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Fractals And Fractional Calculus In Continuum Mechanics
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Book Synopsis Fractals and Fractional Calculus in Continuum Mechanics by : Alberto Carpinteri
Download or read book Fractals and Fractional Calculus in Continuum Mechanics written by Alberto Carpinteri and published by Springer. This book was released on 2014-05-04 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is characterized by the illustration of cases of fractal, self-similar and multi-scale structures taken from the mechanics of solid and porous materials, which have a technical interest. In addition, an accessible and self-consistent treatment of the mathematical technique of fractional calculus is provided, avoiding useless complications.
Book Synopsis Advances in Fractional Calculus by : J. Sabatier
Download or read book Advances in Fractional Calculus written by J. Sabatier and published by Springer Science & Business Media. This book was released on 2007-07-28 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Applications in Physics by : Vasily E. Tarasov
Download or read book Applications in Physics written by Vasily E. Tarasov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This fourth volume collects authoritative chapters covering several applications of fractional calculus in physics, including classical and continuum mechanics.
Book Synopsis Fractional Dynamics by : Joseph Klafter
Download or read book Fractional Dynamics written by Joseph Klafter and published by World Scientific. This book was released on 2012 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides the latest developments in the field of fractional dynamics, which covers fractional (anomalous) transport phenomena, fractional statistical mechanics, fractional quantum mechanics and fractional quantum field theory. The contributors are selected based on their active and important contributions to their respective topics. This volume is the first of its kind that covers such a comprehensive range of topics in fractional dynamics. It will point out to advanced undergraduate and graduate students, and young researchers the possible directions of research in this subject. In addition to those who intend to work in this field and those already in the field, this volume will also be useful for researchers not directly involved in the field, but want to know the current status and trends of development in this subject. This latter group includes theoretical chemists, mathematical biologists and engineers.
Book Synopsis Physics of Fractal Operators by : Bruce West
Download or read book Physics of Fractal Operators written by Bruce West and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text describes the statistcal behavior of complex systems and shows how the fractional calculus can be used to model the behavior. The discussion emphasizes physical phenomena whose evolution is best described using the fractional calculus, such as systems with long-range spatial interactions or long-time memory. The book gives general strategies for understanding wave propagation through random media, the nonlinear response of complex materials, and the fluctuations of heat transport in heterogeneous materials.
Book Synopsis Fractional Dynamics by : Vasily E. Tarasov
Download or read book Fractional Dynamics written by Vasily E. Tarasov and published by Springer Science & Business Media. This book was released on 2011-01-04 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the needs of scientists and graduate students in physics, mechanics and applied mathematics who are interested in electrodynamics, statistical and condensed matter physics, quantum dynamics, complex media theories and kinetics, discrete maps and lattice models, and nonlinear dynamics and chaos. Dr. Vasily E. Tarasov is a Senior Research Associate at Nuclear Physics Institute of Moscow State University and an Associate Professor at Applied Mathematics and Physics Department of Moscow Aviation Institute.
Book Synopsis Multiscale Modeling in Solid Mechanics by : Ugo Galvanetto
Download or read book Multiscale Modeling in Solid Mechanics written by Ugo Galvanetto and published by Imperial College Press. This book was released on 2010 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique volume presents the state of the art in the field of multiscale modeling in solid mechanics, with particular emphasis on computational approaches. For the first time, contributions from both leading experts in the field and younger promising researchers are combined to give a comprehensive description of the recently proposed techniques and the engineering problems tackled using these techniques. The book begins with a detailed introduction to the theories on which different multiscale approaches are based, with regards to linear Homogenisation as well as various nonlinear approaches. It then presents advanced applications of multiscale approaches applied to nonlinear mechanical problems. Finally, the novel topic of materials with self-similar structure is discussed. Sample Chapter(s). Chapter 1: Computational Homogenisation for Non-Linear Heterogeneous Solids (808 KB). Contents: Computational Homogenisation for Non-Linear Heterogeneous Solids (V G Kouznetsova et al.); Two-Scale Asymptotic Homogenisation-Based Finite Element Analysis of Composite Materials (Q-Z Xiao & B L Karihaloo); Multi-Scale Boundary Element Modelling of Material Degradation and Fracture (G K Sfantos & M H Aliabadi); Non-Uniform Transformation Field Analysis: A Reduced Model for Multiscale Non-Linear Problems in Solid Mechanics (J-C Michel & P Suquet); Multiscale Approach for the Thermomechanical Analysis of Hierarchical Structures (M J Lefik et al.); Recent Advances in Masonry Modelling: Micro-Modelling and Homogenisation (P B Louren o); Mechanics of Materials with Self-Similar Hierarchical Microstructure (R C Picu & M A Soare). Readership: Researchers and academics in the field of heterogeneous materials and mechanical engineering; professionals in aeronautical engineering and materials science.
