Download or read book Non Local Partial Differential Equations for Engineering and Biology written by Nikos I. Kavallaris and published by Springer. This book was released on 2017-11-28 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new developments in non-local mathematical modeling and mathematical analysis on the behavior of solutions with novel technical tools. Theoretical backgrounds in mechanics, thermo-dynamics, game theory, and theoretical biology are examined in details. It starts off with a review and summary of the basic ideas of mathematical modeling frequently used in the sciences and engineering. The authors then employ a number of models in bio-science and material science to demonstrate applications, and provide recent advanced studies, both on deterministic non-local partial differential equations and on some of their stochastic counterparts used in engineering. Mathematical models applied in engineering, chemistry, and biology are subject to conservation laws. For instance, decrease or increase in thermodynamic quantities and non-local partial differential equations, associated with the conserved physical quantities as parameters. These present novel mathematical objects are engaged with rich mathematical structures, in accordance with the interactions between species or individuals, self-organization, pattern formation, hysteresis. These models are based on various laws of physics, such as mechanics of continuum, electro-magnetic theory, and thermodynamics. This is why many areas of mathematics, calculus of variation, dynamical systems, integrable systems, blow-up analysis, and energy methods are indispensable in understanding and analyzing these phenomena. This book aims for researchers and upper grade students in mathematics, engineering, physics, economics, and biology.
Download or read book Superlinear Parabolic Problems written by Prof. Dr. Pavol Quittner and published by Springer. This book was released on 2019-06-13 with total page 738 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. The first two chapters introduce to the field and enable the reader to get acquainted with the main ideas by studying simple model problems, respectively of elliptic and parabolic type. The subsequent three chapters are devoted to problems with more complex structure; namely, elliptic and parabolic systems, equations with gradient depending nonlinearities, and nonlocal equations. They include many developments which reflect several aspects of current research. Although the techniques introduced in the first two chapters provide efficient tools to attack some aspects of these problems, they often display new phenomena and specifically different behaviors, whose study requires new ideas. Many open problems are mentioned and commented. The book is self-contained and up-to-date, it has a high didactic quality. It is devoted to problems that are intensively studied but have not been treated so far in depth in the book literature. The intended audience includes graduate and postgraduate students and researchers working in the field of partial differential equations and applied mathematics. The first edition of this book has become one of the standard references in the field. This second edition provides a revised text and contains a number of updates reflecting significant recent advances that have appeared in this growing field since the first edition.
Download or read book Flow and Transport Properties of Unconventional Reservoirs 2018 written by Jianchao Cai and published by MDPI. This book was released on 2019-07-23 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unconventional reservoirs are usually complex and highly heterogeneous, such as shale, coal, and tight sandstone reservoirs. The strong physical and chemical interactions between fluids and pore surfaces lead to the inapplicability of conventional approaches for characterizing fluid flow in these low-porosity and ultralow-permeability reservoir systems. Therefore, new theories and techniques are urgently needed to characterize petrophysical properties, fluid transport, and their relationships at multiple scales for improving production efficiency from unconventional reservoirs. This book presents fundamental innovations gathered from 21 recent works on novel applications of new techniques and theories in unconventional reservoirs, covering the fields of petrophysical characterization, hydraulic fracturing, fluid transport physics, enhanced oil recovery, and geothermal energy. Clearly, the research covered in this book is helpful to understand and master the latest techniques and theories for unconventional reservoirs, which have important practical significance for the economic and effective development of unconventional oil and gas resources.
Download or read book Statistical Rock Physics written by Gabor Korvin and published by Springer Nature. This book was released on with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Methods in Engineering written by K. Tas and published by Springer Science & Business Media. This book was released on 2007-11-25 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains some of the contributions that have been carefully selected and peer-reviewed, which were presented at the International Symposium MME06 Mathematical Methods in Engineering, held in Cankaya University, Ankara, April 2006. The Symposium provided a setting for discussing recent developments in Fractional Mathematics, Neutrices and Generalized Functions, Boundary Value Problems, Applications of Wavelets, Dynamical Systems and Control Theory.
