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The Resource An Introduction to Turbulent Dynamical Systems in Complex Systems

An Introduction to Turbulent Dynamical Systems in Complex Systems

Label
An Introduction to Turbulent Dynamical Systems in Complex Systems
Title
An Introduction to Turbulent Dynamical Systems in Complex Systems
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Subject
Language
eng
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Cataloging source
MiAaPQ
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Frontiers in Applied Dynamical Systems: Reviews and Tutorials Ser
An Introduction to Turbulent Dynamical Systems in Complex Systems
Label
An Introduction to Turbulent Dynamical Systems in Complex Systems
Link
http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/rpi/detail.action?docID=4689337
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Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Preface -- Acknowledgements -- Contents -- 1 Introduction -- 1.1 Turbulent Dynamical Systems for Complex Systems: {u0083} -- 1.2 Detailed Structure and Energy Conservation Principles -- 2 Prototype Examples of Complex Turbulent Dynamical Systems -- 2.1 Turbulent Dynamical Systems for Complex Geophysical Flows: One-Layer Model -- 2.2 The L-96 Model as a Turbulent Dynamical System -- 2.3 Statistical Triad Models, the Building Blocks of Complex Turbulent Dynamical Systems -- 2.4 More Rich Examples of Complex Turbulent Dynamical Systems -- 2.4.1 Quantitative Models -- 2.4.2 Qualitative Models -- 3 The Mathematical Theory of Turbulent Dynamical Systems -- 3.1 Nontrivial Turbulent Dynamical Systems with a Gaussian Invariant Measure -- 3.2 Exact Equations for the Mean and Covariance of the Fluctuations -- 3.2.1 Turbulent Dynamical Systems with Non-Gaussian Statistical Steady States and Nontrivial Third-Order Moments -- 3.2.2 Statistical Dynamics in the L-96 Model and Statistical Energy Conservation -- 3.2.3 One-Layer Geophysical Model as a Turbulent Dynamical System -- 3.3 A Statistical Energy Conservation Principle for Turbulent Dynamical Systems -- 3.3.1 Details About Deterministic Triad Energy Conservation Symmetry -- 3.3.2 A Generalized Statistical Energy Identity -- 3.3.3 Enhanced Dissipation of the Statistical Mean Energy, the Statistical Energy Principle, and È̀ddy Viscosity'' -- 3.3.4 Stochastic Lyapunov Functions for One-Layer Turbulent Geophysical Flows -- 3.4 Geometric Ergodicity for Turbulent Dynamical Systems -- 4 Statistical Prediction and UQ for Turbulent Dynamical Systems -- 4.1 A Brief Introduction -- 4.1.1 Low-Order Truncation Methods for UQ and Their Limitations -- 4.1.2 The Gaussian Closure Method for Statistical Prediction -- 4.1.3 A Fundamental Limitation of the Gaussian Closure Method
  • 4.2 A Mathematical Strategy for Imperfect Model Selection, Calibration, and Accurate Prediction: Blending Information Theory and Statistical Response Theory -- 4.2.1 Imperfect Model Selection, Empirical Information Theory, and Information Barriers -- 4.2.2 Linear Statistical Response and Fluctuation-Dissipation Theorem for Turbulent Dynamical Systems -- 4.2.3 The Calibration and Training Phase Combining Information Theory and Kicked Statistical Response Theory -- 4.2.4 Low-Order Models Illustrating Model Selection, Calibration, and Prediction with UQ -- 4.3 Improving Statistical Prediction and UQ in Complex Turbulent Dynamical Systems by Blending Information Theory and Kicked Statistical Response Theory -- 4.3.1 Models with Consistent Equilibrium Single Point Statistics and Information Barriers -- 4.3.2 Models with Consistent Unperturbed Equilibrium Statistics for Each Mode -- 4.3.3 Calibration and Training Phase -- 4.3.4 Testing Imperfect Model Prediction Skill and UQ with Different Forced Perturbations -- 4.3.5 Reduced-Order Modeling for Complex Turbulent Dynamical Systems -- 5 State Estimation, Data Assimilation, or Filtering for Complex Turbulent Dynamical Systems -- 5.1 Filtering Noisy Lagrangian Tracers for Random Fluid Flows -- 5.2 State Estimation for Nonlinear Turbulent Dynamical Systems Through Hidden Conditional Gaussian Statistics -- 5.2.1 Examples and Applications of Filtering Turbulent Dynamical Systems as Conditional Gaussian Systems -- 5.3 Finite Ensemble Kalman Filters (EnKF): Applied Practice Mathematical Theory, and New Phenomena -- 5.3.1 EnKF and ESRF Formulation -- 5.3.2 Catastrophic Filter Divergence -- 5.3.3 Rigorous Examples of Catastrophic Filter Divergence -- 5.3.4 Rigorous Nonlinear Stability and Geometric Ergodicity for Finite Ensemble Kalman Filters
  • 5.4 Mathematical Strategies and Algorithms for Multi-scale Data Assimilation -- 5.4.1 Conceptual Dynamical Models for Turbulence and Superparameterization -- 5.4.2 Blended Particle Methods with Adaptive Subspaces for Filtering Turbulent Dynamical Systems -- 5.4.3 Extremely Efficient Multi-scale Filtering Algorithms: SPEKF and Dynamic Stochastic Superresolution (DSS) -- References
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{'f': 'http://opac.lib.rpi.edu/record=b4386066'}
Extent
1 online resource (97 pages)
Form of item
online
Isbn
9783319322179
Media category
computer
Media MARC source
rdamedia
Media type code
c
Sound
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Specific material designation
remote

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