Applications of Pad Approximation Theory in Fluid Dynamics PDF Download
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Author: Amilcare Pozzi
Publisher: World Scientific
ISBN: 9810214146
Category : Science
Languages : en
Pages : 257
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Book Description
Although Pad presented his fundamental paper at the end of the last century, the studies on Pad's approximants only became significant in the second part of this century.Pad procedure is related to the theory of continued fractions, and some convergence theorems can be expressed only in terms of continued fractions. Further, Pad approximants have some advantages of practical applicability with respect to the continued-fraction theory. Moreover, as Chisholm notes, a given power series determines a set of approximants which are usually unique, whereas there are many ways of writing an associated continued fraction.The principal advantage of Pad approximants with respect to the generating Taylor series is that they provide an extension beyond the interval of convergence of the series.Pad approximants can be applied in many parts of fluid-dynamics, both in steady and in nonsteady flows, both in incompressible and in compressible regimes.This book is divided into four parts. The first one deals with the properties of the Pad approximants that are useful for the applications and illustrates, with the aid of diagrams and tables, the effectiveness of this technique in the field of applied mathematics. The second part recalls the basic equations of fluid-dynamics (those associated with the names of Navier-Stokes, Euler and Prandtl) and gives a quick derivation of them from the general balance equation. The third shows eight examples of the application of Pad approximants to steady flows, also taking into account the influence of the coupling of heat conduction in the body along which a fluid flows with conduction and convection in the fluid itself. The fourth part considers two examples of the application of Pad approximants to unsteady flows.
Author: Amilcare Pozzi
Publisher: World Scientific
ISBN: 9810214146
Category : Science
Languages : en
Pages : 257
Get Book Here
Book Description
Although Pad presented his fundamental paper at the end of the last century, the studies on Pad's approximants only became significant in the second part of this century.Pad procedure is related to the theory of continued fractions, and some convergence theorems can be expressed only in terms of continued fractions. Further, Pad approximants have some advantages of practical applicability with respect to the continued-fraction theory. Moreover, as Chisholm notes, a given power series determines a set of approximants which are usually unique, whereas there are many ways of writing an associated continued fraction.The principal advantage of Pad approximants with respect to the generating Taylor series is that they provide an extension beyond the interval of convergence of the series.Pad approximants can be applied in many parts of fluid-dynamics, both in steady and in nonsteady flows, both in incompressible and in compressible regimes.This book is divided into four parts. The first one deals with the properties of the Pad approximants that are useful for the applications and illustrates, with the aid of diagrams and tables, the effectiveness of this technique in the field of applied mathematics. The second part recalls the basic equations of fluid-dynamics (those associated with the names of Navier-Stokes, Euler and Prandtl) and gives a quick derivation of them from the general balance equation. The third shows eight examples of the application of Pad approximants to steady flows, also taking into account the influence of the coupling of heat conduction in the body along which a fluid flows with conduction and convection in the fluid itself. The fourth part considers two examples of the application of Pad approximants to unsteady flows.
Author: Tonkid Chantrasmi
Publisher: Stanford University
ISBN:
Category :
Languages : en
Pages : 182
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Book Description
Abstract: The Pade-Legendre (PL) method, a novel approach for uncertainty quantification is introduced. The proposed method uses a rational function expansion and is designed to effectively characterize uncertainties in strongly non-linear or discontinuous systems. The discontinuities can be either in the underlying functions (inherent discontinuities) or from lack of sufficient data resolution (multi-scale discontinuities). In the former case, PL method can produce an accurate response surface without spurious oscillations and does not require prior knowledge of the discontinuities. For the latter type of discontinuities, the PL method can help reduce the number of deterministic simulations required to accurately represent the response surface. If sufficient data resolution is achieved, the PL method degenerates to standard polynomial reconstruction. The present approach is illustrated in a number of applications as an uncertainty propagation technique. Moreover, the method is applied to an inference problem in which a sharp discontinuity in the system input is present. The PL method shows a considerable improvement over the traditional approach when discontinuities are present. In addition, an ongoing effort called the UQ Experiment in which we used the PL method to help design the experimental setup is discussed.
Author: H. Lomax
Publisher: Springer Science & Business Media
ISBN: 3662046547
Category : Science
Languages : en
Pages : 256
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Book Description
The chosen semi-discrete approach of a reduction procedure of partial differential equations to ordinary differential equations and finally to difference equations gives the book its distinctiveness and provides a sound basis for a deep understanding of the fundamental concepts in computational fluid dynamics.
