Author : R. Figueiredo Camargo
Publisher :
Page : 28 pages
File Size : 47,23 MB
Release : 2007
Category : Differential equations, Partial
ISBN :
Author : G. Böhme
Publisher : Elsevier
Page : 364 pages
File Size : 28,45 MB
Release : 2012-12-02
Category : Technology & Engineering
ISBN : 0444597573
This volume is for use in technical universities, and for practising engineers who are involved with flow problems of non-Newtonian fluids. The treatment of the subject is based throughout on continuum mechanics model concepts and methods. Because in Non-Newtonian fluids the material properties operating depend critically on the kinematics of the flow, special attention is paid to the derivation and explanation of the adequate constitutive equations used. The book can be read without reference to other sources. It begins by considering some general principles of continuum mechanics, studies simple motions (steady and unsteady shear flows) and proceeds by degrees to kinematically more complex motions. Problems of various degrees of difficulty at the end of each chapter invite active participation by the reader. Numerous stimulating topics from the literature are considered in the book.
Author : Kai Diethelm
Publisher : Springer
Page : 251 pages
File Size : 40,13 MB
Release : 2010-08-18
Category : Mathematics
ISBN : 3642145744
Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.
Author :
Publisher : Elsevier
Page : 252 pages
File Size : 34,68 MB
Release : 1974-09-05
Category : Mathematics
ISBN : 0080956203
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
Author : A. C. Metaxas
Publisher : IET
Page : 380 pages
File Size : 20,50 MB
Release : 1983
Category : Technology & Engineering
ISBN : 9780906048894
This book offers a broad coverage of the theory and practice of industrial microwave heating. It introduces the physical processes behind dipolar and conductivity loss mechanisms and follows with a thorough presentation of dielectric property data of many industrial materials as a function of the moisture content, temperature and frequency, focussing on the interpretation of such data as regards the suitabiliy for processing these materials with microwave energy. The basic equations which govern the power dissipation, attenuation, phase constant, penetration depth and skin depth are derived from first principles while the transport equations of heat, mass and pressure are qualitatively described, giving particular emphasis to the physical mechanisms behind high frequency drying. The book provides established procedures backed by theoretical formulations for the design of industrial travelling wave and multimode applicators. It also provides extensive coverage of single mode fundamental or higher order resonant cavities and outlines a number of atypical applicator structures. It describes the essential features of processing with microwaves under vacuum and presents a brief introduction to the mechanisms which lead to gas breakdown. It stresses the need for a degree of hybridisation with other electrical or conventional heating systems and discusses a few such schemes. The book outlines a number of systems for limiting leakage from on-line industrial microwave systems and concludes with an extensive discussion of successful industrial applications.
Author : Teodor M. Atanackovic
Publisher : John Wiley & Sons
Page : 437 pages
File Size : 18,58 MB
Release : 2014-02-19
Category : Mathematics
ISBN : 1118909135
The books Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion Processes and Fractional Calculus with Applications in Mechanics: Wave Propagation, Impact and Variational Principles contain various applications of fractional calculus to the fields of classical mechanics. Namely, the books study problems in fields such as viscoelasticity of fractional order, lateral vibrations of a rod of fractional order type, lateral vibrations of a rod positioned on fractional order viscoelastic foundations, diffusion-wave phenomena, heat conduction, wave propagation, forced oscillations of a body attached to a rod, impact and variational principles of a Hamiltonian type. The books will be useful for graduate students in mechanics and applied mathematics, as well as for researchers in these fields. Part 1 of this book presents an introduction to fractional calculus. Chapter 1 briefly gives definitions and notions that are needed later in the book and Chapter 2 presents definitions and some of the properties of fractional integrals and derivatives. Part 2 is the central part of the book. Chapter 3 presents the analysis of waves in fractional viscoelastic materials in infinite and finite spatial domains. In Chapter 4, the problem of oscillations of a translatory moving rigid body, attached to a heavy, or light viscoelastic rod of fractional order type, is studied in detail. In Chapter 5, the authors analyze a specific engineering problem of the impact of a viscoelastic rod against a rigid wall. Finally, in Chapter 6, some results for the optimization of a functional containing fractional derivatives of constant and variable order are presented.
Author : Manuel Duarte Ortigueira
Publisher : Walter de Gruyter GmbH & Co KG
Page : 264 pages
File Size : 30,13 MB
Release : 2020-03-09
Category : Mathematics
ISBN : 3110621320
The book illustrates the theoretical results of fractional derivatives via applications in signals and systems, covering continuous and discrete derivatives, and the corresponding linear systems. Both time and frequency analysis are presented. Some advanced topics are included like derivatives of stochastic processes. It is an essential reference for researchers in mathematics, physics, and engineering.
Author : Vladimir V. Uchaikin
Publisher : Springer Science & Business Media
Page : 400 pages
File Size : 28,21 MB
Release : 2013-07-09
Category : Science
ISBN : 3642339115
The first derivative of a particle coordinate means its velocity, the second means its acceleration, but what does a fractional order derivative mean? Where does it come from, how does it work, where does it lead to? The two-volume book written on high didactic level answers these questions. Fractional Derivatives for Physicists and Engineers— The first volume contains a clear introduction into such a modern branch of analysis as the fractional calculus. The second develops a wide panorama of applications of the fractional calculus to various physical problems. This book recovers new perspectives in front of the reader dealing with turbulence and semiconductors, plasma and thermodynamics, mechanics and quantum optics, nanophysics and astrophysics. The book is addressed to students, engineers and physicists, specialists in theory of probability and statistics, in mathematical modeling and numerical simulations, to everybody who doesn't wish to stay apart from the new mathematical methods becoming more and more popular. Prof. Vladimir V. UCHAIKIN is a known Russian scientist and pedagogue, a Honored Worker of Russian High School, a member of the Russian Academy of Natural Sciences. He is the author of about three hundreds articles and more than a dozen books (mostly in Russian) in Cosmic ray physics, Mathematical physics, Levy stable statistics, Monte Carlo methods with applications to anomalous processes in complex systems of various levels: from quantum dots to the Milky Way galaxy.
Author : J. Sabatier
Publisher : Springer Science & Business Media
Page : 550 pages
File Size : 35,92 MB
Release : 2007-07-28
Category : Technology & Engineering
ISBN : 1402060424
In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation. As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.
Author : Praveen Agarwal
Publisher : CRC Press
Page : 371 pages
File Size : 18,95 MB
Release : 2020-09-08
Category : Mathematics
ISBN : 1000078566
Differential Equations are very important tools in Mathematical Analysis. They are widely found in mathematics itself and in its applications to statistics, computing, electrical circuit analysis, dynamical systems, economics, biology, and so on. Recently there has been an increasing interest in and widely-extended use of differential equations and systems of fractional order (that is, of arbitrary order) as better models of phenomena in various physics, engineering, automatization, biology and biomedicine, chemistry, earth science, economics, nature, and so on. Now, new unified presentation and extensive development of special functions associated with fractional calculus are necessary tools, being related to the theory of differentiation and integration of arbitrary order (i.e., fractional calculus) and to the fractional order (or multi-order) differential and integral equations. This book provides learners with the opportunity to develop an understanding of advancements of special functions and the skills needed to apply advanced mathematical techniques to solve complex differential equations and Partial Differential Equations (PDEs). Subject matters should be strongly related to special functions involving mathematical analysis and its numerous applications. The main objective of this book is to highlight the importance of fundamental results and techniques of the theory of complex analysis for differential equations and PDEs and emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Specific topics include but are not limited to Partial differential equations Least squares on first-order system Sequence and series in functional analysis Special functions related to fractional (non-integer) order control systems and equations Various special functions related to generalized fractional calculus Operational method in fractional calculus Functional analysis and operator theory Mathematical physics Applications of numerical analysis and applied mathematics Computational mathematics Mathematical modeling This book provides the recent developments in special functions and differential equations and publishes high-quality, peer-reviewed book chapters in the area of nonlinear analysis, ordinary differential equations, partial differential equations, and related applications.
