Path Integrals in Stochastic Engineering Dynamics

This book organizes and explains, in a systematic and pedagogically effective manner, recent advances in path integral solution techniques with applications in stochastic engineering dynamics. It fills a gap in the literature by introducing to the engineering mechanics community, for the first time in the form of a book, the Wiener path integral as a potent uncertainty quantification tool. Since the path integral flourished within the realm of quantum mechanics and theoretical physics applications, most books on the topic have focused on the complex-valued Feynman integral with only few exceptions, which present path integrals from a stochastic processes perspective. Remarkably, there are only few papers, and no books, dedicated to path integral as a solution technique in stochastic engineering dynamics. Summarizing recently developed techniques, this volume is ideal for engineering analysts interested in further establishing path integrals as an alternative potent conceptual and computational vehicle in stochastic engineering dynamics.

Organizes and presents in a systematic manner recent advances in Wiener path integral solution techniques Establishes Wiener path integrals as a potent conceptual and computational vehicle in stochastic engineering dynamics Discusses diverse applications in emerging/transformative technologies, such as nano-mechanics and energy harvesting

Autorentext

Dr. Ioannis A. Kougioumtzoglou is an Associate Professor, Department of Civil Engineering and Engineering Mechanics, Columbia University, NY; Dr. Apostolos F. Psaros is a Post-Doctoral Researcher, Department of Civil Engineering and Engineering Mechanics, Columbia University, NY; and Dr. Pol D. Spanos is the L. B. Ryon Professor in Mechanical and Civil Engineering, Rice University, Texas, USA

Inhalt

Introduction.- Wiener path integral formalism.- Linear

systems under Gaussian white noise excitation: exact closed form solutions.- Nonlinear

systems under Gaussian white noise excitation.- Nonlinear systems under

non-white, non-Gaussian and non-stationary excitation.- Nonlinear systems with singular

diffusion matrices: a broad perspective including hysteresis modeling.- High-dimensional

nonlinear systems: circumventing the curse of dimensionality via a

reduced-order formulation.- Efficient numerical implementation strategies via

sparse representations and compressive sampling.- An enhanced quadratic Wiener

path integral approximation with applications to nonlinear system reliability

assessment.- Epilogue.