Author: Mani Mehra
Publisher: Springer
ISBN: 9811325952
Category : Mathematics
Languages : en
Pages : 185
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Book Description
This book provides comprehensive information on the conceptual basis of wavelet theory and it applications. Maintaining an essential balance between mathematical rigour and the practical applications of wavelet theory, the book is closely linked to the wavelet MATLAB toolbox, which is accompanied, wherever applicable, by relevant MATLAB codes. The book is divided into four parts, the first of which is devoted to the mathematical foundations. The second part offers a basic introduction to wavelets. The third part discusses wavelet-based numerical methods for differential equations, while the last part highlights applications of wavelets in other fields. The book is ideally suited as a text for undergraduate and graduate students of mathematics and engineering.
Author: James F. Epperson
Publisher: John Wiley & Sons
ISBN: 1119604745
Category : Mathematics
Languages : en
Pages : 672
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Book Description
The new edition of the popular introductory textbook on numerical approximation methods and mathematical analysis, with a unique emphasis on real-world application An Introduction to Numerical Methods and Analysis helps students gain a solid understanding of a wide range of numerical approximation methods for solving problems of mathematical analysis. Designed for entry-level courses on the subject, this popular textbook maximizes teaching flexibility by first covering basic topics before gradually moving to more advanced material in each chapter and section. Throughout the text, students are provided clear and accessible guidance on a wide range of numerical methods and analysis techniques, including root-finding, numerical integration, interpolation, solution of systems of equations, and many others. This fully revised third edition contains new sections on higher-order difference methods, the bisection and inertia method for computing eigenvalues of a symmetric matrix, a completely re-written section on different methods for Poisson equations, and spectral methods for higher-dimensional problems. New problem sets—ranging in difficulty from simple computations to challenging derivations and proofs—are complemented by computer programming exercises, illustrative examples, and sample code. This acclaimed textbook: Explains how to both construct and evaluate approximations for accuracy and performance Covers both elementary concepts and tools and higher-level methods and solutions Features new and updated material reflecting new trends and applications in the field Contains an introduction to key concepts, a calculus review, an updated primer on computer arithmetic, a brief history of scientific computing, a survey of computer languages and software, and a revised literature review Includes an appendix of proofs of selected theorems and a companion website with additional exercises, application models, and supplemental resources An Introduction to Numerical Methods and Analysis, Third Edition is the perfect textbook for upper-level undergraduate students in mathematics, science, and engineering courses, as well as for courses in the social sciences, medicine, and business with numerical methods and analysis components.
Author: Bernard J. Hamrock
Publisher: CRC Press
ISBN: 1135537755
Category : Technology & Engineering
Languages : en
Pages : 747
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Book Description
Specifically focusing on fluid film, hydrodynamic, and elastohydrodynamic lubrication, this edition studies the most important principles of fluid film lubrication for the correct design of bearings, gears, and rolling operations, and for the prevention of friction and wear in engineering designs. It explains various theories, procedures, and equations for improved solutions to machining challenges. Providing more than 1120 display equations and an introductory section in each chapter, Fundamentals of Fluid Film Lubrication, Second Edition facilitates the analysis of any machine element that uses fluid film lubrication and strengthens understanding of critical design concepts.
Author:
Publisher:
ISBN:
Category : American newspapers
Languages : en
Pages : 1530
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Book Description
Identifies specific print and broadcast sources of news and advertising for trade, business, labor, and professionals. Arrangement is geographic with a thumbnail description of each local market. Indexes are classified (by format and subject matter) and alphabetical (by name and keyword).
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 836
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Book Description
Author: Abdul-Majid Wazwaz
Publisher: Springer Science & Business Media
ISBN: 364200251X
Category : Mathematics
Languages : en
Pages : 746
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Book Description
"Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II will be most useful for graduate students and researchers in mathematics, engineering, and other related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University, Chicago, Illinois, USA.
Author: Jan Awrejcewicz
Publisher: Springer
ISBN: 3319966014
Category : Mathematics
Languages : en
Pages : 507
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Book Description
The book is intended for all those who are interested in application problems related to dynamical systems. It provides an overview of recent findings on dynamical systems in the broadest sense. Divided into 46 contributed chapters, it addresses a diverse range of problems. The issues discussed include: Finite Element Analysis of optomechatronic choppers with rotational shafts; computational based constrained dynamics generation for a model of a crane with compliant support; model of a kinetic energy recuperation system for city buses; energy accumulation in mechanical resonance; hysteretic properties of shell dampers; modeling a water hammer with quasi-steady and unsteady friction in viscoelastic conduits; application of time-frequency methods for the assessment of gas metal arc welding conditions; non-linear modeling of the human body’s dynamic load; experimental evaluation of mathematical and artificial neural network modeling for energy storage systems; interaction of bridge cables and wake in vortex-induced vibrations; and the Sommerfeld effect in a single DOF spring-mass-damper system with non-ideal excitation.
