Build the skills for determining appropriate error limits for quantities that matter with this essential toolkit. Understand how to handle a complete project and how uncertainty enters into various steps. Provides a systematic, worksheet-based process to determine error limits on measured quantities, and all likely sources of uncertainty are explored, measured or estimated. Features instructions on how to carry out error analysis using Excel and MATLAB (R), making previously tedious calculations easy. Whether you are new to the sciences or an experienced engineer, this useful resource provides a practical approach to performing error analysis. Suitable as a text for a junior or senior level laboratory course in aerospace, chemical and mechanical engineering, and for professionals.

Build the skills for determining appropriate error limits for quantities that matter with this essential toolkit. Understand how to handle a complete project and how uncertainty enters into various steps. Provides a systematic, worksheet-based process to determine error limits on measured quantities, and all likely sources of uncertainty are explored, measured or estimated. Features instructions on how to carry out error analysis using Excel and MATLAB (R), making previously tedious calculations easy. Whether you are new to the sciences or an experienced engineer, this useful resource provides a practical approach to performing error analysis. Suitable as a text for a junior or senior level laboratory course in aerospace, chemical and mechanical engineering, and for professionals.

This book presents experimental techniques in the field of aerodynamics, a discipline that is essential in numerous areas, such as the design of aerial and ground vehicles and engines, the production of energy, and understanding the wind resistance of buildings. Aerodynamics is not only concerned with improving the performance and comfort of vehicles, but also with reducing their environmental impact. The book provides updated information on the experimental and technical methods used by aerodynamicists, engineers and researchers. It describes the various types of wind tunnels - from subsonic to hypersonic - as well as the problems posed by their design and operation. The book also focuses on metrology, which has allowed us to gain a detailed understanding of the local properties of flows, and examines current developments toward creating a methodology combining experiments and numerical simulations: the computer-assisted wind tunnel. Lastly, it offers an overview of experimental aerodynamics based on a prospective vision of the discipline, and discusses potential futures challenges. The book can be used as a textbook for graduate courses in aerodynamics, typically offered to students of aerospace and mechanical engineering programs, and as a learning tool for professionals and engineers in the fields of aerodynamics, aeronautics and astronautics automobile.

This will be a substantial revision of a good selling text for upper division/first graduate courses in biomedical transport phenomena, offered in many departments of biomedical and chemical engineering. Each chapter will be updated accordingly, with new problems and examples incorporated where appropriate. A particular emphasis will be on new information related to tissue engineering and organ regeneration. A key new feature will be the inclusion of complete solutions within the body of the text, rather than in a separate solutions manual. Also, Matlab will be incorporated for the first time with this Fourth Edition.

Computational fluid dynamics (CFD), which involves using computers to simulate fluid flow, is emerging as a powerful approach for elucidating the palaeobiology of ancient organisms. Here, Imran A. Rahman describes its applications for studying fossil echinoderms. When properly configured, CFD simulations can be used to test functional hypotheses in extinct species, informing on aspects such as feeding and stability. They also show great promise for addressing ecological questions related to the interaction between organisms and their environment. CFD has the potential to become an important tool in echinoderm palaeobiology over the coming years.

This second edition extends the rigorous, self-contained exposition of the theory for viscoelastic wave propagation in layered media to include head waves and general ray theory. The theory, not published elsewhere, provides solutions for fundamental wave-propagation and ray-theory problems valid for any media with a linear response, elastic or anelastic. It explains measurable variations in wave speed, particle motion, and attenuation of body waves, surface waves, and head waves induced at anelastic material boundaries that do not occur for elastic waves. This book may be used as a textbook for advanced university courses and as a research reference in seismology, exploration geophysics, engineering, solid mechanics, and acoustics. It provides computation steps for ray-tracing computer algorithms to develop a variety of tomography inferred anelastic models, such as those for the Earth's deep interior and petroleum reserves. Numerical results and problem sets emphasize important aspects of the theory for each chapter.

A modern introduction to synchronization phenomena, this text presents recent discoveries and the current state of research in the field, from low-dimensional systems to complex networks. The book describes some of the main mechanisms of collective behaviour in dynamical systems, including simple coupled systems, chaotic systems, and systems of infinite-dimension. After introducing the reader to the basic concepts of nonlinear dynamics, the book explores the main synchronized states of coupled systems and describes the influence of noise and the occurrence of synchronous motion in multistable and spatially-extended systems. Finally, the authors discuss the underlying principles of collective dynamics on complex networks, providing an understanding of how networked systems are able to function as a whole in order to process information, perform coordinated tasks, and respond collectively to external perturbations. The demonstrations, numerous illustrations and application examples will help advanced graduate students and researchers gain an organic and complete understanding of the subject.

