Download or read book Fractional Calculus for Hydrology Soil Science and Geomechanics written by Ninghu Su and published by CRC Press. This book was released on 2020-11-02 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an unique integrated treatise, on the concepts of fractional calculus as models with applications in hydrology, soil science and geomechanics. The models are primarily fractional partial differential equations (fPDEs), and in limited cases, fractional differential equations (fDEs). It develops and applies relevant fPDEs and fDEs mainly to water flow and solute transport in porous media and overland, and in some cases, to concurrent flow and energy transfer. It is an integrated resource with theory and applications for those interested in hydrology, hydraulics and fluid mechanics. The self-contained book summaries the fundamentals for porous media and essential mathematics with extensive references supporting the development of the model and applications.
Download or read book Fractional Differential Equations written by Angelamaria Cardone and published by Springer Nature. This book was released on 2023-06-16 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The content of the book collects some contributions related to the talks presented during the INdAM Workshop "Fractional Differential Equations: Modelling, Discretization, and Numerical Solvers", held in Rome, Italy, on July 12–14, 2021. All contributions are original and not published elsewhere. The main topic of the book is fractional calculus, a topic that addresses the study and application of integrals and derivatives of noninteger order. These operators, unlike the classic operators of integer order, are nonlocal operators and are better suited to describe phenomena with memory (with respect to time and/or space). Although the basic ideas of fractional calculus go back over three centuries, only in recent decades there has been a rapid increase in interest in this field of research due not only to the increasing use of fractional calculus in applications in biology, physics, engineering, probability, etc., but also thanks to the availability of new and more powerful numerical tools that allow for an efficient solution of problems that until a few years ago appeared unsolvable. The analytical solution of fractional differential equations (FDEs) appears even more difficult than in the integer case. Hence, numerical analysis plays a decisive role since practically every type of application of fractional calculus requires adequate numerical tools. The aim of this book is therefore to collect and spread ideas mainly coming from the two communities of numerical analysts operating in this field - the one working on methods for the solution of differential problems and the one working on the numerical linear algebra side - to share knowledge and create synergies. At the same time, the book intends to realize a direct bridge between researchers working on applications and numerical analysts. Indeed, the book collects papers on applications, numerical methods for differential problems of fractional order, and related aspects in numerical linear algebra. The target audience of the book is scholars interested in recent advancements in fractional calculus.
Download or read book Fractional Operators with Constant and Variable Order with Application to Geo hydrology written by Abdon Atangana and published by Academic Press. This book was released on 2017-09-19 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional Operators with Constant and Variable Order with Application to Geo-hydrology provides a physical review of fractional operators, fractional variable order operators, and uncertain derivatives to groundwater flow and environmental remediation. It presents a formal set of mathematical equations for the description of groundwater flow and pollution problems using the concept of non-integer order derivative. Both advantages and disadvantages of models with fractional operators are discussed. Based on the author’s analyses, the book proposes new techniques for groundwater remediation, including guidelines on how chemical companies can be positioned in any city to avoid groundwater pollution. Proposes new aquifer derivatives for leaky, confined and unconfined formations Presents useful aids for applied scientists and engineers seeking to solve complex problems that cannot be handled using constant fractional order derivatives Provides a real physical interpretation of operators relevant to groundwater flow problems Models both fractional and variable order derivatives, presented together with uncertainties analysis
Download or read book Transmutations Singular and Fractional Differential Equations with Applications to Mathematical Physics written by Elina Shishkina and published by Academic Press. This book was released on 2020-07-24 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics connects difficult problems with similar more simple ones. The book's strategy works for differential and integral equations and systems and for many theoretical and applied problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods. In addition to being exposed to recent advances, readers learn to use transmutation methods not only as practical tools, but also as vehicles that deliver theoretical insights. Presents the universal transmutation method as the most powerful for solving many problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods Combines mathematical rigor with an illuminating exposition full of historical notes and fascinating details Enables researchers, lecturers and students to find material under the single "roof"
Download or read book Advances in Modeling Assessment and Prevention of Geotechnical and Geological Disasters written by Xiaodong Fu and published by Frontiers Media SA. This book was released on 2022-10-19 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Element Techniques in Groundwater Flow Studies written by I. Kazda and published by Elsevier Health Sciences. This book was released on 1990-10-22 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite element method (FEM) is one of those modern numerical methods whose rise and development was incited by the rapid development of computers. This method has found applications in all the technical disciplines as well as in the natural sciences.One of the most effective applications of the finite element method is its use for the solution of groundwater flow problems encountered in the design and maintenance of hydraulic structures and tailing dams, in soil mechanics, hydrology, hydrogeology and engineering geology.The stimuli to write this book came from the results obtained in the solution of practical problems connected both with the construction and maintenance of fill-type dams and tailing dams and the utilization of groundwater in Czechoslovakia, and on the other hand from the experience gained in teaching hydraulic structures theory at the Faculty of Civil Engineering of the Technical University of Prague. All the experience so far obtained shows markedly the advantages of the finite element method and the great possibilities of its further development as well as its considerable demands on the algorithmization, programming and use of computer possibilities. The reader will find an explanation of the fundamentals of the finite element method directed mainly toward isoparametric elements having an exceptional adaptability and numerical reliability. The finite element method application to groundwater flow concerns mainly two-dimensional problems, which occur most frequently in practice. Considerable attention is given to non-linear and non-stationary problems, which are most important in application.A computer program (based on the eight-noded isoparametric elements) is included and fully documented.The book will be useful to civil engineers, hydrogeologists and engineering geologists who need the finite element method as a solution tool for the complex problems encountered in engineering practice.
