This monograph surveys the theory of quantitative homogenization for second-order linear elliptic systems in divergence form with rapidly oscillating periodic coefficients in a bounded domain. It begins with a review of the classical qualitative homogenization theory, and addresses the problem of convergence rates of solutions. The main body of the monograph investigates various interior and boundary regularity estimates that are uniform in the small parameter e>0. Additional topics include convergence rates for Dirichlet eigenvalues and asymptotic expansions of fundamental solutions, Green functions, and Neumann functions. The monograph is intended for advanced graduate students and researchers in the general areas of analysis and partial differential equations. It provides the reader with a clear and concise exposition of an important and currently active area of quantitative homogenization.
This monograph surveys the theory of quantitative homogenization for second-order linear elliptic systems in divergence form with rapidly oscillating periodic coefficients in a bounded domain. It begins with a review of the classical qualitative homogenization theory, and addresses the problem of convergence rates of solutions. The main body of the monograph investigates various interior and boundary regularity estimates that are uniform in the small parameter e>0. Additional topics include convergence rates for Dirichlet eigenvalues and asymptotic expansions of fundamental solutions, Green functions, and Neumann functions. The monograph is intended for advanced graduate students and researchers in the general areas of analysis and partial differential equations. It provides the reader with a clear and concise exposition of an important and currently active area of quantitative homogenization.
Abrasive Water Jet Perforation and Multi-Stage Fracturing gives petroleum engineers, well completion managers and fracturing specialists a critical guide to understanding all the details of the technology including materials, tools, design methods and field applications. The exploitation and development of unconventional oil and gas resources has continued to gain importance, and multi-stage fracturing with abrasive water jets has emerged as one of the top three principal methods to recover unconventional oil and gas, yet there is no one collective reference to explain the fundamentals, operations and influence this method can deliver. The book introduces current challenges and gives solutions for the problems encountered. Packed with references and real-world examples, the book equips engineers and specialists with a necessary reservoir stimulation tool to better understand today’s fracturing technology. Provides understanding of the fundamentals, design and application of water jet perforation Examines the pressure boosting assembly in all phases including initiation, hydraulic isolation and production stage Evaluates production analysis, pump pressure predictions and the latest design software Introduces current challenges and gives solutions for the problems encountered
Special Distillation Processes, Second Edition focuses on the latest developments in the field, such as separation methods that may prove useful for solving problems encountered during research. Topics include extraction, membrane and adsorption distillation involving the separation principle, process design and experimental techniques. The relationship between processes and techniques are also presented. Comprehensive and easy-to-read, this book provides key information needed to understand processes. It will be a valuable reference source for chemical engineers and students wishing to branch out in chemical engineering. Provides the only comprehensive book available on special distillation processes Contains a thorough introduction to recent developments in the field Presents a valuable reference for students, academics and engineers in chemical engineering
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