"Although there are many texts and monographs on fluid dynamics, I do not know of any which is as comprehensive as the present book. It surveys nearly the entire field of classical fluid dynamics in an advanced, compact, and clear manner, and discusses the various conceptual and analytical models of fluid flow." — Foundations of Physics on the first edition

Theoretical Fluid Dynamics functions equally well as a graduate-level text and a professional reference. Steering a middle course between the empiricism of engineering and the abstractions of pure mathematics, the author focuses on those ideas and formulations that will be of greatest interest to students and researchers in applied mathematics and theoretical physics. Dr. Shivamoggi covers the main branches of fluid dynamics, with particular emphasis on flows of incompressible fluids. Readers well versed in the physical and mathematical prerequisites will find enlightening discussions of many lesser-known areas of study in fluid dynamics.

This thoroughly revised, updated, and expanded Second Edition features coverage of recent developments in stability and turbulence, additional chapter-end exercises, relevant experimental information, and an abundance of new material on a wide range of topics, including:

• Hamiltonian formulation
• Nonlinear water waves and sound waves
• Stability of a fluid layer heated from below
• Equilibrium statistical mechanics of turbulence
• Two-dimensional turbulence

Acoustics of Fluid-Structure Interactions addresses an increasingly important branch of fluid mechanics - the absorption of noise and vibration by fluid flow. This subject, which offers numerous challenges to conventional areas of acoustics, is of growing concern in places where the environment is adversely affected by sound. Howe presents useful background material on fluid mechanics and the elementary concepts of classical acoustics and structural vibrations. Using examples, many of which include complete worked solutions, he vividly illustrates the theoretical concepts involved. He provides the basis for all calculations necessary for the determination of sound generation by aircraft, ships, general ventilation and combustion systems, as well as musical instruments. Both a graduate textbook and a reference for researchers, Acoustics of Fluid-Structure Interactions is an important synthesis of information in this field. It will also aid engineers in the theory and practice of noise control.

"Fundamentals of Interfacial Engineering" provides chemical, electronic, mechanical, and biomedical engineers with a coherent, integrated introduction to the fundamental concepts that relate to interfacial phenomena with applications to different processes and product situations. This book emphasizes the importance of intermolecular forces in holding materials together within a bulk phase or across an interface. It outlines the fundamental intermolecular interactions that occur in all interfacial systems. The work also describes the properties, processing, and behavior of fluid interfacial systems and treats solid surfaces and interfaces.
In addition to being of direct industrial relevance, this book will provide engineering instructors with an excellent starting point for planning curriculum development in this important area.

This book offers a concise and practical survey of the principles governing compressible flows, along with selected applications. It starts with derivation of the time-dependent, three-dimensional equation of compressible potential flows, and a study of weak waves, including evaluation of the sound speed in gases. The following chapter addresses quasi-one-dimensional flows, the study of normal shock waves, and flow in ducts with constant cross section subjected to friction and/or heat transfer. It also investigates the effects of friction and heat transfer in ducts with variable cross section. The chapter ends by pointing to the analogy between one-dimensional compressible flows and open channel hydraulics. Further, the book discusses supersonic flows, including the study of oblique shock waves, and supersonic flows over corners and wedges. It also examines Riemann problems, numerical resolution of the wave equation, and of nonlinear hyperbolic problems, including propagation of strong waves. A subsequent chapter focuses on the small perturbation theory of subsonic, transonic and supersonic flows around slender bodies aligned or almost aligned to the uniform inflow. In particular, it explores subsonic and supersonic flows over a wavy wall. Lastly, an appendix with a short derivation of the Fluid Mechanics basic equations is included. The final chapter addresses the problem of transonic flows where both subsonic and supersonic are present. Lastly, an appendix with a short derivation of the Fluid Mechanics basic equations is included. Illustrated with several practical examples, this book is a valuable tool to understand the most fundamental mathematical principles of compressible flows. Graduate Mathematics, Physics and Engineering students as well as researchers with an interest in the aerospace sciences benefit from this work.

