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.

The importance of mathematics in the study of problems arising from the real world, and the increasing success with which it has been used to model situations ranging from the purely deterministic to the stochastic, is well established. The purpose of the set of volumes to which the present one belongs is to make available authoritative, up to date, and self-contained accounts of some of the most important and useful of these analytical approaches and techniques. Each volume provides a detailed introduction to a specific subject area of current importance that is summarized below, and then goes beyond this by reviewing recent contributions, and so serving as a valuable reference source. The progress in applicable mathematics has been brought about by the extension and development of many important analytical approaches and techniques, in areas both old and new, frequently aided by the use of computers without which the solution of realistic problems would otherwise have been impossible.

This book provides concise, up-to-date and easy-to-follow information on certain aspects of an ever important research area: multiphase flow in porous media. This flow type is of great significance in many petroleum and environmental engineering problems, such as in secondary and tertiary oil recovery, subsurface remediation and CO2 sequestration. This book contains a collection of selected papers (all refereed) from a number of well-known experts on multiphase flow. The papers describe both recent and state-of-the-art modeling and experimental techniques for study of multiphase flow phenomena in porous media. Specifically, the book analyses three advanced topics: upscaling, pore-scale modeling, and dynamic effects in multiphase flow in porous media.

Althoughtheprinciplesofoperationofhelicalscrewmachines,ascompressors or expanders, have been well known for more than 100 years, it is only during the past 30 years that these machines have become widely used. The main reasons for the long period before they were adopted were their relatively poor e?ciency and the high cost of manufacturing their rotors. Two main developments led to a solution to these di?culties. The ?rst of these was the introduction of the asymmetric rotor pro?le in 1973. This reduced the bl- hole area, which was the main source of internal leakage by approximately 90%, and thereby raised the thermodynamic e?ciency of these machines, to roughly the same level as that of traditional reciprocating compressors. The second was the introduction of precise thread milling machine tools at - proximately the same time. This made it possible to manufacture items of complex shape, such as the rotors, both accurately and cheaply. From then on, as a result of their ever improving e?ciencies, high rel- bility and compact form, screw compressors have taken an increasing share of the compressor market, especially in the ?elds of compressed air production, and refrigeration and air conditioning, and today, a substantial proportion of compressors manufactured for industry are of this type. Despite, the now wide usage of screw compressors and the publication of many scienti?c papers on their development, only a handful of textbooks have been published to date, which give a rigorous exposition of the principles of their operation and none of these are in English.

Flow meters measure the volumetric flow rate in a pipeline. Most meters are based on deriving a signal from the fluid flow and calibrating the signal against the volumetric flow rate. The calibration is done in fully-developed flow, and the same state of flow must exist at the meter’s position when it is in practical use. Because the field of flow metering has been neglected by fluid mechanicists for a long time, this book addresses two major fluid mechanical problems in flow metering: the analysis of signal generation in turbulent pipe flow, which explains the function of the meter beyond a simple calibration, and the possible use of a meter in non-developed flows. These problems are investigated with reference to, and examples from, a variety of meters, e.g. ultrasound cross-correlation meters, vortex meters, and turbine meters. Studying these problems requires consideration of specific phenomena in turbulent non-developed pipe flow, as caused by installations, and finding special solutions with signal processing, both of which are included in the book.

Multi-phase flows are part of our natural environment such as tornadoes, typhoons, air and water pollution and volcanic activities as well as part of industrial technology such as power plants, combustion engines, propulsion systems, or chemical and biological industry. The industrial use of multi-phase systems requires analytical and numerical strategies for predicting their behavior. In its third extended edition this monograph contains theory, methods and practical experience for describing complex transient multi-phase processes in arbitrary geometrical configurations, providing a systematic presentation of the theory and practice of numerical multi-phase fluid dynamics. In the present first volume the fundamentals of multiphase dynamics are provided. This third edition includes various updates, extensions and improvements in all book chapters.

Hydronamics of Explosion presents the research results for the problems of underwater explosions and contains a detailed analysis of the structure and the parameters of the wave fields generated by explosions of cord and spiral charges, a description of the formation mechanisms for a wide range of cumulative flows at underwater explosions near the free surface, and the relevant mathematical models. Shock-wave transformation in bubbly liquids, shock-wave amplification due to collision and focusing, and the formation of bubble detonation waves in reactive bubbly liquids are studied in detail. Particular emphasis is placed on the investigation of wave processes in cavitating liquids, which incorporates the concepts of the strength of real liquids containing natural microinhomogeneities, the relaxation of tensile stress, and the cavitation fracture of a liquid as the inversion of its two-phase state under impulsive (explosive) loading. The problems are classed among essentially nonlinear processes that occur under shock loading of liquids and may be of interest to researchers in physical acoustics, mechanics of multiphase media, shock-wave processes in condensed media, explosive hydroacoustics, and cumulation.