Download or read book Geoenvironmental Engineering written by Lakshmi Reddi and published by CRC Press. This book was released on 2000-04-18 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applies science and engineering principles to the analysis, design, and implementation of technical schemes to characterize, treat, modify, and reuse/store waste and contaminated media. Includes site remediation.
Download or read book Fractional Thermoelasticity written by Yuriy Povstenko and published by Springer. This book was released on 2015-02-26 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to fractional thermoelasticity, i.e. thermoelasticity based on the heat conduction equation with differential operators of fractional order. Readers will discover how time-fractional differential operators describe memory effects and space-fractional differential operators deal with the long-range interaction. Fractional calculus, generalized Fourier law, axisymmetric and central symmetric problems and many relevant equations are featured in the book. The latest developments in the field are included and the reader is brought up to date with current research. The book contains a large number of figures, to show the characteristic features of temperature and stress distributions and to represent the whole spectrum of order of fractional operators. This work presents a picture of the state-of-the-art of fractional thermoelasticity and is suitable for specialists in applied mathematics, physics, geophysics, elasticity, thermoelasticity and engineering sciences. Corresponding sections of the book may also be used as additional reading material for courses on heat and mass transfer, continuum mechanics, thermal stresses as well as in fractional calculus and its applications for graduate and postgraduate students. Extensive references are included in order to stimulate further studies.
Download or read book Computational Fluid and Solid Mechanics 2003 written by K.J Bathe and published by Elsevier. This book was released on 2003-06-02 with total page 2524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bringing together the world's leading researchers and practitioners of computational mechanics, these new volumes meet and build on the eight key challenges for research and development in computational mechanics. Researchers have recently identified eight critical research tasks facing the field of computational mechanics. These tasks have come about because it appears possible to reach a new level of mathematical modelling and numerical solution that will lead to a much deeper understanding of nature and to great improvements in engineering design. The eight tasks are: The automatic solution of mathematical models Effective numerical schemes for fluid flows The development of an effective mesh-free numerical solution method The development of numerical procedures for multiphysics problems The development of numerical procedures for multiscale problems The modelling of uncertainties The analysis of complete life cycles of systems Education - teaching sound engineering and scientific judgement Readers of Computational Fluid and Solid Mechanics 2003 will be able to apply the combined experience of many of the world's leading researchers to their own research needs. Those in academic environments will gain a better insight into the needs and constraints of the industries they are involved with; those in industry will gain a competitive advantage by gaining insight into the cutting edge research being carried out by colleagues in academia. Features Bridges the gap between academic researchers and practitioners in industry Outlines the eight main challenges facing Research and Design in Computational mechanics and offers new insights into the shifting the research agenda Provides a vision of how strong, basic and exciting education at university can be harmonized with life-long learning to obtain maximum value from the new powerful tools of analysis
Download or read book Numerical Methods and Applications written by Geno Nikolov and published by Springer. This book was released on 2019-01-21 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 9th International Conference on Numerical Methods and Applications, NMA 2018, held in Borovets, Bulgaria, in August 2018. The 56 revised regular papers presented were carefully reviewed and selected from 61 submissions for inclusion in this book. The papers are organized in the following topical sections: numerical search and optimization; problem-driven numerical method: motivation and application, numerical methods for fractional diffusion problems; orthogonal polynomials and numerical quadratures; and Monte Carlo and Quasi-Monte Carlo methods.
Download or read book Subsurface Fluid Flow and Imaging written by Donald Wyman Vasco and published by Cambridge University Press. This book was released on 2016-07-21 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unified framework for subsurface imaging based upon asymptotic and trajectory-based methods, with online software applications.
