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ISSN 打印: 2152-5080

ISSN 在线: 2152-5099

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.7 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.9 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 0.5 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.0007 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.5 SJR: 0.584 SNIP: 0.676 CiteScore™:: 3 H-Index: 25

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DIFFERENTIAL CONSTRAINTS FOR THE PROBABILITY DENSITY FUNCTION OF STOCHASTIC SOLUTIONS TO THE WAVE EQUATION

卷 2, 册 3, 2012, pp. 195-213
DOI: 10.1615/Int.J.UncertaintyQuantification.2011003485
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摘要

By using functional integral methods we determine new types of differential constraints satisfied by the joint probability density function of stochastic solutions to the wave equation subject to uncertain boundary and initial conditions. These differential constraints involve unusual limit partial differential operators and, in general, they can be grouped into two main classes: the first one depends on the specific field equation under consideration (i.e., on the stochastic wave equation), the second class includes a set of intrinsic relations determined by the structure of the joint probability density function of the wave and its derivatives. Preliminary results we have obtained for stochastic dynamical systems and first-order nonlinear stochastic particle differential equations (PDEs) suggest that the set of differential constraints is complete and, therefore, it allows determining uniquely the probability density function of the solution to the stochastic problem. The proposed new approach can be extended to arbitrary nonlinear stochastic PDEs and it could be an effective way to overcome the curse of dimensionality for random boundary and initial conditions. An application of the theory developed is presented and discussed for a simple random wave in one spatial dimension.

对本文的引用
  1. Venturi D., Tartakovsky D.M., Tartakovsky A.M., Karniadakis G.E., Exact PDF equations and closure approximations for advective-reactive transport, Journal of Computational Physics, 243, 2013. Crossref

  2. Venturi D., Karniadakis G.E., New evolution equations for the joint response-excitation probability density function of stochastic solutions to first-order nonlinear PDEs, Journal of Computational Physics, 231, 21, 2012. Crossref

  3. Venturi Daniele, Cho Heyrim, Karniadakis George Em, Mori-Zwanzig Approach to Uncertainty Quantification, in Handbook of Uncertainty Quantification, 2016. Crossref

  4. Cho H., Venturi D., Karniadakis G. E., Adaptive Discontinuous Galerkin Method for Response-Excitation PDF Equations, SIAM Journal on Scientific Computing, 35, 4, 2013. Crossref

  5. Tartakovsky Daniel M., Gremaud Pierre A., Method of Distributions for Uncertainty Quantification, in Handbook of Uncertainty Quantification, 2017. Crossref

  6. Venturi Daniele, Cho Heyrim, Karniadakis George Em, Mori-Zwanzig Approach to Uncertainty Quantification, in Handbook of Uncertainty Quantification, 2017. Crossref

  7. Tartakovsky Daniel M., Gremaud Pierre A., Method of Distributions for Uncertainty Quantification, in Handbook of Uncertainty Quantification, 2015. Crossref

  8. Venturi D., Sapsis T. P., Cho H., Karniadakis G. E., A computable evolution equation for the joint response-excitation probability density function of stochastic dynamical systems, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 468, 2139, 2012. Crossref

  9. Venturi Daniele, Cho Heyrim, Karniadakis George Em, Mori-Zwanzig Approach to Uncertainty Quantification, in Handbook of Uncertainty Quantification, 2015. Crossref

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