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.

Transient electric field distribution within the working volume of an NEMP simulator

Nuclear electro-magnetic pulse (NEMP) simulators which are used in the simulation of transient electromagnetic fields due to a high altitude nuclear detonation are generally excited with a double exponential high voltage pulse. This results in a current distribution on the wires of the simulator and hence a transient electric field in the working volume of the simulator where the test object is kept. It is found that for the simulator under study, the current distribution is non-uniform and so is the field distribution along the width of the simulator in the working volume. To make the current distribution uniform, several methods have been suggested and the results of these methods are analyzed and suitable conclusions are arrived at from those results.

Lightning Induced Voltages on a Rocket and its Exhaust Plume

A preliminary attempt has been made to study the time domain characteristics of the induced voltage and current on the rocket and its exhaust plume (ionized trail) when it is coupled with the transient electromagnetic field generated by a nearby lightning discharge. For the computation, finite difference time domain (FDTD) technique has been used where the object is assumed to be a finite vertical nonuniform transmission line above a perfectly conducting ground. It is seen that the amplitude of the first peak of the induced voltage and current at the mid point of the object is 23.5 kV and 4.9 kA respectively.

Design and developement of a pulsed power system for a Vircator based HPM source

Pulse Forming Line (PFL) based high voltage pulsed power systems are well suited for low impedance High Power Microwave (HPM) sources such as a virtual cathode oscillator (VIRCATOR) operating in nanosecond regimes. The system under development consists of a primary voltage source that charges the capacitor bank of a Marx pulser over a long time duration. The Marx pulser output is then conditioned by a PFL to match the requirement of the HPM diode load. This article describes the design and construction of an oil insulated pulse forming line for a REB (Relativistic Electron Beam) diode used in a VIRCATOR for the generation of high power microwaves. Design of a 250 kV/10 kA/60 ns PFL, including the PSPICE simulation for various load conditions are described.

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.