The aim of this book is to: present a systematic account of recent developments in the stability theory in terms of two distinct measures; describe the current state of the art; show the essential unity achieved by wealth of applications; and provide a unified general structure applicable to several nonlinear problems. This book is dedicated to a systematic development of stability criteria in terms of two measures. It demonstrates the manifestations of general Lyapunov method in terms of two measures by showing how this effective technique can be adapted to study various apparently diverse nonlinear problems and shows how, in the present framework of two measures, one can unify criteria of Lyapunov stability, practical stability and boundedness properties. Interesting applications of real world problems are provided # Methods of Multiscale Modeling in Mechanics (W A Curtin) # Efficient and Accurate Boundary Methods for Computational Optics (C Hafner & J Smajic) # Finite Element Modeling of Periodic Structures (Z Lou & J-M Jin) # Factorization of Potential and Field Distributions without Utilizing the Addition Theorem (A-R Baghi-Wadji & E Li) # Virtualization-Aware Application Framework for Hierarchical Multiscale Simulations on a Grid (A Nakano et al.) # Molecular Dynamics Simulation and Local Quantities (T Ikeshoji) # Recent Advances in Modeling and Simulation of High-Speed Interconnects (M Nakhla & R Achar) # Multiscale Modeling of Degradation and Failure of Interconnect Lines Driven by Electromigration and Stress Gradients (R Atkinson & A M Cuitino)