Two-fluid dynamics is a challenging subject rich in physics and prac tical applications. Many of the most interesting problems are tied to the loss of stability which is realized in preferential positioning and shaping of the interface, so that interfacial stability is a major player in this drama. Typically, solutions of equations governing the dynamics of two fluids are not uniquely determined by the boundary data and different configurations of flow are compatible with the same data. This is one reason why stability studies are important; we need to know which of the possible solutions are stable to predict what might be observed. When we started our studies in the early 1980's, it was not at all evident that stability theory could actu ally work in the hostile environment of pervasive nonuniqueness. We were pleasantly surprised, even astounded, by the extent to which it does work. There are many simple solutions, called basic flows, which are never stable, but we may always compute growth rates and determine the wavelength and frequency of the unstable mode which grows the fastest. This proce dure appears to work well even in deeply nonlinear regimes where linear theory is not strictly valid, just as Lord Rayleigh showed long ago in his calculation of the size of drops resulting from capillary-induced pinch-off of an inviscid jet.
This book is about two special topics in rheological fluid mechanics: the elasticity of liquids and asymptotic theories of constitutive models. The major emphasis of the book is on the mathematical and physical consequences of the elasticity of liquids; seventeen of twenty chapters are devoted to this. Constitutive models which are instantaneously elastic can lead to some hyperbolicity in the dynamics of flow, waves of vorticity into rest (known as shear waves), to shock waves of vorticity or velocity, to steady flows of transonic type or to short wave instabilities which lead to ill-posed problems. Other kinds of models, with small Newtonian viscosities, give rise to perturbed instantaneous elasticity, associated with smoothing of discontinuities as in gas dynamics. There is no doubt that liquids will respond like elastic solids to impulses which are very rapid compared to the time it takes for the molecular order associated with short range forces in the liquid, to relax. After this, all liquids look viscous with signals propagating by diffusion rather than by waves. For small molecules this time of relaxation is estimated as lQ-13 to 10-10 seconds depending on the fluids. Waves associated with such liquids move with speeds of 1 QS cm/s, or even faster. For engineering applications the instantaneous elasticity of these fluids is of little interest; the practical dynamics is governed by diffusion, ·say, by the Navier-Stokes equations. On the other hand, there are other liquids which are known to have much longer times of relaxation.
This substantially revised second edition teaches the bifurcation of asymptotic solutions to evolution problems governed by nonlinear differential equations. Written not just for mathematicians, it appeals to the widest audience of learners, including engineers, biologists, chemists, physicists and economists. For this reason, it uses only well-known methods of classical analysis at foundation level, while the applications and examples are specially chosen to be as varied as possible.
Introductory Transport Phenomena by R. Byron Bird, Warren E. Stewart, Edwin N. Lightfoot, and Daniel Klingenberg is a new introductory textbook based on the classic Bird, Stewart, Lightfoot text, Transport Phenomena. The authors’ goal in writing this book reflects topics covered in an undergraduate course. Some of the rigorous topics suitable for the advanced students have been retained. The text covers topics such as: the transport of momentum; the transport of energy and the transport of chemical species. The organization of the material is similar to Bird/Stewart/Lightfoot, but presentation has been thoughtfully revised specifically for undergraduate students encountering these concepts for the first time. Devoting more space to mathematical derivations and providing fuller explanations of mathematical developments—including a section of the appendix devoted to mathematical topics—allows students to comprehend transport phenomena concepts at an undergraduate level.
Music and film - In the beginning - Brother, can you spare a dime? - In glorious Technicolour - Little nifties from the fifties - The sun sinks slowly over the west - The stars; Contains short bibliographies on a number of movie starsars___
The NIV Application Commentary helps you communicate and apply biblical text effectively in today's context. To bring the ancient messages of the Bible into today's world, each passage is treated in three sections: Original Meaning. Concise exegesis to help readers understand the original meaning of the biblical text in its historical, literary, and cultural context. Bridging Contexts. A bridge between the world of the Bible and the world of today, built by discerning what is timeless in the timely pages of the Bible. Contemporary Significance. This section identifies comparable situations to those faced in the Bible and explores relevant application of the biblical messages. The author alerts the readers of problems they may encounter when seeking to apply the passage and helps them think through the issues involved. This unique, award-winning commentary is the ideal resource for today's preachers, teachers, and serious students of the Bible, giving them the tools, ideas, and insights they need to communicate God's Word with the same powerful impact it had when it was first written.
We Will Help You Get Your Best Score!With more than 125 years of experience in education, McGraw-Hill Education is the name you trust to deliver results. This MHE guide is the most comprehensive and relevant SAT Subject Test prep tool on the market. This edition provides:•6 full-length practice tests with thorough answer explanations•A comprehensive review of all United States History concepts essential to success on the SAT Subject Test•An extensive overview of the format of the test based on the most recent SAT U.S. History exams•Unique test-taking strategies and tips recommended by teachers to help you raise your score•A customizable study plan to help you maximize the time you have to prepareTOP 30 LISTThe book includes a description of the 30 topics most crucial to review before you take the Subject Test in U.S. HistoryTEST-TAKING STRATEGIESLearn unique tips developed by teachers to help you avoid the test maker’s traps.
Now in its Fifth Edition, Neuropsychological Assessment reviews the major neurobehavioral disorders associated with brain dysfunction and injury. This is the 35th anniversary of the landmark first edition. As with previous editions, this edition provides a comprehensive coverage of the field of adult clinical neuropsychology in a single source. By virtue of the authors' clinical and research specializations, this book provides a broad-based and in-depth coverage of current neuroscience research and clinical neuropsychology practice. While the new edition is updated to include new features and topics, it remains true to the highly-regarded previous editions. Methods for obtaining optimum data are given in the form of hypothesis-testing techniques, clinical tips, and clinical examples. In the seven years since the previous edition, many advancements have been made in techniques for examining brain function and in our knowledge about brain-behavior relationships. For example, a surge of functional imaging data has emerged and new structural imaging techniques have provided exquisite detail about brain structure. For the first time, this edition includes examples of these advancements, many in stunning color. This edition also includes new tools for clinicians such as a neuroimaging primer and a comparison table of the neuropsychological features of progressive dementias. The chapters on assessment procedures include discussion of issues related to test selection and reviews of recently published as well as older test batteries used in general neuropsychological assessment, plus newly developed batteries for specific issues.
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