The objective of this book is to contribute to specialized literature with the most significant results obtained by the author in Continuous Mechanics and Astrophysics. The nature of the book is largely determined by the fact that it describes Fluid Dynamics,Magnetohydrodynamics,and Classical Thermodynamics as branches of Lagrange’s Analytical Mechanics; and in that sense, the approach presented in it is markedly different from the treatment given to them in traditional text books. In order to reach that goal, a Hamilton-Type Variational Principle, as the proper mathermatical technique for the theoretical description of the dy- mic state of any fluid is formulated. The scheme is completed proposing a new group of variations regarding the evolution parameter which is time; and with the demonstration of a theorem concerning the invariance of the action integral under continuous and infinitesimal temporary transfor- tions. With all that has been mentioned before and taking into account the methodsof thecalculusof variationsandtheadequateboundaryconditions, a general methodology for the mathematical treatment of fluid flows characteristic of Fluid Dynamics, Magnetohydrodynamics, and also fluids at rest proper of Classical Thermodynamics is presented.

Besides turbulence, there is hardly any other scientific topic which has been considered a prominent scientific challenge for such a long time. The special interest in turbulence is not only based on it being a difficult scientific problem but also on its meaning in the technical world and our daily life. This carefully edited book comprises recent basic research as well as research related to the applications of turbulence. Therefore, both leading engineers and physicists working in the field of turbulence were invited to the iTi Conference on Turbulence held in Bad Zwischenahn, Gemany 21st - 24th of September 2003. Topics discussed include, for example, scaling laws and intermittency, thermal convection, boundary layers at large Reynolds numbers, isotropic turbulence, stochastic processes, passive and active scalars, coherent structures, numerical simulations, and related subjects.

Mathematics is playing an ever more important role in the physical and biol- ical sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and tea- ing, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mat- matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs. Pasadena, California J.E. Marsden Providence, Rhode Island L. Sirovich College Park, Maryland S.S. Antman Contents The starred sections are self-contained and may be omitted at a ?rst reading.

Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.

This book is an introduction to modern numerical methods in engineering. It covers applications in fluid mechanics, structural mechanics, and heat transfer as the most relevant fields for engineering disciplines such as computational engineering, scientific computing, mechanical engineering as well as chemical and civil engineering. The content covers all aspects in the interdisciplinary field which are essential for an ''up-to-date'' engineer.

The second edition (1997) of this text was a completely rewritten version of the original text Basic Coastal Engineering published in 1978. This third edition makes several corrections, improvements and additions to the second edition. Basic Coastal Engineering is an introductory text on wave mechanics and coastal processes along with fundamentals that underline the practice of coastal engineering. This book was written for a senior or first postgraduate course in coastal engineering. It is also suitable for self study by anyone having a basic engineering or physical science background. The level of coverage does not require a math or fluid mechanics background beyond that presented in a typical undergraduate civil or mechanical engineering curriculum. The material p- sented in this text is based on the author’s lecture notes from a one-semester course at Virginia Polytechnic Institute, Texas A&M University, and George Washington University, and a senior elective course at Lehigh University. The text contains examples to demonstrate the various analysis techniques that are presented and each chapter (except the first and last) has a collection of problems for the reader to solve that further demonstrate and expand upon the text material. Chapter 1 briefly describes the coastal environment and introduces the re- tively new field of coastal engineering. Chapter 2 describes the two-dimensional characteristics of surface waves and presents the small-amplitude wave theory to support this description.

In the last few years there has been significant progress in the development of microfluidics and nanofluidics at the application as well as at the fundamental and simulation levels. This book provides a comprehensive summary of these changes describing fluid flow in micro and nano configurations. Where as in their previous book entitled Microflows: Fundamentals and Simulation the authors covered scales from one hundred nanometers to microns (and beyond), in this new book they discuss length scales from angstroms to microns (and beyond). While still maintaining the emphasis on fundamental concepts with a mix of semianalytical, experimental, and numerical results, this book outlines their relevance to modeling and analyzing functional devices.