Introduction to turbulent dynamical systems in complex systems. (2016)

• Record Type: Book
• Further Information: Note: Andrew J. Majda.
• Authors: Majda, Andrew, 1949-
• Contents: Preface; Acknowledgements; Contents; 1 Introduction; 1.1 Turbulent Dynamical Systems for Complex Systems: #x83;; 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 Systems3.1 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 Symmetry3.3.2 A Generalized Statistical Energy Identity; 3.3.3 Enhanced Dissipation of the Statistical Mean Energy, the Statistical Energy Principle, and ``Eddy 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 Method4.2 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 UQ4.3 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.
• Publisher Details: Switzerland : Springer
• Publication Date: 2016
• Extent: 1 online resource (xi, 91 pages), color illustrations
• Subjects: 532/.0527; 510; Mathematics; Turbulence -- Mathematical models; TECHNOLOGY & ENGINEERING -- Hydraulics; Turbulence -- Mathematical models; Mathematics -- Mathematical Analysis; Science -- Geophysics; Science -- Mechanics -- Dynamics -- Fluid Dynamics; Nonlinear science; Geophysics; Fluid mechanics; Differentiable dynamical systems; Physical geography; Mathematics -- Applied; Applied mathematics; Electronic books
• Languages: English
• ISBNs: 9783319322179; 3319322176
• Related ISBNs: 9783319322155; 331932215X
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (SpringerLink, viewed September 26, 2016).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.