Picture water droplets

Developing mathematical theories of the physical world: Open Access research on fluid dynamics from Strathclyde

Strathprints makes available Open Access scholarly outputs by Strathclyde's Department of Mathematics & Statistics, where continuum mechanics and industrial mathematics is a specialism. Such research seeks to understand fluid dynamics, among many other related areas such as liquid crystals and droplet evaporation.

The Department of Mathematics & Statistics also demonstrates expertise in population modelling & epidemiology, stochastic analysis, applied analysis and scientific computing. Access world leading mathematical and statistical Open Access research!

Explore all Strathclyde Open Access research...

Modifications to the von Laue statistical distribution of the times to breakdown at a polymer-oil interface

Given, Martin J. and Wilson, Mark P. and Timoshkin, Igor V. and MacGregor, Scott J. and Wang, Tao and Sinclair, Mark A. and Thomas, Ken J. and Lehr, Jane M. (2017) Modifications to the von Laue statistical distribution of the times to breakdown at a polymer-oil interface. IEEE Transactions on Dielectrics and Electrical Insulation. ISSN 1070-9878 (In Press)

[img]
Preview
Text (Given-etal-IEEE-2017-Modifications-to-the-von-Laue-statistical-distribution)
Given_etal_IEEE_2017_Modifications_to_the_von_Laue_statistical_distribution.pdf
Accepted Author Manuscript

Download (738kB) | Preview

Abstract

A statistical analysis has been undertaken to determine the statistical and formative times associated with breakdowns along a polymer-oil interface under impulse conditions. Early analysis was based on an assumption that the breakdown data followed the von Laue Distribution. However, it was found that in the Laue plots there were deviations from the expected straight line behavior at short times to breakdown, which may be due to a normal distribution in values of the formative times. In addition, the plots showed multiple straight line sections, which suggested that changes were occurring to the breakdown processes during the experimental run, or that more than one mechanism of breakdown was occurring. Values of the statistical time ts and the formative time tf were determined from the data by making choices on the straight line section to be considered, and ignoring the effects of the normal distribution on the derived values of ts and tf. The present paper is focused on further development of this statistical method, including a rigorous analysis of the experimental data, taking into account the effect that a normal distribution of the formative times has on the derived values of ts and tf. Optimal fits in terms of three parameters: ts, tf, and f (the standard deviation of the formative time) have been derived using Kolmogorov-Smirnov statistics to quantify the quality of fit. The quality of these fits and the applicability of this approach is discussed.