Mathematical Models of Solids and Fluids: a short introduction PDF Download

Author: Pascal Grange
Publisher: Liverpool University Press
ISBN: 1800855575
Category : Science
Languages : en
Pages : 171

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Book Description
This textbook provides an introduction to continuum mechanics, which models the behaviour of elastic solids and viscous fluids. It assumes only a working knowledge of classical mechanics, linear algebra and multivariable calculus. Every chapter contains exercises, with detailed solutions. The book is aimed at undergraduate students from scientific disciplines. Mathematics students will find examples of applications involving techniques from different branches of mathematics, such as geometry and differential equations. Physics students will find a gentle introduction to the notions of stress and material laws. Engineering students will find examples of classic exactly-solvable problems. The emphasis is on the thorough derivation of exact solutions, but estimates of the relevant orders of magnitude are provided.

Author: J. Tinsley Oden
Publisher: John Wiley & Sons
ISBN: 1118105745
Category : Mathematics
Languages : en
Pages : 348

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Book Description
A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equations Electromagnetic Field Theory and Quantum Mechanics contains a brief account of electromagnetic wave theory and Maxwell's equations as well as an introductory account of quantum mechanics with related topics including ab initio methods and Spin and Pauli's principles Statistical Mechanics presents an introduction to statistical mechanics of systems in thermodynamic equilibrium as well as continuum mechanics, quantum mechanics, and molecular dynamics Each part of the book concludes with exercise sets that allow readers to test their understanding of the presented material. Key theorems and fundamental equations are highlighted throughout, and an extensive bibliography outlines resources for further study. Extensively class-tested to ensure an accessible presentation, An Introduction to Mathematical Modeling is an excellent book for courses on introductory mathematical modeling and statistical mechanics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for professionals working in the areas of modeling and simulation, physics, and computational engineering.

Author: Edward A. Bender
Publisher: Courier Corporation
ISBN: 0486137120
Category : Mathematics
Languages : en
Pages : 273

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Book Description
Employing a practical, "learn by doing" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields — including science, engineering, and operations research — to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications.

Author: Thomas Richter
Publisher: Springer
ISBN: 3319639706
Category : Mathematics
Languages : en
Pages : 452

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Book Description
This book starts by introducing the fundamental concepts of mathematical continuum mechanics for fluids and solids and their coupling. Special attention is given to the derivation of variational formulations for the subproblems describing fluid- and solid-mechanics as well as the coupled fluid-structure interaction problem. Two monolithic formulations for fluid-structure interactions are described in detail: the well-established ALE formulation and the modern Fully Eulerian formulation, which can effectively deal with problems featuring large deformation and contact. Further, the book provides details on state-of-the-art discretization schemes for fluid- and solid-mechanics and considers the special needs of coupled problems with interface-tracking and interface-capturing techniques. Lastly, advanced topics like goal-oriented error estimation, multigrid solution and gradient-based optimization schemes are discussed in the context of fluid-structure interaction problems.

Author: Richard Fitzpatrick
Publisher:
ISBN: 9780750315531
Category : SCIENCE
Languages : en
Pages : 0

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Book Description
"Theoretical Fluid Mechanics' has been written to aid physics students who wish to pursue a course of self-study in fluid mechanics. It is a comprehensive, completely self-contained text with equations of fluid mechanics derived from first principles, and any required advanced mathematics is either fully explained in the text, or in an appendix. It is accompanied by about 180 exercises with completely worked out solutions. It also includes extensive sections on the application of fluid mechanics to topics of importance in astrophysics and geophysics. These topics include the equilibrium of rotating, self-gravitating, fluid masses; tidal bores; terrestrial ocean tides; and the Eddington solar model."--Prové de l'editor.

Author: John Crank
Publisher: Oxford University Press
ISBN: 9780198534112
Category : Mathematics
Languages : en
Pages : 428

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Book Description
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.

Author: A. Rushton
Publisher: Springer Science & Business Media
ISBN: 9400950918
Category : Science
Languages : en
Pages : 405

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Book Description
The separation of finely-divided solids from liquids constitutes an important stage in many industrial processes. Separation of mixtures ranging from highly concentrated slurries to slightly turbid liquids must be effected in circumstances where the solids, liquid or both phases may have value. Separations may be achieved by use of a membrane or filter medium which, positioned in the path of a flowing suspension, will allow passage of the fluid whilst retaining solids on the surface or within the medium. Alternatively the two phases may be separated by sedimentation processes involving gravitational or centrifugal force. In either mode, separation difficulties are sometimes experienced with the result that solid-liquid separation is often a bottleneck in commercial plants. Operational difficulties and plant failures are associated with the random nature of the particles being separated; variations in size, shape, states of aggregation, compressibility, etc. , produce a wide range of problems. Plugging of the filter medium or the collapse of the solids under applied stress lead to slow flowrates of liquid. The colloidal nature of some precipitates makes separation by settling virtually impossible without the use of chemical agents to enhance the size of basic units and to reduce repulsive surface forces. Unit operations such as filtration, comminution, etc. , involve a seemingly bewildering array of machines which makes plant selection a difficult step and reflects the uncer tainties attaching to operations involving the solid )hase. Many types of pressure, vacuum and centrifugal filter are available.

Author: Karan S. Surana
Publisher: CRC Press
ISBN: 1498708110
Category : Science
Languages : en
Pages : 760

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Book Description
Explore the Computational Methods and Mathematical Models That Are Possible through Continuum Mechanics FormulationsMathematically demanding, but also rigorous, precise, and written using very clear language, Advanced Mechanics of Continua provides a thorough understanding of continuum mechanics. This book explores the foundation of continuum mecha

Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 934

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Book Description

Author: Jing Tang Xing
Publisher: Academic Press
ISBN: 0128193530
Category : Technology & Engineering
Languages : en
Pages : 682

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Book Description
Fluid-Solid Interaction Dynamics: Theory, Variational Principles, Numerical Methods and Applications gives a comprehensive accounting of fluid-solid interaction dynamics, including theory, numerical methods and their solutions for various FSI problems in engineering. The title provides the fundamental theories, methodologies and results developed in the application of FSI dynamics. Four numerical approaches that can be used with almost all integrated FSI systems in engineering are presented. Methods are linked with examples to illustrate results. In addition, numerical results are compared with available experiments or numerical data in order to demonstrate the accuracy of the approaches and their value to engineering applications. The title gives readers the state-of-the-art in theory, variational principles, numerical modeling and applications for fluid-solid interaction dynamics. Readers will be able to independently formulate models to solve their engineering FSI problems using information from this book. - Presents the state-of-the-art in fluid-solid interaction dynamics, providing theory, method and results - Takes an integrated approach to formulate, model and simulate FSI problems in engineering - Illustrates results with concrete examples - Gives four numerical approaches and related theories that are suitable for almost all integrated FSI systems - Provides the necessary information for bench scientists to independently formulate, model, and solve physical FSI problems in engineering