This monograph considers the motion of incompressible fluids described by the Navier-Stokes equations with large inflow and outflow, and proves the existence of global regular solutions without any restrictions on the magnitude of the initial velocity, the external force, or the flux. To accomplish this, some assumptions are necessary: The flux is close to homogeneous, and the initial velocity and the external force do not change too much along the axis of the cylinder. This is achieved by utilizing a sophisticated method of deriving energy type estimates for weak solutions and global estimates for regular solutions-an approach that is wholly unique within the existing literature on the Navier-Stokes equations. To demonstrate these results, three main steps are followed: first, the existence of weak solutions is shown; next, the conditions guaranteeing the regularity of weak solutions are presented; and, lastly, global regular solutions are proven. This volume is ideal for mathematicians whose work involves the Navier-Stokes equations, and, more broadly, researchers studying fluid mechanics.

The book reviews the two features of the variational approach: its use as a universal tool to describe physical phenomena and as a source for qualitative and quantitative methods of studying particular problems.

Berdichevsky's work differs from other books on the subject in focusing mostly on the physical origin of variational principles as well as establishing their interrelations. For example, the Gibbs principles appear as a consequence of the Einstein formula for thermodynamic fluctuations rather than as the first principles of the theory of thermodynamic equilibrium. Mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for the direct study of variational problems. In addition, a thorough account of variational principles discovered in various branches of continuum mechanics is given.

This book, the second volume, describes how the variational approach can be applied to constructing models of continuum media, such as the theory of elastic plates; shells and beams; shallow water theory; heterogeneous mixtures; granular materials; and turbulence. It goes on to apply the variational approach to asymptotical analysis of problems with small parameters, such as the derivation of the theory of elastic plates, shells and beams from three-dimensional elasticity theory; and the basics of homogenization theory. A theory of stochastic variational problems is considered in detail too, along with applications to the homogenization of continua with random microstructures.

This introductory book addresses a broad range of classical Fluid Dynamics topics, interesting applications, and related problems in everyday life. The geophysical and astrophysical applications discussed concern e.g. the shape and internal structure of the Earth and stars, the dynamics of the atmosphere and ocean, hydrodynamic instabilities, and the different kinds of waves that can be found in the atmosphere, ocean and solid Earth. Non-linear waves (solitons) are also mentioned. In turn, the book explores problems from everyday life, including the motion of golf balls, life at low Reynolds numbers, the physics of sailing, and the aerodynamics of airplanes and Grand Prix cars. No book on this topic would be complete without a look at chaos and turbulence; here the problems span from Gaussian plumes to chaotic dynamos, to stochastic climate modeling. Advances in fluid dynamics have produced a wealth of numerical methods and techniques, which are used in many of the applications. Given its structure, the book can be used both for an introductory course to fluid dynamics and as preparation for more advanced problems typical of graduate-level courses.

This book offers an overview of the fundamental dynamical processes, which are necessary to understand astrophysical phenomena, from the viewpoint of hydrodynamics, magnetohydrodynamics, and radiation hydrodynamics. The book consists of three parts: The first discusses the fundamentals of hydrodynamics necessary to understand the dynamics of astrophysical objects such as stars, interstellar gases and accretion disks. The second part reviews the interactions between gases and magnetic fields on fluid motions - the magnetohydrodynamics - highlighting the important role of magnetic fields in dynamical phenomena under astrophysical environments. The third part focuses on radiation hydrodynamics, introducing the hydrodynamic phenomena characterized by the coupling of radiation and gas motions and further on relativistic radiation hydrodynamics. Intended as a pedagogical introduction for advanced undergraduate and graduate students, it also provides comprehensive coverage of the fundamentals of astrophysical fluid dynamics, making it an effective resource not only for graduate courses, but also for beginners wanting to learn about hydrodynamics, magnetohydrodynamics, and radiation hydrodynamics in astrophysics independently.

Special relativity is the basis of many fields in modern physics: particle physics, quantum field theory, high-energy astrophysics, etc. This theory is presented here by adopting a four-dimensional point of view from the start. An outstanding feature of the book is that it doesn't restrict itself to inertial frames but considers accelerated and rotating observers. It is thus possible to treat physical effects such as the Thomas precession or the Sagnac effect in a simple yet precise manner. In the final chapters, more advanced topics like tensorial fields in spacetime, exterior calculus and relativistic hydrodynamics are addressed. In the last, brief chapter the author gives a preview of gravity and shows where it becomes incompatible with Minkowsky spacetime. Well illustrated and enriched by many historical notes, this book also presents many applications of special relativity, ranging from particle physics (accelerators, particle collisions, quark-gluon plasma) to astrophysics (relativistic jets, active galactic nuclei), and including practical applications (Sagnac gyrometers, synchrotron radiation, GPS). In addition, the book provides some mathematical developments, such as the detailed analysis of the Lorentz group and its Lie algebra. The book is suitable for students in the third year of a physics degree or on a masters course, as well as researchers and any reader interested in relativity. Thanks to the geometric approach adopted, this book should also be beneficial for the study of general relativity. "A modern presentation of special relativity must put forward its essential structures, before illustrating them using concrete applications to specific dynamical problems. Such is the challenge (so successfully met!) of the beautiful book by Eric Gourgoulhon." (excerpt from the Foreword by Thibault Damour)

