Fiber Bundles

This book presents a critical overview of statistical fiber bundle models, including existing models and potential new ones. The authors focus on both the physical and statistical aspects of a specific load-sharing example: the breakdown for circuits of capacitors and related dielectrics. In addition, they investigate some areas of open research.

This book is designed for graduate students and researchers in statistics, materials science, engineering, physics, and related fields, as well as practitioners and technicians in materials science and mechanical engineering.

Explains practical applications in probability, statistics, physics, material science, and engineering Examines both the physical and statistical aspects of fibre bundle models and related methodologies and theories Presents potential future directions as well as an overview of the state of the field

Autorentext

James U. Gleaton is Professor Emeritus in the Department of Mathematics and Statistics at the University of North Florida. David Han is Associate Professor of Management Science and Statistics at the University of Texas at San Antonio. James D. Lynch is Distinguished Professor Emeritus in the Department of Statistics at the University of South Carolina. Hon Keung Tony Ng is Professor in the Department of Mathematical Sciences at Bentley University. Fabrizio Ruggeri is Research Director at the Italian National Research Council in Milan.

Inhalt

1. Introduction and Preliminaries.- 2. Electrical Circuits of Ordinary Capacitors.- 3. Breakdown of Thin-Film Dielectrics.- 4. Cell Models for Dielectrics.- 5. Electrical Breakdown and the Breakdown Formalism.- 6. Statistical Properties of a Load-Sharing Bundle.- 7. Statistical Analysis of Kim and Lee (2004)'s Data.- 8. Circuits of Ordinary Capacitors.- 9. Size Effects Relationships Motivated by the Load-Sharing Cell Model.- 10. Concluding Comments and Future Research Directions.