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Author: V.K. Stokes Publisher: Springer Science & Business Media ISBN: 3642823513 Category : Science Languages : en Pages : 220
Book Description
This book provides an introduction to theories of fluids with microstruc ture, a subject that is still evolving, and information on which is mainly available in technical journals. Several approaches to such theories, employ ing different levels of mathematics, are now available. This book presents the subject in a connected manner, using a common notation and a uniform level of mathematics. The only prerequisite for understanding this material is an exposure to fluid mechanics using Cartesian tensors. This introductory book developed from a course of semester-length lec tures that were first given in the Department of Chemical Engineering at the University of Delaware and subsequently were given in the Department of Mechanical Engineering at the Indian Institute of Technology, Kanpur. The encouragement of Professor A. B. Metzner and the warm hospitality of the Department of Chemical Engineering, University of Delaware, where the first set of notes for this book were prepared (1970-71), are acknowledged with deep appreciation. Two friends and colleagues, Dr. Raminder Singh and Dr. Thomas F. Balsa, made helpful suggestions for the improvement of this manuscript. The financial support provided by the Education Development Centre of the Indian Institute of Technology, Kanpur, for the preparation of the manuscript is gratefully acknowledged.
Author: V.K. Stokes Publisher: Springer Science & Business Media ISBN: 3642823513 Category : Science Languages : en Pages : 220
Book Description
This book provides an introduction to theories of fluids with microstruc ture, a subject that is still evolving, and information on which is mainly available in technical journals. Several approaches to such theories, employ ing different levels of mathematics, are now available. This book presents the subject in a connected manner, using a common notation and a uniform level of mathematics. The only prerequisite for understanding this material is an exposure to fluid mechanics using Cartesian tensors. This introductory book developed from a course of semester-length lec tures that were first given in the Department of Chemical Engineering at the University of Delaware and subsequently were given in the Department of Mechanical Engineering at the Indian Institute of Technology, Kanpur. The encouragement of Professor A. B. Metzner and the warm hospitality of the Department of Chemical Engineering, University of Delaware, where the first set of notes for this book were prepared (1970-71), are acknowledged with deep appreciation. Two friends and colleagues, Dr. Raminder Singh and Dr. Thomas F. Balsa, made helpful suggestions for the improvement of this manuscript. The financial support provided by the Education Development Centre of the Indian Institute of Technology, Kanpur, for the preparation of the manuscript is gratefully acknowledged.
Author: Grzegorz Lukaszewicz Publisher: Springer Science & Business Media ISBN: 1461206413 Category : Technology & Engineering Languages : en Pages : 262
Book Description
Micropolar fluids are fluids with microstructure. They belong to a class of fluids with nonsymmetric stress tensor that we shall call polar fluids, and include, as a special case, the well-established Navier-Stokes model of classical fluids that we shall call ordinary fluids. Physically, micropolar fluids may represent fluids consisting of rigid, randomly oriented (or spherical) particles suspended in a viscous medium, where the deformation of fluid particles is ignored. The model of micropolar fluids introduced in [65] by C. A. Eringen is worth studying as a very well balanced one. First, it is a well-founded and significant generalization of the classical Navier-Stokes model, covering, both in theory and applications, many more phenomena than the classical one. Moreover, it is elegant and not too complicated, in other words, man ageable to both mathematicians who study its theory and physicists and engineers who apply it. The main aim of this book is to present the theory of micropolar fluids, in particular its mathematical theory, to a wide range of readers. The book also presents two applications of micropolar fluids, one in the theory of lubrication and the other in the theory of porous media, as well as several exact solutions of particular problems and a numerical method. We took pains to make the presentation both clear and uniform.
Author: L D Landau Publisher: Elsevier ISBN: 1483161048 Category : Technology & Engineering Languages : en Pages : 556
Book Description
Fluid Mechanics, Second Edition deals with fluid mechanics, that is, the theory of the motion of liquids and gases. Topics covered range from ideal fluids and viscous fluids to turbulence, boundary layers, thermal conduction, and diffusion. Surface phenomena, sound, and shock waves are also discussed, along with gas flow, combustion, superfluids, and relativistic fluid dynamics. This book is comprised of 16 chapters and begins with an overview of the fundamental equations of fluid dynamics, including Euler's equation and Bernoulli's equation. The reader is then introduced to the equations of motion of a viscous fluid; energy dissipation in an incompressible fluid; damping of gravity waves; and the mechanism whereby turbulence occurs. The following chapters explore the laminar boundary layer; thermal conduction in fluids; dynamics of diffusion of a mixture of fluids; and the phenomena that occur near the surface separating two continuous media. The energy and momentum of sound waves; the direction of variation of quantities in a shock wave; one- and two-dimensional gas flow; and the intersection of surfaces of discontinuity are also also considered. This monograph will be of interest to theoretical physicists.
Author: Iain W. Stewart Publisher: CRC Press ISBN: 1351989022 Category : Science Languages : en Pages : 377
Book Description
Given the widespread interest in macroscopic phenomena in liquid crystals, stemming from their applications in displays and devices. The need has arisen for a rigorous yet accessible text suitable for graduate students, whatever their scientific background. This book satisfies that need. The approach taken in this text, is to introduce the basic continuum theory for nematic liquid crystals in equilibria, then it proceeds to simple application of this theory- in particular, there is a discussion of electrical and magnetic field effects which give rise to Freedericksz transitions, which are important in devices. This is followed by an account of dynamic theory and elementary viscometry of nemantics Discussions of backflow and flow-induced instabilities are also included. Smetic theory is also briefly introduced and summarised with some examples of equilibrium solutions as well as those with dynamic effects. A number of mathematical techniques, such as Cartesian tensors and some variational calculus, are presented in the appendices.