Book Synopsis Applied and Computational Complex Analysis, Volume 2 by : Peter Henrici
Download or read book Applied and Computational Complex Analysis, Volume 2 written by Peter Henrici and published by Wiley-Interscience. This book was released on 1991-03-21 with total page 682 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained presentation of the major areas of complex analysis that are referred to and used in applied mathematics and mathematical physics. Topics discussed include infinite products, ordinary differential equations and asymptotic methods.
Book Synopsis Functional Fractional Calculus for System Identification and Controls by : Shantanu Das
Download or read book Functional Fractional Calculus for System Identification and Controls written by Shantanu Das and published by Springer Science & Business Media. This book was released on 2007-09-26 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, not only are mathematical abstractions discussed in a lucid manner, but also several practical applications are given particularly for system identification, description and then efficient controls. The reader gets a feeling of the wide applicability of fractional calculus in the field of science and engineering. With this book, a starter can understand the concepts of this emerging field with a minimal effort and basic mathematics.
Book Synopsis Fractional Dynamics by : Carlo Cattani
Download or read book Fractional Dynamics written by Carlo Cattani and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-01-01 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to recent developments in the theory of fractional calculus and its applications. Particular attention is paid to the applicability of this currently popular research field in various branches of pure and applied mathematics. In particular, the book focuses on the more recent results in mathematical physics, engineering applications, theoretical and applied physics as quantum mechanics, signal analysis, and in those relevant research fields where nonlinear dynamics occurs and several tools of nonlinear analysis are required. Dynamical processes and dynamical systems of fractional order attract researchers from many areas of sciences and technologies, ranging from mathematics and physics to computer science.
Book Synopsis Fractional Calculus: Theory and Applications by : Francesco Mainardi
Download or read book Fractional Calculus: Theory and Applications written by Francesco Mainardi and published by MDPI. This book was released on 2018-09-20 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Fractional Calculus: Theory and Applications" that was published in Mathematics
Book Synopsis Fractional Calculus with Applications in Mechanics by : Teodor M. Atanackovic
Download or read book Fractional Calculus with Applications in Mechanics written by Teodor M. Atanackovic and published by John Wiley & Sons. This book was released on 2014-02-19 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains mathematical preliminaries in which basic definitions of fractional derivatives and spaces are presented. The central part of the book contains various applications in classical mechanics including fields such as: viscoelasticity, heat conduction, wave propagation and variational Hamilton–type principles. Mathematical rigor will be observed in the applications. The authors provide some problems formulated in the classical setting and some in the distributional setting. The solutions to these problems are presented in analytical form and these solutions are then analyzed numerically. Theorems on the existence of solutions will be presented for all examples discussed. In using various constitutive equations the restrictions following from the second law of thermodynamics will be implemented. Finally, the physical implications of obtained solutions will be discussed in detail.
Book Synopsis Kindergarten of Fractional Calculus by : Shantanu Das
Download or read book Kindergarten of Fractional Calculus written by Shantanu Das and published by Cambridge Scholars Publishing. This book was released on 2020-02-18 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a simplified deliberation of fractional calculus, which will appeal not only to beginners, but also to various applied science mathematicians and engineering researchers. The text develops the ideas behind this new field of mathematics, beginning at the most elementary level, before discussing its actual applications in different areas of science and engineering. This book shows that the simple, classical laws based on Newtonian calculus, which work quite well under limiting and idealized conditions, are not of much use in describing the dynamics of actual systems. As such, the application of non-Newtonian, or generalized, calculus in the governing equations, allows the order of differentiation and integration to take on non-integer values.
Book Synopsis Discrete Fractional Calculus by : Piotr Ostalczyk
Download or read book Discrete Fractional Calculus written by Piotr Ostalczyk and published by World Scientific. This book was released on 2015-11-26 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main subject of the monograph is the fractional calculus in the discrete version. The volume is divided into three main parts. Part one contains a theoretical introduction to the classical and fractional-order discrete calculus where the fundamental role is played by the backward difference and sum. In the second part, selected applications of the discrete fractional calculus in the discrete system control theory are presented. In the discrete system identification, analysis and synthesis, one can consider integer or fractional models based on the fractional-order difference equations. The third part of the book is devoted to digital image processing.