Download or read book Abel Integral Equations written by Rudolf Gorenflo and published by Springer. This book was released on 2006-11-14 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many fields of application of mathematics, progress is crucially dependent on the good flow of information between (i) theoretical mathematicians looking for applications, (ii) mathematicians working in applications in need of theory, and (iii) scientists and engineers applying mathematical models and methods. The intention of this book is to stimulate this flow of information. In the first three chapters (accessible to third year students of mathematics and physics and to mathematically interested engineers) applications of Abel integral equations are surveyed broadly including determination of potentials, stereology, seismic travel times, spectroscopy, optical fibres. In subsequent chapters (requiring some background in functional analysis) mapping properties of Abel integral operators and their relation to other integral transforms in various function spaces are investi- gated, questions of existence and uniqueness of solutions of linear and nonlinear Abel integral equations are treated, and for equations of the first kind problems of ill-posedness are discussed. Finally, some numerical methods are described. In the theoretical parts, emphasis is put on the aspects relevant to applications.
Download or read book The Cell Method written by Elena Ferretti and published by Momentum Press. This book was released on 2014-02-02 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Cell Method (CM) is a computational tool that maintains critical multidimensional attributes of physical phenomena in analysis. This information is neglected in the differential formulations of the classical approaches of finite element, boundary element, finite volume, and finite difference analysis, often leading to numerical instabilities and spurious results. This book highlights the central theoretical concepts of the CM that preserve a more accurate and precise representation of the geometric and topological features of variables for practical problem solving. Important applications occur in fields such as electromagnetics, electrodynamics, solid mechanics and fluids. CM addresses non-locality in continuum mechanics, an especially important circumstance in modeling heterogeneous materials. Professional engineers and scientists, as well as graduate students, are offered: • A general overview of physics and its mathematical descriptions; • Guidance on how to build direct, discrete formulations; • Coverage of the governing equations of the CM, including nonlocality; • Explanations of the use of Tonti diagrams; and • References for further reading.
Download or read book Fractional Calculus and Its Applications written by B. Ross and published by Springer. This book was released on 2006-11-15 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Handbook of Applied Hydrology Second Edition written by Vijay P. Singh and published by McGraw Hill Professional. This book was released on 2016-03-07 with total page 1808 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fully Updated Hydrology Principles, Methods, and Applications Thoroughly revised for the first time in 50 years, this industry-standard resource features chapter contributions from a “who’s who” of international hydrology experts. Compiled by a colleague of the late Dr. Chow, Chow’s Handbook of Applied Hydrology, Second Edition, covers scientific and engineering fundamentals and presents all-new methods, processes, and technologies. Complete details are provided for the full range of ecosystems and models. Advanced chapters look to the future of hydrology, including climate change impacts, extraterrestrial water, social hydrology, and water security. Chow’s Handbook of Applied Hydrology, Second Edition, covers: · The Fundamentals of Hydrology · Data Collection and Processing · Hydrology Methods · Hydrologic Processes and Modeling · Sediment and Pollutant Transport · Hydrometeorologic and Hydrologic Extremes · Systems Hydrology · Hydrology of Large River and Lake Basins · Applications and Design · The Future of Hydrology
Download or read book Computational Geomechanics written by Andrew H. C. Chan and published by John Wiley & Sons. This book was released on 2022-04-04 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: COMPUTATIONAL GEOMECHANICS The new edition of the first book to cover the computational dynamic aspects of geomechanics, now including more practical applications and up-to-date coverage of current research in the field Advances in computational geomechanics have dramatically improved understanding of the behavior of soils and the ability of engineers to design increasingly sophisticated constructions in the ground. When Professor Olek Zienkiewicz began the application of numerical approaches to solid dynamics at Swansea University, it became evident that realistic prediction of the behavior of soil masses could only be achieved if the total stress approaches were abandoned. Computational Geomechanics introduces the theory and application of Zienkiewicz’s computational approaches that remain the basis for work in the area of saturated and unsaturated soil to this day. Written by past students and colleagues of Professor Zienkiewicz, this extended Second Edition provides formulations for a broader range of problems, including failure load under static loading, saturated and unsaturated consolidation, hydraulic fracturing, and liquefaction of soil under earthquake loading. The internationally-recognized team of authors incorporates current computer technologies and new developments in the field, particularly in the area of partial saturation, as they guide readers on how to properly apply the formulation in their work. This one-of-a-kind volume: Explains the Biot-Zienkiewicz formulation for saturated and unsaturated soil Covers multiple applications to static and dynamic problems for saturated and unsaturated soil in areas such as earthquake engineering and fracturing of soils and rocks Features a completely new chapter on fast catastrophic landslides using depth integrated equations and smoothed particle hydrodynamics with applications Presents the theory of porous media in the saturated and unsaturated states to establish the foundation of the problem of soil mechanics Provides a quantitative description of soil behavior including simple plasticity models, generalized plasticity, and critical state soil mechanics Includes numerous questions, problems, hands-on experiments, applications to other situations, and example code for GeHoMadrid Computational Geomechanics: Theory and Applications, Second Edition is an ideal textbook for specialist and general geotechnical postgraduate courses, and a must-have reference for researchers in geomechanics and geotechnical engineering, for software developers and users of geotechnical finite element software, and for geotechnical analysts and engineers making use of the numerical results obtained from the Biot-Zienkiewicz formulation.
