This book provides a self-contained introduction to cellular automata and lattice Boltzmann techniques. Beginning with a chapter introducing the basic concepts of this developing field, a second chapter describes methods used in cellular automata modeling. Following chapters discuss the statistical mechanics of lattice gases, diffusion phenomena, reaction-diffusion processes and non-equilibrium phase transitions. A final chapter looks at other models and applications, such as wave propagation and multiparticle fluids. With a pedagogic approach, the volume focuses on the use of cellular automata in the framework of equilibrium and non-equilibrium statistical physics. It also emphasises application-oriented problems such as fluid dynamics and pattern formation. The book contains many examples and problems. A glossary and a detailed bibliography are also included. This will be a valuable book for graduate students and researchers working in statistical physics, solid state physics, chemic
The instability of fluid flows is a key topic in classical fluid mechanics because it has huge repercussions for applied disciplines such as chemical engineering, hydraulics, aeronautics, and geophysics. This modern introduction is written for any student, researcher, or practitioner working in the area, for whom an understanding of hydrodynamic instabilities is essential. Based on a decade's experience of teaching postgraduate students in fluid dynamics, this book brings the subject to life by emphasizing the physical mechanisms involved. The theory of dynamical systems provides the basic structure of the exposition, together with asymptotic methods. Wherever possible, Charru discusses the phenomena in terms of characteristic scales and dimensional analysis. The book includes numerous experimental studies, with references to videos and multimedia material, as well as over 150 exercises which introduce the reader to new problems.
Presenting a rigorous treatment of the physical and mechanical basis for the modelling of sedimentary basins, this book supplies geoscientists with practical tools for creating their own models. It begins with a thorough grounding in properties of porous media, linear elasticity, continuum mechanics and rock compressibility. Chapters on heat flow, subsidence, rheology, flexure and gravity consider sedimentary basins in the context of the Earth's lithosphere, and the book concludes with coverage of pore space cementation, compaction and fluid flow. The volume introduces basic, state-of-the-art models and demonstrates how to reproduce results using tools like MATLAB® and Octave. Main equations are derived from first principles, and their basic solutions are obtained and then applied. Separate notes sections supply more technical details, and the text is illustrated throughout with real-world examples, applications and test exercises. This is an accessible introduction to quantitative mod
The book is an introduction to the branch of fluid mechanics concerned with the production of sound by hydrodynamic flows. It is designed for a one semester introductory course at advanced undergraduate or graduate level. Great care is taken to explain underlying fluid mechanical and acoustic concepts, and to describe as fully as possible the steps in a complicated derivation. The discussion deals specifically with low Mach number flows, which enables the sound produced by 'vortex-surface' interactions to be analysed using the 'compact Green's function'. This provides a routine procedure for estimating the sound, and an easy identification of those parts of a structure that are likely to be important sources of sound. Each chapter ends with a set of problems, many of which can form the basis of an extended student project. The final chapter contains worked examples that have been investigated by students at Boston University.
This is a reissue of Professor Batchelor's text on the theory of turbulent motion, which was first published by Cambridge Unviersity Press in 1953. It continues to be widely referred to in the professional literature of fluid mechanics, but has not been available for several years. This classic account includes an introduction to the study of homogeneous turbulence, including its mathematic representation and kinematics. Linear problems, such as the randomly-perturbed harmonic oscillator and turbulent flow through a wire gauze, are then treated. The author also presents the general dynamics of decay, universal equilibrium theory, and the decay of energy-containing eddies. There is a renewed interest in turbulent motion, which finds applications in atmospheric physics, fluid mechanics, astrophysics, and planetary science.
This new edition of Professor Sethian's successful text provides an introduction to level set methods and fast marching methods, which are powerful numerical techniques for analyzing and computing interface motion in a host of settings. They rely on a fundamental shift in how one views moving boundaries; rethinking the natural geometric Lagrangian perspective and exchanging it for an Eulerian, initial value partial differential equation perspective. For this edition, the collection of applications provided in the text has been expanded, including examples from physics, chemistry, fluid mechanics, combustion, image processing, material science, fabrication of microelectronic components, computer vision, computer-aided design, and optimal control theory. This book will be a useful resource for mathematicians, applied scientists, practising engineers, computer graphic artists, and anyone interested in the evolution of boundaries and interfaces.