This monograph focuses on the partial regularity theorem, as developed by Caffarelli, Kohn, and Nirenberg (CKN), and offers a proof of the upper bound on the Hausdorff dimension of the singular set of weak solutions of the Navier-Stokes inequality, while also providing a clear and insightful presentation of Scheffer's constructions showing their bound cannot be improved. A short, complete, and self-contained proof of CKN is presented in the second chapter, allowing the remainder of the book to be fully dedicated to a topic of central importance: the sharpness result of Scheffer. Chapters three and four contain a highly readable proof of this result, featuring new improvements as well. Researchers in mathematical fluid mechanics, as well as those working in partial differential equations more generally, will find this monograph invaluable.

This book collects together a unique set of articles dedicated to several fundamental aspects of the Navier-Stokes equations. As is well known, understanding the mathematical properties of these equations, along with their physical interpretation, constitutes one of the most challenging questions of applied mathematics. Indeed, the Navier-Stokes equations feature among the Clay Mathematics Institute's seven Millennium Prize Problems (existence of global in time, regular solutions corresponding to initial data of unrestricted magnitude). The text comprises three extensive contributions covering the following topics: (1) Operator-Valued H -calculus, R-boundedness, Fourier multipliers and maximal Lp-regularity theory for a large, abstract class of quasi-linear evolution problems with applications to Navier-Stokes equations and other fluid model equations; (2) Classical existence, uniqueness and regularity theorems of solutions to the Navier-Stokes initial-value problem, along with space-time partial regularity and investigation of the smoothness of the Lagrangean flow map; and (3) A complete mathematical theory of R-boundedness and maximal regularity with applications to free boundary problems for the Navier-Stokes equations with and without surface tension. Offering a general mathematical framework that could be used to study fluid problems and, more generally, a wide class of abstract evolution equations, this volume is aimed at graduate students and researchers who want to become acquainted with fundamental problems related to the Navier-Stokes equations.

This textbook gives an introduction to fluid dynamics based on flows for which analytical solutions exist, like individual vortices, vortex streets, vortex sheets, accretions disks, wakes, jets, cavities, shallow water waves, bores, tides, linear and non-linear free-surface waves, capillary waves, internal gravity waves and shocks. Advanced mathematical techniques ("calculus") are introduced and applied to obtain these solutions, mostly from complex function theory (Schwarz-Christoffel theorem and Wiener-Hopf technique), exterior calculus, singularity theory, asymptotic analysis, the theory of linear and nonlinear integral equations and the theory of characteristics. Many of the derivations, so far contained only in research journals, are made available here to a wider public.

This book presents a sequential representation of the electrodynamics of conducting media with dispersion. In addition to the general electrodynamic formalism, specific media such as classical nondegenerate plasma, degenerate metal plasma, magnetoactive anisotropic plasma, atomic hydrogen gas, semiconductors, and molecular crystals are considered. The book draws on such classics as Electrodynamics of plasma and plasma-like media (Silin and Rukhadze) and Principles of Plasma Electrodynamics (Alexandrov, Bogdankevich, and Rukhadze), yet its outlook is thoroughly modern-both in content and presentation, including both classical and quantum approaches. It explores such recent topics as surface waves on thin layers of plasma and non-dispersive media, the permittivity of a monatomic gas with spatial dispersion, and current-driven instabilities in plasma, among many others. Each chapter is equipped with a large number of problems with solutions that have academic and practical importance. This book will appeal to graduate students as well as researchers and other professionals due to its straight-forward yet thorough treatment of electrodynamics in conducting dispersive media.

This unique text provides engineering students and practicing professionals with a comprehensive set of practical, hands-on guidelines and dozens of step-by-step examples for performing state-of-the-art, reliable computational fluid dynamics (CFD) and turbulence modeling. Key CFD and turbulence programs are included as well. The text first reviews basic CFD theory, and then details advanced applied theories for estimating turbulence, including new algorithms created by the author. The book gives practical advice on selecting appropriate turbulence models and presents best CFD practices for modeling and generating reliable simulations. The author gathered and developed the book's hundreds of tips, tricks, and examples over three decades of research and development at three national laboratories and at the University of New Mexico-many in print for the first time in this book. The book also places a strong emphasis on recent CFD and turbulence advancements found in the literature over the past five to 10 years. Readers can apply the author's advice and insights whether using commercial or national laboratory software such as ANSYS Fluent, STAR-CCM, COMSOL, Flownex, SimScale, OpenFOAM, Fuego, KIVA, BIGHORN, or their own computational tools. Applied Computational Fluid Dynamics and Turbulence Modeling is a practical, complementary companion for academic CFD textbooks and senior project courses in mechanical, civil, chemical, and nuclear engineering; senior undergraduate and graduate CFD and turbulence modeling courses; and for professionals developing commercial and research applications.

