Fractional Calculus with Applications in Mechanics

Wave Propagation, Impact and Variational Principles

Author: Teodor M. Atanackovic,Stevan Pilipovic,Bogoljub Stankovic,Dusan Zorica

Publisher: John Wiley & Sons

ISBN: 1118909135

Category: Mathematics

Page: 406

View: 5456

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.

Variational and Extremum Principles in Macroscopic Systems

Author: Stanislaw Sieniutycz,Henrik Farkas

Publisher: Elsevier

ISBN: 9780080456140

Category: Science

Page: 810

View: 3402

Recent years have seen a growing trend to derive models of macroscopic phenomena encountered in the fields of engineering, physics, chemistry, ecology, self-organisation theory and econophysics from various variational or extremum principles. Through the link between the integral extremum of a functional and the local extremum of a function (explicit, for example, in the Pontryagin’s maximum principle variational and extremum principles are mutually related. Thus it makes sense to consider them within a common context. The main goal of Variational and Extremum Principles in Macroscopic Systems is to collect various mathematical formulations and examples of physical reasoning that involve both basic theoretical aspects and applications of variational and extremum approaches to systems of the macroscopic world. The first part of the book is focused on the theory, whereas the second focuses on applications. The unifying variational approach is used to derive the balance or conservation equations, phenomenological equations linking fluxes and forces, equations of change for processes with coupled transfer of energy and substance, and optimal conditions for energy management. A unique multidisciplinary synthesis of variational and extremum principles in theory and application A comprehensive review of current and past achievements in variational formulations for macroscopic processes Uses Lagrangian and Hamiltonian formalisms as a basis for the exposition of novel approaches to transfer and conversion of thermal, solar and chemical energy

The Mathematics of Diffusion

Author: John Crank

Publisher: Oxford University Press

ISBN: 9780198534112

Category: Mathematics

Page: 414

View: 7297

Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.

Fractional Calculus with Applications in Mechanics

Vibrations and Diffusion Processes

Author: Teodor M. Atanackovic,Stevan Pilipovic,Bogoljub Stankovic,Dusan Zorica

Publisher: John Wiley & Sons

ISBN: 1848214170

Category: Mathematics

Page: 336

View: 655

Fractional Calculus with Applications in Mechanics is the first complete compilation of fractional calculus applications to mechanics. It examines classical mechanics topics, such as viscoelasticity, heat conduction, wave propagation, and variational principles of Hamilton?s type. Author Teodor Atanackovic presents students and researchers in physics, mechanical engineering, and civil engineering with a systematic description of mathematical solutions to mechanical problems.

Waves And Rays In Seismology: Answers To Unasked Questions (Second Edition)

Author: Slawinski Michael A

Publisher: World Scientific

ISBN: 9813239891

Category: Science

Page: 576

View: 3148

The author dedicates this book to readers who are concerned with finding out the status of concepts, statements and hypotheses, and with clarifying and rearranging them in a logical order. It is thus not intended to teach tools and techniques of the trade, but to discuss the foundations on which seismology -- and in a larger sense, the theory of wave propagation in solids -- is built. A key question is: why and to what degree can a theory developed for an elastic continuum be used to investigate the propagation of waves in the Earth, which is neither a continuum nor fully elastic. But the scrutiny of the foundations goes much deeper: material symmetry, effective tensors, equivalent media; the influence (or, rather, the lack thereof) of gravitational and thermal effects and the rotation of the Earth, are discussed ab initio. The variational principles of Fermat and Hamilton and their consequences for the propagation of elastic waves, causality, Noether's theorem and its consequences on conservation of energy and conservation of linear momentum are but a few topics that are investigated in the process to establish seismology as a science and to investigate its relation to subjects like realism and empiricism in natural sciences, to the nature of explanations and predictions, and to experimental verification and refutation. In the second edition, new sections, figures, examples, exercises and remarks are added. Most importantly, however, four new appendices of about one-hundred pages are included, which can serve as a self-contained continuum-mechanics course on finite elasticity. Also, they broaden the scope of elasticity theory commonly considered in seismology. Contents: Science of Seismology Seismology and Continuum Mechanics Hookean Solid: Material Symmetry Hookean Solid: Effective Symmetry and Equivalent Medium Body Waves Surface, Guided and Interface Waves Variational Principles in Seismology Gravitational and Thermal Effects in Seismology Seismology as Science Appendices: On Strains On Stresses On Thermoelasticity On Hyperelasticity On Covariant and Contravariant Transformations On Covariant Derivatives List of Symbols Readership: Students, professionals, researchers, and laypersons interested in seismology. Keywords: Elasticity Theory;Inverse Problems;Seismology;Continuum Mechanics;Mathematical PhysicsReview: "This one-of-a-kind book is refreshing in its presentation of an amazing blend of fundamental scientific and philosophical questions with their practical implications to concrete examples in Seismology. It is refined in its style, in the sophistication of its quotes, in the breadth of its sources and in the many details that reveal a labour of love. As an additional bonus, the book is also extremely useful. It presents the underlying theory of the relevant aspects of Continuum Mechanics in a clear and sufficiently rigorous way, while challenging the reader's intellect at every step of the way ... This inspiring book is highly recommended." Professor Marcelo Epstein University of Calgary, Canada "This book provides an extensive and self-contained treatment of the mathematical theory of wave propagation in elastic continua, with special attention to topics, some of them well advanced, which are most important for their applications in geophysics ... The author's wide culture, clear style and rigorous approach make this book a first foundation stone of a field which should be called Rational Seismology." Professor Maurizio Vianello Politecnico di Milano, Italy 0

Crystals, Defects and Microstructures

Modeling Across Scales

Author: Rob Phillips

Publisher: Cambridge University Press

ISBN: 9780521793575

Category: Mathematics

Page: 780

View: 8428

Examines the advances made in the field in recent years and looks at the various methods now used; ideal for graduate students and researchers.

Advances in Continuum Mechanics and Thermodynamics of Material Behavior

In Recognition of the 60th Birthday of Roger L. Fosdick

Author: Roger Fosdick,Donald E. Carlson

Publisher: Springer Science & Business Media

ISBN: 9780792369714

Category: Mathematics

Page: 436

View: 5406

The papers included in this volume were presented at the Symposium on Advances in the Continuum Mechanics and Thermodynamics of Material Behavior, held as part of the 1999 Joint ASME Applied Mechanics and Materials Summer Conference at Virginia Tech on June 27-30, 1999. The Symposium was held in honor of Professor Roger L. Fosdick on his 60th birthday. The papers are written by prominent researchers in the fields of mechanics, thermodynamics, materials modeling, and applied mathematics. They address open questions and present the latest development in these and related areas. This volume is a valuable reference for researchers and graduate students in universities and research laboratories.

Computer Vision

Algorithms and Applications

Author: Richard Szeliski

Publisher: Springer Science & Business Media

ISBN: 9781848829350

Category: Computers

Page: 812

View: 1220

Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of “recipes,” this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques. Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.

Electromagnetic Seabed Logging

A new tool for geoscientists

Author: Stéphane Sainson

Publisher: Springer

ISBN: 3319453556

Category: Science

Page: 536

View: 6241

Seabed logging (SBL) gathers the electromagnetic methods of marine subsoil exploration and more specifically those dedicated to the exploration of oil and gas at sea. Appeared in 2000, these techniques, with more than 500 industrial jobs, present after 15 years of commercial success a discovery record rate of nearly 90 % and seem now to turn the world in the offshore exploration field. Proposing a serious index of the presence of hydrocarbons , electromagnetic SBL coupled with seismic reflection survey is probably the first reliable method for direct detection of hydrocarbons. Complementing the structural concepts of oil exploration used since the 1920s, the SBL now radically modifies the approach and the philosophies of exploration especially those then including drilling and well logging activities. Electromagnetic Seabed Logging: a new tool for oil and gas prospecting, which original publication in French was in 2012, presents these methods, its principles, advantages, limitations, instruments, modeling and applications. It is also designed to be a tool for a reflection on the use of electromagnetic energy for the exploration in a conductive medium as sea water thus setting the theoretical and practical limits of these investigations for future developments. “/p> This book is intended of course for the geophysicists and the petroleum geologists, but also for the earth scientists, the reservoir engineers and the log analysts

