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Introduction to Turbulent Dynamical Systems in Complex Systems 1st ed. 2016 [Pehme köide]

  • Formaat: Paperback / softback, 91 pages, kõrgus x laius: 235x155 mm, kaal: 1708 g, 9 Illustrations, color; XI, 91 p. 9 illus. in color., 1 Paperback / softback
  • Sari: Frontiers in Applied Dynamical Systems: Reviews and Tutorials 5
  • Ilmumisaeg: 22-Sep-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 331932215X
  • ISBN-13: 9783319322155
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Introduction to Turbulent Dynamical Systems in Complex Systems 1st ed. 2016Suurem pilt
  • Formaat: Paperback / softback, 91 pages, kõrgus x laius: 235x155 mm, kaal: 1708 g, 9 Illustrations, color; XI, 91 p. 9 illus. in color., 1 Paperback / softback
  • Sari: Frontiers in Applied Dynamical Systems: Reviews and Tutorials 5
  • Ilmumisaeg: 22-Sep-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 331932215X
  • ISBN-13: 9783319322155
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319322155.html
Märksõnad:
This volume is a research expository article on the applied mathematics of turbulent dynamical systems through the paradigm of modern applied mathematics. It involves the blending of rigorous mathematical theory, qualitative and quantitative modeling, and novel numerical procedures driven by the goal of understanding physical phenomena which are of central importance to the field. The contents cover general framework, concrete examples, and instructive qualitative models. Accessible open problems are mentioned throughout.Topics covered include:· Geophysical flows with rotation, topography, deterministic and random forcing· New statistical energy principles for general turbulent dynamical systems, with applications· Linear statistical response theory combined with information theory to cope with model errors· Reduced low order models· Recent mathematical strategies for online data assimilation of turbulent dynamical systems as well as rigorous results for finit

e ensemble Kalman filtersThe volume will appeal to graduate students and researchers working mathematics, physics and engineering and particularly those in the climate, atmospheric and ocean sciences interested in turbulent dynamical as well as other complex systems.

Introduction.- Prototype Examples of Complex Turbulent Dynamical Systems.- The Mathematical Theory of Turbulent Dynamical Systems.- Statistical Prediction and UQ for Turbulent Dynamical Systems.- State Estimation, Data Assimilation, or Filtering for Complex Turbulent Dynamical Systems.- Finite Ensemble Kalman Filders (EnKF): Applied Practice, Mathematical Theory, and New Phenomena.

Arvustused

This research monograph presents recent mathematical results in the field of turbulent dynamical systems. Numerous references are cited. The book is certainly of some interest for graduate students and researchers in the field of mathematical modeling of geophysical flows. (Kai Schneider, zbMATH 1377.37003, 2018) This is a beautifully written research expository book on turbulent dynamical systems that arise in complex systems. it contains a wealth of new information including many penetrating insights that are not available elsewhere systematically. It belongs on the bookshelf of everybody who is seriously interested in turbulent dynamical systems in high-dimensional phase space and many related applied issues. (Xiaoming Wang, Mathematical Reviews, July, 2017)