This indispensable guide will equip the reader with a thorough understanding of the field of foaming chemistry. Assuming only basic theoretical background knowledge, the book provides a straightforward introduction to the principles and properties of foams and foaming surfactants. It discusses the key ideas that underpin why foaming occurs, how it can be avoided and how different degrees of antifoaming can be achieved, and covers the latest test methods, including laboratory and industrial developed techniques. Detailing a variety of different kinds of foams, from wet detergents and food foams, to polymeric, material and metal foams, it connects theory to real-world applications and recent developments in foam research. Combining academic and industrial viewpoints, this book is the definitive stand-alone resource for researchers, students and industrialists working on foam technology, colloidal systems in the field of chemical engineering, fluid mechanics, physical chemistry, and appli
This is an introduction to the dynamics of fluids at small scales, the physical and mathematical underpinnings of Brownian motion, and the application of these subjects to the dynamics and flow of complex fluids such as colloidal suspensions and polymer solutions. It brings together continuum mechanics, statistical mechanics, polymer and colloid science, and various branches of applied mathematics, in a self-contained and integrated treatment that provides a foundation for understanding complex fluids, with a strong emphasis on fluid dynamics. Students and researchers will find that this book is extensively cross-referenced to illustrate connections between different aspects of the field. Its focus on fundamental principles and theoretical approaches provides the necessary groundwork for research in the dynamics of flowing complex fluids.
Music, calm speech, whispering leaves fluttering in a breeze are pleasant and desirable sounds. Noise, howling gales, explosions and screeching traffic are less so. A quantitative understanding of the sources of all such sounds can be obtained by careful analysis of the mechanical equations of motion. This is provided by Acoustics and Aerodynamic Sound, which serves as a short, one semester introduction to acoustics and aerodynamic sound at the advanced undergraduate and graduate level. Sound is treated as a branch of fluid mechanics, which is possible because students embarking on an advanced course in acoustics will be familiar with this topic. It is also desirable because an ability to relate acoustic events to hydrodynamic phenomena provides insight into acoustic principles, in particular into the role of vorticity in the mechanics of sound production by vibrating bodies and in the scattering and diffraction of sound.
Providing a fundamental introduction to all aspects of modern plasma chemistry, this book describes mechanisms and kinetics of chemical processes in plasma, plasma statistics, thermodynamics, fluid mechanics and electrodynamics, as well as all major electric discharges applied in plasma chemistry. Fridman considers most of the major applications of plasma chemistry, from electronics to thermal coatings, from treatment of polymers to fuel conversion and hydrogen production and from plasma metallurgy to plasma medicine. It is helpful to engineers, scientists and students interested in plasma physics, plasma chemistry, plasma engineering and combustion, as well as chemical physics, lasers, energy systems and environmental control. The book contains an extensive database on plasma kinetics and thermodynamics and numerical formulas for practical calculations related to specific plasma-chemical processes and applications. Problems and concept questions are provided, helpful in courses relate
Bernard Helffer's graduate-level introduction to the basic tools in spectral analysis is illustrated by numerous examples from the Schrödinger operator theory and various branches of physics: statistical mechanics, superconductivity, fluid mechanics and kinetic theory. The later chapters also introduce non self-adjoint operator theory with an emphasis on the role of the pseudospectra. The author's focus on applications, along with exercises and examples, enables readers to connect theory with practice so that they develop a good understanding of how the abstract spectral theory can be applied. The final chapter provides various problems that have been the subject of active research in recent years and will challenge the reader's understanding of the material covered.
This book presents a coherent introduction to boundary integral, boundary element and singularity methods for steady and unsteady flow at zero Reynolds number. The focus of the discussion is not only on the theoretical foundation, but also on the practical application and computer implementation. The text is supplemented with a number of examples and unsolved problems, many drawn from the field of particulate creeping flows. The material is selected so that the book may serve both as a reference monograph and as a textbook in a graduate course on fluid mechanics or computational fluid mechanics.
