04630nam a22006495i 4500 978-3-031-57863-2 DE-He213 20251030112300.0 cr nn 008mamaa 240605s2024 sz | s |||| 0|eng d 9783031578632 978-3-031-57863-2 10.1007/978-3-031-57863-2 doi TA352-356 QC20.7.N6 TBJ bicssc GPFC bicssc SCI064000 bisacsh TBJ thema GPFC thema Kougioumtzoglou, Ioannis A. author. aut http://id.loc.gov/vocabulary/relators/aut 78337 Path Integrals in Stochastic Engineering Dynamics [electronic resource] / by Ioannis A. Kougioumtzoglou, Apostolos F. Psaros, Pol D. Spanos. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XIII, 228 p. 73 illus., 67 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda 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. 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. Dynamics. 65524 Nonlinear theories. 65525 Engineering mathematics. 64145 Engineering Data processing. Stochastic analysis. 59375 Mathematical analysis. 64178 Mathematical physics. Applied Dynamical Systems. 65530 Mathematical and Computational Engineering Applications. Stochastic Analysis. 59375 Integral Transforms and Operational Calculus. 67269 Theoretical, Mathematical and Computational Physics. 65563 Psaros, Apostolos F. author. aut http://id.loc.gov/vocabulary/relators/aut 78338 Spanos, Pol D. author. aut http://id.loc.gov/vocabulary/relators/aut 78339 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031578625 Printed edition: 9783031578649 Printed edition: 9783031578656 https://doi.org/10.1007/978-3-031-57863-2 ZDB-2-PHA ZDB-2-SXP 60553 60553