Probability Distribution of the Eigenvalues of the Random String Equation

The probability distribution of the eigenvalues of a second-order stochastic boundary value problem is considered. The solution is characterized in terms of the zeros of an associated initial value problem. It is further shown that the probability distribution is related to the solution of a first-order nonlinear stochastic differential equation. Solutions of this equation based on the theory of Markov processes and also on the closure approximation are presented. A string with stochastic mass distribution is considered as an example for numerical work. The theoretical probability distribution functions are compared with digital simulation results. The comparison is found to be reasonably good.

Radio interference measurements on a ceramic disc insulator string with field reduction electrode

This paper presents a laboratory study of the discharge radio noise generated by ceramic insulator strings under normal conditions. In the course of study, a comparison on the performance of two types of insulator strings under two different conditions was studied namely (a) normal disc insulators in a string and (b) disc insulators integrated with a newly developed field reduction electrode fixed to the disc insulator at the pin junction. The results obtained during the study are discussed and presented.

A Case Study in Matching Service Descriptions to Implementations in an Existing System

A number of companies are trying to migrate large monolithic software systems to Service Oriented Architectures. A common approach to do this is to first identify and describe desired services (i.e., create a model), and then to locate portions of code within the existing system that implement the described services. In this paper we describe a detailed case study we undertook to match a model to an open-source business application. We describe the systematic methodology we used, the results of the exercise, as well as several observations that throw light on the nature of this problem. We also suggest and validate heuristics that are likely to be useful in partially automating the process of matching service descriptions to implementations.

Linear dynamics and active control of an elastically supported travelling string

In this paper, the linear dynamics and active control of a string travelling with uniform velocity is presented. Discrete elastic supports are introduced along the length of the string. Finite element formulation is adopted to obtain the governing equations of motion. The velocity of translation introduces gyroscopic terms in the system equations. The effect of translation and the discrete elastic supports on the free vibration solution is studied. The solution is utilized in actively controlling the string vibrations due to an initial disturbance. The control, affected in modal space, is optimal with respect to a quadratic performance index. Numerical results are presented to demonstrate the effectiveness of the control strategy in regulating the travelling string vibrations.

Violin string shape functions for finite element analysis of rotating Timoshenko beams

Violin strings are relatively short and stiff and are well modeled by Timoshenko beam theory. We use the static part of the homogeneous differential equation of violin strings to obtain new shape functions for the finite element analysis of rotating Timoshenko beams. For deriving the shape functions, the rotating beam is considered as a sequence of violin strings. The violin string shape functions depend on rotation speed and element position along the beam length and account for centrifugal stiffening effects as well as rotary inertia and shear deformation on dynamic characteristics of rotating Timoshenko beams. Numerical results show that the violin string basis functions perform much better than the conventional polynomials at high rotation speeds and are thus useful for turbo machine applications. (C) 2011 Elsevier B.V. All rights reserved.

Matching sender and receiver: poikilothermy and frequency tuning in a tree cricket

Animals communicate in non-ideal and noisy conditions. The primary method they use to improve communication efficiency is sender-receiver matching: the receiver's sensory mechanism filters the impinging signal based on the expected signal. In the context of acoustic communication in crickets, such a match is made in the frequency domain. The males broadcast a mate attraction signal, the calling song, in a narrow frequency band centred on the carrier frequency (CF), and the females are most sensitive to sound close to this frequency. In tree crickets, however, the CF changes with temperature. The mechanisms used by female tree crickets to accommodate this change in CF were investigated at the behavioural and biomechanical level. At the behavioural level, female tree crickets were broadly tuned and responded equally to CFs produced within the naturally occurring range of temperatures (18 to 27 degrees C). To allow such a broad response, however, the transduction mechanisms that convert sound into mechanical and then neural signals must also have a broad response. The tympana of the female tree crickets exhibited a frequency response that was even broader than suggested by the behaviour. Their tympana vibrate with equal amplitude to frequencies spanning nearly an order of magnitude. Such a flat frequency response is unusual in biological systems and cannot be modelled as a simple mechanical system. This feature of the tree cricket auditory system not only has interesting implications for mate choice and species isolation but may also prove exciting for bio-mimetic applications such as the design of miniature low frequency microphones.

Study of temperature distribution along an artificially polluted insulator string

Insulator becomes wet partially or completely, and the pollution layer on it becomes conductive, when collecting pollutants for an extended period during dew, light rain, mist, fog or snow melting. Heavy rain is a complicated factor that it may wash away the pollution layer without initiating other stages of breakdown or it may bridge the gaps between sheds to promote flashover. The insulator with a conducting pollution layer being energized, can cause a surface leakage current to flow (also temperature-rise). As the surface conductivity is non-uniform, the conducting pollution layer becomes broken by dry bands (at spots of high current density), interrupting the flow of leakage current. Voltage across insulator gets concentrated across dry bands, and causes high electric stress and breakdown (dry band arcing). If the resistance of the insulator surface is sufficiently low, the dry band arcs can be propagated to bridge the terminals causing flashover. The present paper concerns the evaluation of the temperature distribution along the surface of an energized artificially polluted insulator string.

String-like propagation of the 5-coordinated defect state in supercooled water: molecular origin of dynamic and thermodynamic anomalies

We find that at low temperature water, large amplitude (similar to 60 degrees) rotational jumps propagate like a string, with the length of propagation increasing with lowering temperature. The strings are formed by mobile 5-coordinated water molecules which move like a Glarum defect (J. Chem. Phys., 1960, 33, 1371), causing water molecules on the path to change from 4-coordinated to 5-coordinated and again back to 4-coordinated water, and in the process cause the tagged water molecule to jump, by following essentially the Laage-Hynes mechanism (Science, 2006, 311, 832-835). The effects on relaxation of the propagating defect causing large amplitude jumps are manifested most dramatically in the mean square displacement (MSD) and also in the rotational time correlation function of the O-H bond of the molecule that is visited by the defect (transient transition to the 5-coordinated state). The MSD and the decay of rotational time correlation function, both remain quenched in the absence of any visit by the defect, as postulated by Glarum long time ago. We establish a direct connection between these propagating events and the known thermodynamic and dynamic anomalies in supercooled water. These strings are found largely in the regions that surround the relatively rigid domains of 4-coordinated water molecules. The propagating strings give rise to a noticeable dynamical heterogeneity, quantified here by a sharp rise in the peak of the four-point density response function, chi(4)(t). This dynamics heterogeneity is also responsible for the breakdown of the Stokes-Einstein relation.

Potential and electric field distribution in a ceramic disc insulator string with faulty insulators

Ceramic/Porcelain suspension disc insulators are widely used in power systems to provide electrical insulation and mechanically support for high-voltage transmission lines. These insulators are subjected to a variety of stresses, including mechanical, electrical and environmental. These stresses act in unison. The exact nature and magnitude of these stresses vary significantly and depends on insulator design, application and its location. Due to various reasons the insulator disc can lose its electrical insulation properties without any noticeable mechanical failure. Such a condition while difficult to recognize, can enhance the stress on remaining healthy insulator discs in the string further may lead to a flashover. To understand the stress enhancement due to faulty discs in a string, attempt has been made to simulate the potential and electric field profiles for various disc insulators presently used in the country. The results of potential and electric filed stress obtained for normal and strings with faulty insulator discs are presented.