Microcontinuum Field Theories

I. Foundations and Solids

Author: A. Cemal Eringen

Publisher: Springer Science & Business Media

ISBN: 1461205557

Category: Science

Page: 325

View: 7762

Microcontinuum field theories extend classical field theories to microscopic spaces and short time scales. This volume is concerned with the kinematics of microcontinua. It begins with a discussion of strain, stress tensors, balance laws, and constitutive equations, and then discusses applications of the fundamental ideas to the theory of elasticity. The ideas developed here are important in modeling the fluid or elastic properties of porous media, polymers, liquid crystals, slurries, and composite materials.

Nonlocal Diffusion Problems

Author: Fuensanta Andreu-Vaillo

Publisher: American Mathematical Soc.

ISBN: 0821852302

Category: Mathematics

Page: 256

View: 2358

Nonlocal diffusion problems arise in a wide variety of applications, including biology, image processing, particle systems, coagulation models, and mathematical finance. These types of problems are also of great interest for their purely mathematical content. This book presents recent results on nonlocal evolution equations with different boundary conditions, starting with the linear theory and moving to nonlinear cases, including two nonlocal models for the evolution of sandpiles. Both existence and uniqueness of solutions are considered, as well as their asymptotic behaviour. Moreover, the authors present results concerning limits of solutions of the nonlocal equations as a rescaling parameter tends to zero. With these limit procedures the most frequently used diffusion models are recovered: the heat equation, the $p$-Laplacian evolution equation, the porous media equation, the total variation flow, a convection-diffusion equation and the local models for the evolution of sandpiles due to Aronsson-Evans-Wu and Prigozhin. Readers are assumed to be familiar with the basic concepts and techniques of functional analysis and partial differential equations. The text is otherwise self-contained, with the exposition emphasizing an intuitive understanding and results given with full proofs. It is suitable for graduate students or researchers. The authors cover a subject that has received a great deal of attention in recent years. The book is intended as a reference tool for a general audience in analysis and PDEs, including mathematicians, engineers, physicists, biologists, and others interested in nonlocal diffusion problems.

Mathematical Analysis of Physical Problems

Author: Philip Russell Wallace

Publisher: Courier Corporation

ISBN: 0486646769

Category: Science

Page: 616

View: 4529

This mathematical reference for theoretical physics employs common techniques and concepts to link classical and modern physics. It provides the necessary mathematics to solve most of the problems. Topics include the vibrating string, linear vector spaces, the potential equation, problems of diffusion and attenuation, probability and stochastic processes, and much more. 1972 edition.

Theory of Simple Liquids

Author: Jean-Pierre Hansen,I.R. McDonald

Publisher: Elsevier

ISBN: 9780080455075

Category: Science

Page: 428

View: 3707

The third edition of Theory of Simple Liquids is an updated, advanced, but self-contained introduction to the principles of liquid-state theory. It presents the modern, molecular theory of the structural, thermodynamic interfacial and dynamical properties of the liquid phase of materials constituted of atoms, small molecules or ions. This book leans on concepts and methods form classical Statistical Mechanics in which theoretical predictions are systematically compared with experimental data and results from numerical simulations. The overall layout of the book is similar to that of the previous two editions however, there are considerable changes in emphasis and several key additions including: •up-to-date presentation of modern theories of liquid-vapour coexistence and criticality •areas of considerable present and future interest such as super-cooled liquids and the glass transition •the area of liquid metals, which has grown into a mature subject area, now presented as part of the chapter ionic liquids •Provides cutting-edge research in the principles of liquid-state theory •Includes frequent comparisons of theoretical predictions with experimental and simulation data •Suitable for researchers and post-graduates in the field of condensed matter science (Physics, Chemistry, Material Science), biophysics as well as those in the oil industry