filtering complex turbulent systems

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Filtering Complex Turbulent Systems

Author : Andrew J. Majda
ISBN : 9781107016668
Genre : Mathematics
File Size : 58. 76 MB
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The authors develop a systematic applied mathematics perspective on the problems associated with filtering complex turbulent systems. The book contains background material from filtering, turbulence theory and numerical analysis, making it suitable for graduate courses as well as for researchers in a range of disciplines where applied mathematics is required.

Introduction To Turbulent Dynamical Systems In Complex Systems

Author : Andrew Majda
ISBN : 9783319322179
Genre : Mathematics
File Size : 88. 33 MB
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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 finite ensemble Kalman filters The 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.

Large Scale And High Performance Computations Of Complex Turbulent Reacting Flows

Author : Asghar Afshari
ISBN : 0542906554
Genre : Fluid dynamics
File Size : 22. 46 MB
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A density-based; multi-block, computational model has been developed for large eddy simulation (LES) of reacting and nonreacting, single- and multi-phase, compressible turbulent flows in complex geometries and generalized coordinate systems. The spatially-filtered form of the compressible continuity, momentum, energy, and scalar equations are solved together with various subgrid turbulence closures. All spatial derivatives are approximated by a high-order compact differencing scheme and time derivatives are modeled via a low-storage, three-stage, third-order, Runge-Kutta method. Both Smagorinsky and algebraic RNG (renormalization group) subgrid scale models are employed. The nonreacting, single-phase large eddy and direct numerical simulations (DNS) results for isotropic turbulence, round/planar jets, and axisymmetric sudden expansion (dump combustor) flows are found to be in good agreement with those obtained via other validated high-order, numerical methods and with the available experimental data. The results obtained for nonreacting single-phase flows are described. A generalized Lagrangian/Eulerian, theoretical/numerical methodology is considered for LES of turbulent reacting flows in complex geometrical configurations via the filtered mass density function (FMDF) for subgrid-scale (SGS) combustion closure. The LES/FMDF method has some advantages over conventional methods. A novel numerical algorithm is developed for solving the Lagrangian equations which is much more efficient than similar unstructured grid system algorithms. The Lagrangian scheme is coupled with my high-order multi-block flow solver. This allows LES/FMDF to be extended to general coordinate systems. The consistency, conver gence, and accuracy of the FMDF and the Monte Carlo solution of its equivalent, stochastic differential equations are assessed for different flows. The consistency be tween Eulerian and Lagrangian fields is established for non-reacting isothermal and non-isothermal flows as well as reacting flows in a dump combustor. The results show good consistency between conventional LES and FMDF method for nonreacting and reacting cases. (Abstract shortened by UMI.)

Ports In A Storm

Author : John D. Donahue
ISBN : 9780815722373
Genre : Technology & Engineering
File Size : 66. 11 MB
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Recounts the efforts of U.S. Coast Guard Commander Suzanne Englebert in the wake of 9/11 to revamp the system for protecting America's ports. Original.

Environmental Transport Processes

Author : Bruce E. Logan
ISBN : 9780470619599
Genre : Science
File Size : 65. 46 MB
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Developed as a reference for transport phenomena courses, this completely revised second edition of Environmental Transport Processes provides a readable and approachable treatment of environmental systems. The text features a unique combination of material from different fields (mass transport, kinetics, wastewater treatment, unit processes) and includes pertinent literature not available in any other texts. Rich with examples and problems to help reinforce students? learning, the updated edition addresses new and emerging topics, such as non-aqueous phase liquids (NAPLs), the subject of aggregates, and biofilm kinetic models merged with mass transport concepts.

Feedback Systems

Author : Karl Johan Aström
ISBN : 9781400828739
Genre : Mathematics
File Size : 50. 4 MB
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This book provides an introduction to the mathematics needed to model, analyze, and design feedback systems. It is an ideal textbook for undergraduate and graduate students, and is indispensable for researchers seeking a self-contained reference on control theory. Unlike most books on the subject, Feedback Systems develops transfer functions through the exponential response of a system, and is accessible across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. They provide exercises at the end of every chapter, and an accompanying electronic solutions manual is available. Feedback Systems is a complete one-volume resource for students and researchers in mathematics, engineering, and the sciences. Covers the mathematics needed to model, analyze, and design feedback systems Serves as an introductory textbook for students and a self-contained resource for researchers Includes exercises at the end of every chapter Features an electronic solutions manual Offers techniques applicable across a range of disciplines

Fundamental Limitations In Filtering And Control

Author : Maria M. Seron
ISBN : 144711244X
Genre : Technology & Engineering
File Size : 46. 61 MB
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This book deals with the issue of fundamental limitations in filtering and control system design. This issue lies at the very heart of feedback theory since it reveals what is achievable, and conversely what is not achievable, in feedback systems. The subject has a rich history beginning with the seminal work of Bode during the 1940's and as subsequently published in his well-known book Feedback Amplifier Design (Van Nostrand, 1945). An interesting fact is that, although Bode's book is now fifty years old, it is still extensively quoted. This is supported by a science citation count which remains comparable with the best contemporary texts on control theory. Interpretations of Bode's results in the context of control system design were provided by Horowitz in the 1960's. For example, it has been shown that, for single-input single-output stable open-loop systems having rela tive degree greater than one, the integral of the logarithmic sensitivity with respect to frequency is zero. This result implies, among other things, that a reduction in sensitivity in one frequency band is necessarily accompa nied by an increase of sensitivity in other frequency bands. Although the original results were restricted to open-loop stable systems, they have been subsequently extended to open-loop unstable systems and systems having nonminimum phase zeros.

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