Download or read book Spaces of Measures and their Applications to Structured Population Models written by Christian Düll and published by Cambridge University Press. This book was released on 2021-10-07 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Structured population models are transport-type equations often applied to describe evolution of heterogeneous populations of biological cells, animals or humans, including phenomena such as crowd dynamics or pedestrian flows. This book introduces the mathematical underpinnings of these applications, providing a comprehensive analytical framework for structured population models in spaces of Radon measures. The unified approach allows for the study of transport processes on structures that are not vector spaces (such as traffic flow on graphs) and enables the analysis of the numerical algorithms used in applications. Presenting a coherent account of over a decade of research in the area, the text includes appendices outlining the necessary background material and discusses current trends in the theory, enabling graduate students to jump quickly into research.
Download or read book Basic Partial Differential Equations written by David. Bleecker and published by CRC Press. This book was released on 2018-01-18 with total page 974 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods of solution for partial differential equations (PDEs) used in mathematics, science, and engineering are clarified in this self-contained source. The reader will learn how to use PDEs to predict system behaviour from an initial state of the system and from external influences, and enhance the success of endeavours involving reasonably smooth, predictable changes of measurable quantities. This text enables the reader to not only find solutions of many PDEs, but also to interpret and use these solutions. It offers 6000 exercises ranging from routine to challenging. The palatable, motivated proofs enhance understanding and retention of the material. Topics not usually found in books at this level include but examined in this text: the application of linear and nonlinear first-order PDEs to the evolution of population densities and to traffic shocks convergence of numerical solutions of PDEs and implementation on a computer convergence of Laplace series on spheres quantum mechanics of the hydrogen atom solving PDEs on manifolds The text requires some knowledge of calculus but none on differential equations or linear algebra.
Download or read book Advanced Applications of Fractional Differential Operators to Science and Technology written by Matouk, Ahmed Ezzat and published by IGI Global. This book was released on 2020-04-24 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional-order calculus dates to the 19th century but has been resurrected as a prevalent research subject due to its provision of more adequate and realistic descriptions of physical aspects within the science and engineering fields. What was once a classical form of mathematics is currently being reintroduced as a new modeling technique that engineers and scientists are finding modern uses for. There is a need for research on all facets of these fractional-order systems and studies of its potential applications. Advanced Applications of Fractional Differential Operators to Science and Technology provides emerging research exploring the theoretical and practical aspects of novel fractional modeling and related dynamical behaviors as well as its applications within the fields of physical sciences and engineering. Featuring coverage on a broad range of topics such as chaotic dynamics, ecological models, and bifurcation control, this book is ideally designed for engineering professionals, mathematicians, physicists, analysts, researchers, educators, and students seeking current research on fractional calculus and other applied mathematical modeling techniques.
Download or read book Numerical Integration of Space Fractional Partial Differential Equations written by Younes Salehi and published by Springer Nature. This book was released on 2022-06-01 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partial differential equations (PDEs) are one of the most used widely forms of mathematics in science and engineering. PDEs can have partial derivatives with respect to (1) an initial value variable, typically time, and (2) boundary value variables, typically spatial variables. Therefore, two fractional PDEs can be considered, (1) fractional in time (TFPDEs), and (2) fractional in space (SFPDEs). The two volumes are directed to the development and use of SFPDEs, with the discussion divided as: Vol 1: Introduction to Algorithms and Computer Coding in R Vol 2: Applications from Classical Integer PDEs. Various definitions of space fractional derivatives have been proposed. We focus on the Caputo derivative, with occasional reference to the Riemann-Liouville derivative. In the second volume, the emphasis is on applications of SFPDEs developed mainly through the extension of classical integer PDEs to SFPDEs. The example applications are: Fractional diffusion equation with Dirichlet, Neumann and Robin boundary conditions Fisher-Kolmogorov SFPDE Burgers SFPDE Fokker-Planck SFPDE Burgers-Huxley SFPDE Fitzhugh-Nagumo SFPDE /div These SFPDEs were selected because they are integer first order in time and integer second order in space. The variation in the spatial derivative from order two (parabolic) to order one (first order hyperbolic) demonstrates the effect of the spatial fractional order with 1 ≤ ≤ 2. All of the example SFPDEs are one dimensional in Cartesian coordinates. Extensions to higher dimensions and other coordinate systems, in principle, follow from the examples in this second volume. The examples start with a statement of the integer PDEs that are then extended to SFPDEs. The format of each chapter is the same as in the first volume. The R routines can be downloaded and executed on a modest computer (R is readily available from the Internet).
Download or read book Advanced Numerical Methods for Differential Equations written by Harendra Singh and published by CRC Press. This book was released on 2021-07-29 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.
