Theory of Stochastic Processes: with Applications to Financial Mathematics and Risk Theory

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Providing the necessary materials within a theoretical framework, this volume presents stochastic principles and processes, and related areas. Over 1000 exercises illustrate the concepts discussed, including modern approaches to sample paths and optimal stopping.

Theory of Electromagnetoelasticity

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【簡介】 Theory of Electromagnetoelasticity presents a systematic and unique treatment of elastic, electric and magnetic interactions in solids including various thermal and dissipative effects such as viscoelasticity and electrical conduction. In this book, a general and nonlinear continuum theory is constructed. The fundamental building blocks of the theory — the electromagnetic body force, couple and power — are calculated from a multi-continuum model consisting of a lattice continuum for elastic deformation, a bound charge continuum for electric polarization, a circulating current continuum for magnetization, and a free charge fluid for electrical conduction. The multi-continuum model is simpler than the common charged particle model and reveals the underlying physics from a unique angle. The complete set of Maxwell's equations for the electromagnetic fields is included without the widely used quasistatic approximations of the electric and/or magnetic fields. The theory established can be used to describe different kinds of interactions between acoustic and optical fields or waves. Some linear problems are analyzed as examples to show some of the simplest elastic and electromagnetic couplings. 【目錄】 Electromagnetism Continuum Kinematics Elasticity Electromagnetoelastic Interaction Model Electromagnetoelastic Balance Laws Electromagnetoelastic Constitutive Relations Linear Problems Thermal and Dissipative Effects Appendices