Kougioumtzoglou, Ioannis A. creator author. aut http://id.loc.gov/vocabulary/relators/aut Psaros, Apostolos F. author. aut http://id.loc.gov/vocabulary/relators/aut Spanos, Pol D. author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) text sz 2024 1st ed. 2024. monographic eng

electronic

electronic resource

access XIII, 228 p. 73 illus., 67 illus. in color. online resource. 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. 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. by Ioannis A. Kougioumtzoglou, Apostolos F. Psaros, Pol D. Spanos. Dynamics Nonlinear theories Engineering mathematics Engineering Data processing Stochastic analysis Mathematical analysis Mathematical physics Applied Dynamical Systems Mathematical and Computational Engineering Applications Stochastic Analysis Integral Transforms and Operational Calculus Theoretical, Mathematical and Computational Physics TA352-356 QC20.7.N6 9783031578632 https://doi.org/10.1007/978-3-031-57863-2 https://doi.org/10.1007/978-3-031-57863-2 240605 20251030112300.0 978-3-031-57863-2