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020 _a9783031578632
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024 7 _a10.1007/978-3-031-57863-2
_2doi
050 4 _aTA352-356
050 4 _aQC20.7.N6
072 7 _aTBJ
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072 7 _aSCI064000
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100 1 _aKougioumtzoglou, Ioannis A.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978337
245 1 0 _aPath Integrals in Stochastic Engineering Dynamics
_h[electronic resource] /
_cby Ioannis A. Kougioumtzoglou, Apostolos F. Psaros, Pol D. Spanos.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXIII, 228 p. 73 illus., 67 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aIntroduction -- 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.
520 _aThis 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.
650 0 _aDynamics.
_965524
650 0 _aNonlinear theories.
_965525
650 0 _aEngineering mathematics.
_964145
650 0 _aEngineering
_xData processing.
650 0 _aStochastic analysis.
_959375
650 0 _aMathematical analysis.
_964178
650 0 _aMathematical physics.
650 1 4 _aApplied Dynamical Systems.
_965530
650 2 4 _aMathematical and Computational Engineering Applications.
650 2 4 _aStochastic Analysis.
_959375
650 2 4 _aIntegral Transforms and Operational Calculus.
_967269
650 2 4 _aTheoretical, Mathematical and Computational Physics.
_965563
700 1 _aPsaros, Apostolos F.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978338
700 1 _aSpanos, Pol D.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978339
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031578625
776 0 8 _iPrinted edition:
_z9783031578649
776 0 8 _iPrinted edition:
_z9783031578656
856 4 0 _uhttps://doi.org/10.1007/978-3-031-57863-2
912 _aZDB-2-PHA
912 _aZDB-2-SXP
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