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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.

Fibre bundles play an important role in just about every aspect of modern geometry and topology. Basic properties, homotopy classification, and characteristic classes of fibre bundles have become an essential part of graduate mathematical education for students in geometry and mathematical physics. In this third edition two new chapters on the gauge group of a bundle and on the differential forms representing characteristic classes of complex vector bundles on manifolds have been added. These chapters result from the important role of the gauge group in mathematical physics and the continual usefulness of characteristic classes defined with connections on vector bundles.

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This book begins with the claims of policymakers and explores charter schools at each stage of the policymaking process, from legislation to implementation. Powers carefully and thoroughly examines how features of schools' policy contexts shape the ways that charter school reform unfolds at schools, providing a nuanced portrait of the schools participating in this much discussed and little understood reform movement. While policymakers are often prone to making sweeping claims about the efficacy of charter schools, in practice charter school reform is much more complex. By drawing on an extensive and compelling range of data, Powers assesses the validity of policymakers claims.

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