Modern cosmology and high energy astrophysics have become interdisciplinary research subjects and new graduate students are now expected to assimilate a broad range of physical concepts. This innovative book provides a clear and pedagogical introduction to research in these areas through a series of problems and answers. The problems are designed to develop each core topic in a simple and coherent way and full solutions are provided to make this book completely self-contained. The first half of the book covers the core subjects of astrophysical processes, gravitational dynamics, radiative processes, fluid mechanics and general relativity. The second half uses these concepts to develop modern cosmology: topics include the Friedmann model and thermal history, dynamics of dark matter and baryons in an expanding universe, physics of high-redshift objects and the very early universe. This unique self-study textbook will be of key interest to graduate students and researchers in cosmology, a
Boundary-layer separation from a rigid body surface is one of the fundamental problems of classical and modern fluid dynamics. The major successes achieved since the late 1960s in the development of the theory of separated flows at high Reynolds numbers are in many ways associated with the use of asymptotic methods. The most fruitful of these has proved to be the method of matched asymptotic expansions, which has been widely used in mechanics and mathematical physics. There have been many papers devoted to different problems in the asymptotic theory of separated flows and we can confidently speak of the appearance of a very productive direction in the development of theoretical hydrodynamics. This book will present this theory in a systematic account. The book will serve as a useful introduction to the theory, and will draw attention to the possibilities that application of the asymptotic approach provides.
In his book, John Green presents a unique personal insight into the fundamentals of fluid mechanics and atmospheric dynamics. Generations of students have benefited from his lectures, and this book, many years in the making, is the result of his wide teaching and research experience. The theory of fluid flow has developed to such an extent that very complex mathematics and models are currently used to describe it, but many of the fundamental results follow from relatively simple considerations: these classic principles are derived here in a novel, distinctive, and at times even idiosyncratic, way. The book is an introduction to fluid mechanics in the atmosphere for students and researchers that are already familiar with the subject, but who wish to extend their knowledge and philosophy beyond the currently popular development of conventional undergraduate instruction.
In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.
The text is a self-contained, comprehensive introduction to the theory of hydrodynamic lattice gases. Lattice-gas cellular automata are discrete models of fluids. Identical particles hop from site to site on a regular lattice, obeying simple conservative scattering rules when they collide. Remarkably, at a scale larger than the lattice spacing, these discrete models simulate the Navier-Stokes equations of fluid mechanics. This book addresses three important aspects of lattice gases. First, it shows how such simple idealised microscopic dynamics give rise to isotropic macroscopic hydrodynamics. Second, it details how the simplicity of the lattice gas provides for equally simple models of fluid phase separation, hydrodynamic interfaces, and multiphase flow. Lastly, it illustrates how lattice-gas models and related lattice-Boltzmann methods have been used to solve problems in applications as diverse as flow through porous media, phase separation, and interface dynamics. Many exercises and
This book presents and analyses vortex methods as a tool for the direct numerical simulation of incompressible viscous flows. Vortex methods have matured, offering an interesting alternative to finite difference and spectral methods for high-resolution numerical solutions of the Navier–Stokes equations. Research in the numerical analysis aspects of vortex methods has provided a solid mathematical background for understanding the accuracy and stability of the method. At the same time vortex methods retain their appealing physical character that was the motivation for their introduction. Scientists working in the areas of numerical analysis and fluid mechanics will benefit from this book, which may serve both communities as both a reference monograph and a textbook for computational fluid dynamics courses.
The phenomena treated in this book all depend on the action of gravity on small density differences in a non-rotating fluid. The author gives a connected account of the various motions which can be driven or influenced by buoyancy forces in a stratified fluid, including internal waves, turbulent shear flows and buoyant convection. This excellent introduction to a rapidly developing field, first published in 1973, can be used as the basis of graduate courses in university departments of meteorology, oceanography and various branches of engineering. This edition is reprinted with corrections, and extra references have been added to allow readers to bring themselves up to date on specific topics. Professor Turner is a physicist with a special interest in laboratory modelling of small-scale geophysical processes. An important feature is the superb illustration of the text with many fine photographs of laboratory experiments and natural phenomena.
Hydrodynamic stability is of fundamental importance in fluid mechanics and is concerned with the problem of transition from laminar to turbulent flow. Drazin and Reid emphasise throughout the ideas involved, the physical mechanisms, the methods used, and the results obtained, and, wherever possible, relate the theory to both experimental and numerical results. A distinctive feature of the book is the large number of problems it contains. These problems not only provide exercises for students but also provide many additional results in a concise form. This new edition of this celebrated introduction differs principally by the inclusion of detailed solutions for those exercises, and by the addition of a Foreword by Professor J. W. Miles.
