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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: 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: 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: Giacomo Caviglia
Publisher: World Scientific
ISBN: 9789810208042
Category : Science
Languages : en
Pages : 328
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Book Description
The book may be viewed as an introduction to time-harmonic waves in dissipative bodies, notably viscoelastic solids and fluids. The inhomogeneity of the waves, which is due to the fact that planes of constant phase are not parallel to planes of constant amplitude, is shown to be strictly related to the dissipativity of the medium. A preliminary analysis is performed on the propagation of inhomogeneous waves in unbounded media and of reflection and refraction at plane interfaces. Then emphasis is given to those features that are of significance for applications. In essence, they regard surface waves, scattering by (curved) obstacles, wave propagation in layered heterogeneous media, and ray methods. The pertinent mathematical techniques are discussed so as to make the book reasonably self-contained.
Author: Frank Smith
Publisher: World Scientific
ISBN: 1786340283
Category : Mathematics
Languages : en
Pages : 226
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Book Description
This book leads readers from a basic foundation to an advanced-level understanding of fluid and solid mechanics. Perfect for graduate or PhD mathematical-science students looking for help in understanding the fundamentals of the topic, it also explores more specific areas such as multi-deck theory, time-mean turbulent shear flows, non-linear free surface flows, and internal fluid dynamics.Fluid and Solid Mechanics is the second volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Edited by the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.
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: Saverio E. Spagnolie
Publisher: Springer
ISBN: 1493920650
Category : Science
Languages : en
Pages : 449
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Book Description
This book serves as an introduction to the continuum mechanics and mathematical modeling of complex fluids in living systems. The form and function of living systems are intimately tied to the nature of surrounding fluid environments, which commonly exhibit nonlinear and history dependent responses to forces and displacements. With ever-increasing capabilities in the visualization and manipulation of biological systems, research on the fundamental phenomena, models, measurements, and analysis of complex fluids has taken a number of exciting directions. In this book, many of the world’s foremost experts explore key topics such as: Macro- and micro-rheological techniques for measuring the material properties of complex biofluids and the subtleties of data interpretation Experimental observations and rheology of complex biological materials, including mucus, cell membranes, the cytoskeleton, and blood The motility of microorganisms in complex fluids and the dynamics of active suspensions Challenges and solutions in the numerical simulation of biologically relevant complex fluid flows This volume will be accessible to advanced undergraduate and beginning graduate students in engineering, mathematics, biology, and the physical sciences, but will appeal to anyone interested in the intricate and beautiful nature of complex fluids in the context of living systems.
Author: Julian L. Davis
Publisher: Springer Science & Business Media
ISBN: 1461232848
Category : Science
Languages : en
Pages : 303
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Book Description
This is the second work of a set of two volumes on the phenomena of wave propagation in nonreacting and reacting media. The first, entitled Wave Propagation in Solids and Fluids (published by Springer-Verlag in 1988), deals with wave phenomena in nonreacting media (solids and fluids). This book is concerned with wave propagation in reacting media-specifically, in electro magnetic materials. Since these volumes were designed to be relatively self contained, we have taken the liberty of adapting some of the pertinent material, especially in the theory of hyperbolic partial differential equations (concerned with electromagnetic wave propagation), variational methods, and Hamilton-Jacobi theory, to the phenomena of electromagnetic waves. The purpose of this volume is similar to that of the first, except that here we are dealing with electromagnetic waves. We attempt to present a clear and systematic account of the mathematical methods of wave phenomena in electromagnetic materials that will be readily accessible to physicists and engineers. The emphasis is on developing the necessary mathematical tech niques, and on showing how these methods of mathematical physics can be effective in unifying the physics of wave propagation in electromagnetic media. Chapter 1 presents the theory of time-varying electromagnetic fields, which involves a discussion of Faraday's laws, Maxwell's equations, and their appli cations to electromagnetic wave propagation under a variety of conditions.