Download or read book Topics in Numerical Partial Differential Equations and Scientific Computing written by Susanne C. Brenner and published by Springer. This book was released on 2016-08-26 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical partial differential equations (PDEs) are an important part of numerical simulation, the third component of the modern methodology for science and engineering, besides the traditional theory and experiment. This volume contains papers that originated with the collaborative research of the teams that participated in the IMA Workshop for Women in Applied Mathematics: Numerical Partial Differential Equations and Scientific Computing in August 2014.
Download or read book Mathematics for Life Science and Medicine written by Yasuhiro Takeuchi and published by Springer Science & Business Media. This book was released on 2007-01-25 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this volume is to present and discuss the many rich properties of the dynamical systems that appear in life science and medicine. It provides a fascinating survey of the theory of dynamical systems in biology and medicine. Each chapter will serve to introduce students and scholars to the state-of-the-art in an exciting area, to present new results, and to inspire future contributions to mathematical modeling in life science and medicine.
Download or read book Epithelial Cells Advances in Research and Application 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 832 pages. Available in PDF, EPUB and Kindle. Book excerpt: Epithelial Cells: Advances in Research and Application: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Epithelial Cells. The editors have built Epithelial Cells: Advances in Research and Application: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Epithelial Cells in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Epithelial Cells: Advances in Research and Application: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Download or read book Uncertainty in Biology written by Liesbet Geris and published by Springer. This book was released on 2015-10-26 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational modeling allows to reduce, refine and replace animal experimentation as well as to translate findings obtained in these experiments to the human background. However these biomedical problems are inherently complex with a myriad of influencing factors, which strongly complicates the model building and validation process. This book wants to address four main issues related to the building and validation of computational models of biomedical processes: 1. Modeling establishment under uncertainty 2. Model selection and parameter fitting 3. Sensitivity analysis and model adaptation 4. Model predictions under uncertainty In each of the abovementioned areas, the book discusses a number of key-techniques by means of a general theoretical description followed by one or more practical examples. This book is intended for graduate students and researchers active in the field of computational modeling of biomedical processes who seek to acquaint themselves with the different ways in which to study the parameter space of their model as well as its overall behavior.
Download or read book Variational and Free Boundary Problems written by Avner Friedman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications VARIATIONAL AND FREE BOUNDARY PROBLEMS is based on the proceedings of a workshop which was an integral part of the 1990- 91 IMA program on "Phase Transitions and Free Boundaries. " The aim of the workshop was to highlight new methods, directions and problems in variational and free boundary theory, with a concentration on novel applications of variational methods to applied problems. We thank R. Fosdick, M. E. Gurtin, W. -M. Ni and L. A. Peletier for organizing the year-long program and, especially, J. Sprock for co-organizing the meeting and co-editing these proceedings. We also take this opportunity to thank the National Science Foundation whose financial support made the workshop possible. Avner Friedman Willard Miller, Jr. PREFACE In a free boundary one seeks to find a solution u to a partial differential equation in a domain, a part r of its boundary of which is unknown. Thus both u and r must be determined. In addition to the standard boundary conditions on the un known domain, an additional condition must be prescribed on the free boundary. A classical example is the Stefan problem of melting of ice; here the temperature sat isfies the heat equation in the water region, and yet this region itself (or rather the ice-water interface) is unknown and must be determined together with the tempera ture within the water. Some free boundary problems lend themselves to variational formulation.
Download or read book Partial Differential Equations in Ecology written by Sergei Petrovski and published by MDPI. This book was released on 2021-03-17 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots.
Download or read book Numerical Methods for Fractal Fractional Differential Equations and Engineering written by Muhammad Altaf Khan and published by CRC Press. This book was released on 2023-05-16 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the simulation and modeling of novel chaotic systems within the frame of fractal-fractional operators. The methods used, their convergence, stability, and error analysis are given, and this is the first book to offer mathematical modeling and simulations of chaotic problems with a wide range of fractal-fractional operators, to find solutions. Numerical Methods for Fractal-Fractional Differential Equations and Engineering: Simulations and Modeling provides details for stability, convergence, and analysis along with numerical methods and their solution procedures for fractal-fractional operators. The book offers applications to chaotic problems and simulations using multiple fractal-fractional operators and concentrates on models that display chaos. The book details how these systems can be predictable for a while and then can appear to become random. Practitioners, engineers, researchers, and senior undergraduate and graduate students from mathematics and engineering disciplines will find this book of interest._