Book Synopsis Fractional Calculus And Waves In Linear Viscoelasticity: An Introduction To Mathematical Models (Second Edition) by : Francesco Mainardi
Download or read book Fractional Calculus And Waves In Linear Viscoelasticity: An Introduction To Mathematical Models (Second Edition) written by Francesco Mainardi and published by World Scientific. This book was released on 2022-08-16 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional Calculus and Waves in Linear Viscoelasticity (Second Edition) is a self-contained treatment of the mathematical theory of linear (uni-axial) viscoelasticity (constitutive equation and waves) with particular regard to models based on fractional calculus. It serves as a general introduction to the above-mentioned areas of mathematical modeling. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to delve further into the subject and explore the research literature. In particular the relevant role played by some special functions is pointed out along with their visualization through plots. Graphics are extensively used in the book and a large general bibliography is included at the end.This new edition keeps the structure of the first edition but each chapter has been revised and expanded, and new additions include a novel appendix on complete monotonic and Bernstein functions that are known to play a fundamental role in linear viscoelasticity.This book is suitable for engineers, graduate students and researchers interested in fractional calculus and continuum mechanics.
Book Synopsis Functional Fractional Calculus by : Shantanu Das
Download or read book Functional Fractional Calculus written by Shantanu Das and published by Springer Science & Business Media. This book was released on 2011-06-01 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with ‘ordinary’ differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematical and geometrical explanations, but also several practical applications are given particularly for system identification, description and then efficient controls. The normal physical laws like, transport theory, electrodynamics, equation of motions, elasticity, viscosity, and several others of are based on ‘ordinary’ calculus. In this book these physical laws are generalized in fractional calculus contexts; taking, heterogeneity effect in transport background, the space having traps or islands, irregular distribution of charges, non-ideal spring with mass connected to a pointless-mass ball, material behaving with viscous as well as elastic properties, system relaxation with and without memory, physics of random delay in computer network; and several others; mapping the reality of nature closely. The concept of fractional and complex order differentiation and integration are elaborated mathematically, physically and geometrically with examples. The practical utility of local fractional differentiation for enhancing the character of singularity at phase transition or characterizing the irregularity measure of response function is deliberated. Practical results of viscoelastic experiments, fractional order controls experiments, design of fractional controller and practical circuit synthesis for fractional order elements are elaborated in this book. The book also maps theory of classical integer order differential equations to fractional calculus contexts, and deals in details with conflicting and demanding initialization issues, required in classical techniques. The book presents a modern approach to solve the ‘solvable’ system of fractional and other differential equations, linear, non-linear; without perturbation or transformations, but by applying physical principle of action-and-opposite-reaction, giving ‘approximately exact’ series solutions. Historically, Sir Isaac Newton and Gottfried Wihelm Leibniz independently discovered calculus in the middle of the 17th century. In recognition to this remarkable discovery, J.von Neumann remarked, “...the calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more equivocally than anything else the inception of modern mathematical analysis which is logical development, still constitute the greatest technical advance in exact thinking.” This XXI century has thus started to ‘think-exactly’ for advancement in science & technology by growing application of fractional calculus, and this century has started speaking the language which nature understands the best.
Book Synopsis Fracture and Complexity by : Alberto Carpinteri
Download or read book Fracture and Complexity written by Alberto Carpinteri and published by Springer Nature. This book was released on 2021-06-26 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book explores the two opposite natural trends of composite systems: (i) order and structure emerging from heterogeneity and randomness, and (ii) instability and chaos arising from simple nonlinear rules. Providing insights into the rapidly growing field of complexity sciences, the book focuses on the role of complexity in fracture mechanics. It firstly discusses the occurrence of self-similarity and fractal patterns in deformation, damage, fracture, and fragmentation of heterogeneous materials and the apparent scaling of the nominal mechanical properties of disordered materials, as well as of the time-to-failure after fatigue and creep loading. Then the book addresses criticality in the acoustic emissions from damaged structures and tectonic faults. Further, it examines the snap-back instability in the structural behavior of relatively large composite structures in the framework of catastrophe theory, and lastly describes the transition toward chaos in the dynamics of cracked elements.
