strip of land. Due to this sharing of the right-of-way, verhead AC power line electric field may induce voltages on the metallic pipelines running in close vicinity leading to serious adverse effects. In this paper, the induced voltages on metallic pipelines running in close vicinity of high voltage power transmission lines have been computed. Before computing the induced voltages, an optimum configuration of the phase conductors based on the lowest conductor surface gradient and field under transmission line has been arrived at. This paper reports the conductor surface field gradients calculated for the various configurations. Also the electric fields under transmission line, for single circuit and double circuit (various phase arrangements) have been analyzed. Based on the above results, an optimum configuration giving the lowest field under the power line as well as the lowest conductor surface gradient has been arrived at and for this configuration, induced voltage on the pipeline has been computed using the Charge Simulation Method (CSM). For comparison, induced voltages on the pipeline has been computed for the various other phase configurations also.

Measurement of Electron Spin Lifetime and Optical Orientation Efficiency in Germanium Using Electrical Detection of Radio Frequency Modulated Spin Polarization

We propose and demonstrate a technique for electrical detection of polarized spins in semiconductors in zero applied magnetic fields. Spin polarization is generated by optical injection using circularly polarized light which is modulated rapidly using an electro-optic cell. The modulated spin polarization generates a weak time-varying magnetic field which is detected by a sensitive radio-frequency coil. Using a calibrated pickup coil and amplification electronics, clear signals were obtained for bulk GaAs and Ge samples from which an optical spin orientation efficiency of 4.8% could be determined for Ge at 1342 nm excitation wavelength. In the presence of a small external magnetic field, the signal decayed according to the Hanle effect, from which a spin lifetime of 4.6 +/- 1.0 ns for electrons in bulk Ge at 127 K was extracted.

Nanostructuration via solid state transformation as a strategy for improving the thermoelectric efficiency of PbTe alloys

The approach taken in this paper in order to modify the scattering features of electrons and phonons and improve the figure of merit (ZT) of thermoelectric PbTe is to alter the microstructure at constant chemistry. A lamellar pattern of PbTe/GeTe at the nano- and microscale was produced in Pb(0.36)Ge(0.64)Te alloy by the diffusional decomposition of a supersaturated solid solution. The mechanism of nanostructuration is most likely a discontinuous spinodal decomposition. A simple model relating the interface velocity to the observed lamellar spacing is proposed. The effects of nanostructuration in Pb(0.36)Ge(0.64)Te alloy on the electrical and thermal conductivity, thermopower and ZT were investigated. It was shown that nanostructuration through the formation of a lamellar pattern of PbTe/GeTe is unlikely to provide a significant improvement due to the occurrence of discontinuous coarsening. However, the present study allows an analysis of possible strategies to improve thermoelectric materials via optimal design of the microstructure and optimized heat treatment. (C) 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

A new matched thermochemical diagram for vacuum refining of nickel and cupronickel alloys

Sulfur and oxygen dissolved in nickel and cupronickel melts can be remwed as gaseous oxides of sulfur by a vacuum treatment. Presented in this paper is a new matched thermcxhemical disgran~ that permit.. direct evaluation of the equilibrium partial pressure of SO, as a function of temperature wer an alloy of specified compition. The matched thermochemical diagram consists of a central plot which shows the integral Gibbs' energy of mixing for the binary system SO, at different temperatures. The central plot is flanked on either side by terminal plots of the chemical potentials of oxygen and sulfur, as functions of temperature, for different alloy compositions. By projecting the chemical wtentials of oxygen and sulfur from the terminal lots on to the central diagram, ihe equilibrium partial pressure of S0,can be directly ;cad on the nomograms on the central plot at different temperatures. The matched therrnochemical diagrams are useful in assuring the efficiency of vacuum refining.

Fuel Cell Efficiency Redefined; Carnot Limit Reassessed

There are deficiencies in current definition of thermodynamic efficiency of fuel cells (ηcth = ΔG/ΔH); efficiency greater than unity is obtained when AS for the cell reaction is positive, and negative efficiency is obtained for endothermic reactions. The origin of the flow is identified. A new definition of thennodynamic efficiency is proposed that overcomes these limitations. Consequences of the new definition are examined. Against the conventional view that fuel cells are not Carnot limited, several recent articles have argued that the second law of thermodynamics restricts fuel cell energy conversion in the same way as heat engines. This controversy is critically examined. A resolution is achieved in part from an understanding of the contextual assumptions in the different approaches and in part from identifying some conceptual limitations.