The risks posed by climate change and its effect on climate extremes are an increasingly pressing societal problem. This book provides an accessible overview of the statistical analysis methods which can be used to investigate climate extremes and analyse potential risk. The statistical analysis methods are illustrated with case studies on extremes in the three major climate variables: temperature, precipitation, and wind speed. The book also provides datasets and access to appropriate analysis software, allowing the reader to replicate the case study calculations. Providing the necessary tools to analyse climate risk, this book is invaluable for students and researchers working in the climate sciences, as well as risk analysts interested in climate extremes.

This book highlights by careful documentation of developments what led to tracking the growth of deterministic disturbances inside the shear layer from receptivity to fully developed turbulent flow stages. Associated theoretical and numerical developments are addressed from basic level so that an uninitiated reader can also follow the materials which lead to the solution of a long-standing problem. Solving Navier-Stokes equation by direct numerical simulation (DNS) from the first principle has been considered as one of the most challenging problems of understanding what causes transition to turbulence. Therefore, this book is a very useful addition to advanced CFD and advanced fluid mechanics courses.

This book is an introduction to a comprehensive and unified dynamic transition theory for dissipative systems and to applications of the theory to a range of problems in the nonlinear sciences. The main objectives of this book are to introduce a general principle of dynamic transitions for dissipative systems, to establish a systematic dynamic transition theory, and to explore the physical implications of applications of the theory to a range of problems in the nonlinear sciences. The basic philosophy of the theory is to search for a complete set of transition states, and the general principle states that dynamic transitions of all dissipative systems can be classified into three categories: continuous, catastrophic and random. The audience for this book includes advanced graduate students and researchers in mathematics and physics as well as in other related fields. This second edition introduces a unified theory for topological phase transitions, provides a first-principle approach to statistical and quantum physics, and offers a microscopic mechanism of quantum condensates (Bose-Einstein condensation, superfluidity, and superconductivity). Reviews of first edition: "The goals of this interesting book are to derive a general principle of dynamic transitions for dissipative systems and to establish a systematic dynamic transition theory for a wide range of problems in the nonlinear sciences. ... The intended audience for this book includes students and researchers working on nonlinear problems in physics, meteorology, oceanography, biology, chemistry, and the social sciences." (Carlo Bianca, Mathematical Reviews, December, 2014) "This is a clearly written book on numerous types of phase transitions taken in a broad sense when a dynamical dissipative system transforms from one physical state into another. ... The book is a very useful literature not only for the professionals in the field of dynamic systems and phase transitions but also for graduate students due to its interdisciplinary coverage and state-of-the-art level." (Vladimir Cadez, zbMATH, Vol. 1285, 2014)

In this concise yet comprehensive book, the author discusses the principles of mass, momentum, and energy transport, and derives balance equations for single-component fluids and multicomponent mixtures based on the direct application of natural laws and principles of thermodynamics. Transport equations over control volumes are formulated with reference to the Reynolds transport equation, thereby circumventing the need for ad-hoc balances for open systems that are best justified in hindsight. Notable features with regard to mass transport include the interpretation of diffusion in mixtures in terms of species parcel motion and separation, the introduction of Fick's and fractional diffusion laws with reference to random molecular excursions, a detailed account of species and mixture kinematics and dynamics, and the discussion of partial stresses, energies, and entropies of individual mixture components. Key features of this book include: * The governing equations are derived from first principles based on the application of natural laws and principles of thermodynamics * Balances over control volumes are derived from rigorous equations governing material parcel property evolution * Fick's law, a fractional diffusion law, and other diffusion laws are discussed with reference to random walks * A detailed account of species and mixture kinematics and dynamics is presented for binary and multicomponent solutions * A tabulated summary of transport equations is presented in differential and integral forms, and an overview of classical thermodynamics is given in an appendix for a self-contained discourse C. Pozrikidis has taught at the University of California and the University of Massachusetts. He is the author of several books on theoretical and computational topics in science and engineering, applied mathematics, scientific computing, and computer science.