1 Introduction
1(4)
1.1 Turbulent Dynamical Systems for Complex Systems: Basic Issues for Prediction, Uncertainty Quantification, and State Estimation
1(2)
1.2 Detailed Structure and Energy Conservation Principles
3(2)
2 Prototype Examples of Complex Turbulent Dynamical Systems
5(8)
2.1 Turbulent Dynamical Systems for Complex Geophysical Flows: One-Layer Model
5(2)
2.2 The L-96 Model as a Turbulent Dynamical System
7(1)
2.3 Statistical Triad Models, the Building Blocks of Complex Turbulent Dynamical Systems
8(2)
2.4 More Rich Examples of Complex Turbulent Dynamical Systems
10(3)
2.4.1 Quantitative Models
11(1)
2.4.2 Qualitative Models
11(2)
3 The Mathematical Theory of Turbulent Dynamical Systems
13(30)
3.1 Nontrivial Turbulent Dynamical Systems with a Gaussian Invariant Measure
14(1)
3.2 Exact Equations for the Mean and Co variance of the Fluctuations
15(7)
3.2.1 Turbulent Dynamical Systems with Non-Gaussian Statistical Steady States and Nontrivial Third-Order Moments
16(1)
3.2.2 Statistical Dynamics in the L-96 Model and Statistical Energy Conservation
17(2)
3.2.3 One-Layer Geophysical Model as a Turbulent Dynamical System
19(3)
3.3 A Statistical Energy Conservation Principle for Turbulent Dynamical Systems
22(17)
3.3.1 Details About Deterministic Triad Energy Conservation Symmetry
24(6)
3.3.2 A Generalized Statistical Energy Identity
30(6)
3.3.3 Enhanced Dissipation of the Statistical Mean Energy, the Statistical Energy Principle, and "Eddy Viscosity"
36(2)
3.3.4 Stochastic Lyapunov Functions for One-Layer Turbulent Geophysical Flows
38(1)
3.4 Geometric Ergodicity for Turbulent Dynamical Systems
39(4)
4 Statistical Prediction and UQ for Turbulent Dynamical Systems
43(22)
4.1 A Brief Introduction
43(3)
4.1.1 Low-Order Truncation Methods for UQ and Their Limitations
43(1)
4.1.2 The Gaussian Closure Method for Statistical Prediction
44(1)
4.1.3 A Fundamental Limitation of the Gaussian Closure Method
45(1)
4.2 A Mathematical Strategy for Imperfect Model Selection, Calibration, and Accurate Prediction: Blending Information Theory and Statistical Response Theory
46(9)
4.2.1 Imperfect Model Selection, Empirical Information Theory, and Information Barriers
46(2)
4.2.2 Linear Statistical Response and Fluctuation-Dissipation Theorem for Turbulent Dynamical Systems
48(3)
4.2.3 The Calibration and Training Phase Combining Information Theory and Kicked Statistical Response Theory
51(2)
4.2.4 Low-Order Models Illustrating Model Selection, Calibration, and Prediction with UQ
53(2)
4.3 Improving Statistical Prediction and UQ in Complex Turbulent Dynamical Systems by Blending Information Theory and Kicked Statistical Response Theory
55(10)
4.3.1 Models with Consistent Equilibrium Single Point Statistics and Information Barriers
57(1)
4.3.2 Models with Consistent Unperturbed Equilibrium Statistics for Each Mode
57(2)
4.3.3 Calibration and Training Phase
59(1)
4.3.4 Testing Imperfect Model Prediction Skill and UQ with Different Forced Perturbations
59(3)
4.3.5 Reduced-Order Modeling for Complex Turbulent Dynamical Systems
62(3)
5 State Estimation, Data Assimilation, or Filtering for Complex Turbulent Dynamical Systems
65(20)
5.1 Filtering Noisy Lagrangian Tracers for Random Fluid Flows
66(1)
5.2 State Estimation for Nonlinear Turbulent Dynamical Systems Through Hidden Conditional Gaussian Statistics
67(5)
5.2.1 Examples and Applications of Filtering Turbulent Dynamical Systems as Conditional Gaussian Systems
68(4)
5.3 Finite Ensemble Kalman Filters (EnKF): Applied Practice Mathematical Theory, and New Phenomena
72(4)
5.3.1 EnKF and ESRF Formulation
73(1)
5.3.2 Catastrophic Filter Divergence
74(1)
5.3.3 Rigorous Examples of Catastrophic Filter Divergence
75(1)
5.3.4 Rigorous Nonlinear Stability and Geometric Ergodicity for Finite Ensemble Kalman Filters
75(1)
5.4 Mathematical Strategies and Algorithms for Multi-scale Data Assimilation
76(9)
5.4.1 Conceptual Dynamical Models for Turbulence and Superparameterization
77(6)
5.4.2 Blended Particle Methods with Adaptive Subspaces for Filtering Turbulent Dynamical Systems
83(1)
5.4.3 Extremely Efficient Multi-scale Filtering Algorithms: SPEKF and Dynamic Stochastic Superresolution (DSS)
83(2)
References 85