Author: Jacek Banasiak Publisher: Springer Nature ISBN: 3030460797 Category : Mathematics Languages : en Pages : 446
Book Description
This book features selected and peer-reviewed lectures presented at the 3rd Semigroups of Operators: Theory and Applications Conference, held in Kazimierz Dolny, Poland, in October 2018 to mark the 85th birthday of Jan Kisyński. Held every five years, the conference offers a forum for mathematicians using semigroup theory to discover what is happening outside their particular field of research and helps establish new links between various sub-disciplines of semigroup theory, stochastic processes, differential equations and the applied fields. The book is intended for researchers, postgraduate and senior students working in operator theory, partial differential equations, probability and stochastic processes, analytical methods in biology and other natural sciences, optimisation and optimal control. The theory of semigroups of operators is a well-developed branch of functional analysis. Its foundations were laid at the beginning of the 20th century, while Hille and Yosida’s fundamental generation theorem dates back to the forties. The theory was originally designed as a universal language for partial differential equations and stochastic processes but, at the same time, it started to become an independent branch of operator theory. Today, it still has the same distinctive character: it develops rapidly by posing new ‘internal’ questions and, in answering them, discovering new methods that can be used in applications. On the other hand, it is being influenced by questions from PDE’s and stochastic processes as well as from applied sciences such as mathematical biology and optimal control and, as a result, it continually gathers new momentum. However, many results, both from semigroup theory itself and the applied sciences, are phrased in discipline-specific languages and are hardly known to the broader community.
Author: Vladimir I. Erofeyev Publisher: World Scientific ISBN: 9789812794505 Category : Science Languages : en Pages : 282
Book Description
1. The fundamental hypothesis of microstructured elastic solids. Structural-phenomenological model. 1.1. Mathematical models of solids with microstructure. 1.2. Definition of material constants -- 2. Gradient elasticity media. Dispersion. Dissipation. Non-linearity. 2.1. Dynamic equations. Energy and momentum variation law. 2.2. Dispersion properties of longitudinal and shear waves. Surface Rayleigh waves. 2.3. Dissipative properties. 2.4. Nonlinear plain stationary waves. 2.5. Quasi-plain wave beams. 2.6. Self-modulation of quasi-harmonic shear waves. 2.7. Resonant interaction of quasi-harmonic waves. 2.8. Noise waves -- 3. Gradient elasticity media. Damaged medium. Magnetoelasticity. 3.1. Waves in damaged medium with microstructure. 3.2. Magneto-elastic waves in the medium with microstructure -- 4. Cosserat continuum. 4.1. Basic equations of micropolar elasticity theory. 4.2. Dispersion properties of volume waves. 4.3. Wave reflection from the free interface of micropolar halfspace. Rayleigh surface waves. 4.4. Normal waves in a micropolar layer. 4.5. Nonlinear resonant interaction of longitudinal and rotation waves. 4.6. Waves in Cosserat pseudocontinuum. 4.7. Waves in the Cosserat continuum with symmetric stress tensor -- 5. Waves in two-component mixture of solids. 5.1. Dispersion properties. 5.2. Some nonlinear wave effects -- 6. Waves in micromorphic solids. 6.1. Dynamics equations. 6.2. Different types of volume waves and their dispersion properties. 6.3. Surface shear waves in the gradient-elastic half-space with surface energy -- 7. Elasto-plastic waves in the medium with dislocations. 7.1. Equations of dynamics. 7.2. Dispersion properties. 7.3. Some nonlinear problems. 7.4. Correlation of elasto-plastic continuum and Cosserat continuum. 7.5. Example of research of the influence of dislocations on dispersion and damping of ultrasound in solid body -- 8. Wave problems of micropolar hydrodynamics. 8.1. Rotational waves in micropolar liquids. 8.2. Shear surface wave at the interface of elastic body and micropolar liquid. 8.3. Shear surface wave at the interface between elastic half-space and conducting viscous liquid in a magnetic field.
Author: Gérard A. Maugin Publisher: Springer ISBN: 9811024340 Category : Science Languages : en Pages : 268
Book Description
This dictionary offers clear and reliable explanations of over 100 keywords covering the entire field of non-classical continuum mechanics and generalized mechanics, including the theory of elasticity, heat conduction, thermodynamic and electromagnetic continua, as well as applied mathematics. Every entry includes the historical background and the underlying theory, basic equations and typical applications. The reference list for each entry provides a link to the original articles and the most important in-depth theoretical works. Last but not least, ever y entry is followed by a cross-reference to other related subject entries in the dictionary.
Author: T. D. Papathanasiou Publisher: Woodhead Publishing ISBN: 9781855732544 Category : Computers Languages : en Pages : 384
Book Description
The purpose of aligning short fibers in a fiber-reinforced material is to improve the mechanical properties of the resulting composite. Aligning the fibers, generally in a preferred direction, allows them to contribute as much as possible to reinforcing the material. In some cases, the mechanical properties of these aligned, short-fiber composites can approach those of continuous-fiber composites, with the advantages of lower production costs and greater ease of production. Since its publication, this book has been consistently recognized as one of the most important contributions to this field.
Author: V.K. Stokes
Author: V.K. Stokes
Author: Grzegorz Lukaszewicz
Author: L D Landau
Author: Iain W. Stewart
Author: 
Author: Jacek Banasiak
Author: Vladimir I. Erofeyev
Author: Gérard A. Maugin
Author: T. D. Papathanasiou
Author: