Although multifractals are rooted in probability, much of the related literature comes from the physics and mathematics arena. Multifractals: Theory and Applications pulls together ideas from both these areas using a language that makes them accessible and useful to statistical scientists. It provides a framework, in particular, for the evaluation of statistical properties of estimates of the Renyi fractal dimensions. The first section provides introductory material and different definitions of a multifractal measure. The author then examines some of the various constructions for describing multifractal measures. Building from the theory of large deviations, he focuses on constructions based on lattice coverings, covering by point-centered spheres, and cascades processes. The final section presents estimators of Renyi dimensions of integer order two and greater and discusses their properties. It also explores various applications of dimension estimation and provides a detailed case study of spatial point patterns of earthquake locations. Estimating fractal dimensions holds particular value in studies of nonlinear dynamical systems, time series, and spatial point patterns. With its careful yet practical blend of multifractals, estimation methods, and case studies, Multifractals: Theory and Applications provides a unique opportunity to explore the estimation methods from a statistical perspective.

Presents in a systematic and unified manner the ray method, in its various forms, for studying nonlinear wave propagation in situations of physical interest, essentially fluid dynamics and plasma physics.

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 reports on the latest developments in computational fluid dynamics and turbulence modeling, with a special emphasis on hybrid RANS-LES methods and their industrial applications. It gathers the proceedings of the Sixth Symposium on Hybrid RANS-LES Methods, held on September 26-28 in Strasbourg, France. The different chapters covers a wealth of topics such as flow control, aero-acoustics, aero-elasticity and CFD-based multidisciplinary optimization. Further topics include wall-modelled Large Eddy Simulation (WMLES), embedded LES, Lattice-Bolzman methods, turbulence-resolving applications and comparisons between LES, hybrid RANS-LES and URANS methods. The book addresses academic researchers, graduate students, industrial engineers, as well as industrial R&D managers and consultants dealing with turbulence modelling, simulation and measurement, and with multidisciplinary applications of computational fluid dynamics.

Surface tension provides a thermodynamic avenue for analyzing systems in equilibrium and formulating phenomenological explanations for the behavior of constituent molecules in the surface region. While there are extensive experimental observations and established ideas regarding desorption of ions from the surfaces of aqueous salt solutions, a more successful discussion of the theory has recently emerged, which allows the quantitative calculation of the distribution of ions in the surface region. Surface Tension and Related Thermodynamic Quantities of Aqueous Electrolyte Solutions provides a detailed and systematic analysis of the properties of ions at the air/water interface. Unifying older and newer theories and measurements, this book emphasizes the contributions of simple ions to surface tension behavior, and the practical consequences. It begins with a general discussion on Gibbs surface thermodynamics, offering a guide to his theoretical insight and formulation of the boundary between fluids. The text then discusses the thermodynamic formulae that are useful for practical experimental work in the analysis of fluid/fluid interfaces. Chapters cover surface tension of pure water at air/water and air/oil interfaces, surface tension of solutions and the thermodynamic quantities associated with the adsorption and desorption of solutes, and surface tension of simple salt solutions. They also address adsorption of ions at the air/water interface, surface tension of solutions and the effect of temperature, adsorption from mixed electrolyte solutions, and thermodynamic properties of zwitterionic amino acids in the surface region. Focusing on the thermodynamic properties of ions at air/fluid interfaces, this book gives scientists a quantitative, rigorous, and objectively experimental methodology they can employ in their research.

Mathematical Techniques for Wave Interaction with Flexible Structures is a thoughtful compilation of the various mathematical techniques used to deal with wave structure interaction problems. The book emphasizes unique determination of the solution for a class of physical problems associated with Laplace- or Helmholtz-type equations satisfying higher order boundary conditions with the applications of the theory of ordinary and partial differential equations, Fourier analysis, and more. Features: Provides a focused mathematical treatment for gravity wave interaction with floating and submerged flexible structures Highlights solution methods for a special class of boundary value problems in wave structure interaction Introduces and expands upon differential equations and the fundamentals of wave structure interaction problems This is an ideal handbook for naval architects, ocean engineers, and geophysicists dealing with the design of floating and/or flexible marine structures. The book's underlying mathematical tools can be easily extended to deal with physical problems in the area of acoustics, electromagnetic waves, wave propagation in elastic media, and solid-state physics. Designed for both the classroom and independent study, Mathematical Techniques for Wave Interaction with Flexible Structures enables readers to appreciate and apply the mathematical tools of wave structure interaction research to their own work.

In recent years, stylized forms of the Boltzmann equation, now going by the name of "Lattice Boltzmann equation" (LBE), have emerged, which relinquish most mathematical complexities of the true Boltzmann equation without sacrificing physical fidelity in the description of many situations involving complex fluid motion. This book provides the first detailed survey of LBE theory and its major applications to date. Accessible to a broad audience of scientists dealing with complex system dynamics, the book also portrays future developments in allied areas of science (material science, biology etc.) where fluid motion plays a distinguished role.

The International Conference on Computational Fluid Dynamics (ICCFD) is the merger of the International Conference on Numerical Methods in Fluid Dynamics (ICNMFD) and the International Symposium on Computational Fluid Dynamics (ISCFD). It is held every two years and brings together physicists, mathematicians and engineers to review and share recent advances in mathematical and computational techniques for modeling fluid dynamics. The proceedings of the 2004 conference held in Toronto, Canada, contain a selection of refereed contributions and are meant to serve as a source of reference for all those interested in the state of the art in computational fluid dynamics.

Perturbation Methods for Engineers and Scientists examines the main techniques of perturbation expansions applied to both differential equations and integral expressions. It describes several fluid dynamics applications, including aerofoils, boundary layers in momentum heat, and mass transfer. In addition, it applies the multiple scale technique to the description of surface roughness effects in lubrication. The book's intuitive, rather than formal, approach enables these advanced techniques to be used by scientists and engineers as well as by students.

The understanding and control of transport phenomena in materials processing play an important role in the improvement of conventional processes and in the development of new techniques. Computer modeling of these phenomena can be used effectively for this purpose. Although there are several books in the literature covering the analysis of heat transfer and fluid flow, Computer Modelling of Heat and Fluid Flow in Materials Processing specifically addresses the understanding of these phenomena in materials processing situations. Written at a level suitable for graduate students in materials science and engineering and subjects, this book is ideal for those wishing to learn how to approach computer modeling of transport phenomena and apply these techniques in materials processing. The text includes a number of relevant case studies and each chapter is supported by numerous examples of transport modeling programs.

This monograph discusses modeling, adaptive discretisation techniques and the numerical solution of fluid structure interaction. An emphasis in part I lies on innovative discretisation and advanced interface resolution techniques. The second part covers the efficient and robust numerical solution of fluid-structure interaction. In part III, recent advances in the application fields vascular flows, binary-fluid-solid interaction, and coupling to fractures in the solid part are presented. Moreover each chapter provides a comprehensive overview in the respective topics including many references to concurring state-of-the art work. Contents Part I: Modeling and discretization On the implementation and benchmarking of an extended ALE method for FSI problems The locally adapted parametric finite element method for interface problems on triangular meshes An accurate Eulerian approach for fluid-structure interactions Part II: Solvers Numerical methods for unsteady thermal fluid structure interaction Recent development of robust monolithic fluid-structure interaction solvers A monolithic FSI solver applied to the FSI 1,2,3 benchmarks Part III: Applications Fluid-structure interaction for vascular flows: From supercomputers to laptops Binary-fluid-solid interaction based on the Navier-Stokes-Cahn-Hilliard Equations Coupling fluid-structure interaction with phase-field fracture: Algorithmic details

This book compiles a variety of experimental data on blast waves. The book begins with an introductory chapter and proceeds to the topic of blast wave phenomenology, with a discussion on Rankine-Hugoniot equations and the Friedlander equation, used to describe the pressure-time history of a blast wave. Additional topics include arrival time measurement, the initiation of detonation by exploding wires, a discussion of TNT equivalency, and small scale experiments. Gaseous and high explosive detonations are covered as well. The topics and experiments covered were chosen based on the comparison of used scale sizes, from small to large. Each characteristic parameter of blast waves is analyzed and expressed versus scaled distance in terms of energy and mass. Finally, the appendix compiles a number of polynomial laws that will prove indispensable for engineers and researchers.

The Navier-Stokes equations describe the motion of fluids and are an invaluable addition to the toolbox of every physicist, applied mathematician, and engineer. The equations arise from applying Newton's laws of motion to a moving fluid and are considered, when used in combination with mass and energy conservation rules, to be the fundamental governing equations of fluid motion. They are relevant across many disciplines, from astrophysics and oceanic sciences to aerospace engineering and materials science. This Student's Guide provides a clear and focused presentation of the derivation, significance and applications of the Navier-Stokes equations, along with the associated continuity and energy equations. Designed as a useful supplementary resource for undergraduate and graduate students, each chapter concludes with a selection of exercises intended to reinforce and extend important concepts. Video podcasts demonstrating the solutions in full are provided online, along with written solutions and other additional resources.

On November 3, 2005, Alexander Vasil'evich Kazhikhov left this world, untimely and unexpectedly. He was one of the most in?uential mathematicians in the mechanics of ?uids, and will be remembered for his outstanding results that had, and still have, a c- siderablysigni?cantin?uenceinthe?eld.Amonghis manyachievements,werecall that he was the founder of the modern mathematical theory of the Navier-Stokes equations describing one- and two-dimensional motions of a viscous, compressible and heat-conducting gas. A brief account of Professor Kazhikhov's contributions to science is provided in the following article "Scienti?c portrait of Alexander Vasil'evich Kazhikhov". This volume is meant to be an expression of high regard to his memory, from most of his friends and his colleagues. In particular, it collects a selection of papers that represent the latest progress in a number of new important directions of Mathematical Physics, mainly of Mathematical Fluid Mechanics. These papers are written by world renowned specialists. Most of them were friends, students or colleagues of Professor Kazhikhov, who either worked with him directly, or met him many times in o?cial scienti?c meetings, where they had the opportunity of discussing problems of common interest.

Newly updated and translated into English for the first time, this standalone handbook perfectly combines background and theory with real-world experiments. All key topics are covered, including environmental conditions, wave theories, hydrostatics, and wave and current loads, with emphasis on nonlinear wave body interaction. Focus is given to model testing, an important component in the design of offshore structures. Recent results on the hydrodynamics of perforated structures, moonpool and gap resonance, and third-order interaction effects, have been added to this updated version. Based on practical experience from multiple industry collaborations, combined with lectures that have been honed and improved over more than 30 years, the pedagogical, real-world approach in this book make it an ideal companion for graduate students and researchers as well as ocean engineers.

Gravity pervades the whole universe; hence buoyancy drives fluids everywhere including those in the atmospheres and interiors of planets and stars. Prime examples of such flows are mantle convection, atmospheric flows, solar convection, dynamo process, heat exchangers, airships and hot air balloons. In this book we present fundamentals and applications of thermal convection and stratified flows.Buoyancy brings in extremely rich phenomena including waves and instabilities, patterns, chaos, and turbulence. In this book we present these topics in a systematic manner. First we present a unified treatment of linear theory that yields waves and thermal instability for stably and unstably-stratified flows respectively. We extend this analysis to include rotation and magnetic field. We also describe nonlinear saturation and pattern formation in Rayleigh-Benard convection.The second half of the book is dedicated to buoyancy-driven turbulence, both in stably-stratified flow and in thermal convection. We describe the spectral theory including energy flux and show that the thermally-driven turbulence is similar to hydrodynamic turbulence. We also describe large-scale quantities like Reynolds and Nusselt numbers, flow anisotropy, and the dynamics of flow structures, namely flow reversals. Thus, this book presents all the major aspects of the buoyancy-driven flows in a coherent manner that would appeal to advanced graduate students and researchers.

This valuable resource summarizes the past fifty years' basic research accomplishments in plasma dynamics for aerospace engineering, presenting these results in a comprehensive volume that will be an asset to any professional in the field. It offers a comprehensive review of the foundation of plasma dynamics while integrating the most recently developed modeling and simulation techniques with the theoretic physics, including the state-of-the-art numerical algorithms. Several first-ever demonstrations for innovations and incisive explanations for previously unexplained observations are included. All the necessary formulations for technical evaluation to engineering applications are derived from the first principle by statistic and quantum mechanics, and led to physics-based computational simulations for practical applications. The computer-aided procedures directly engage the reader to duplicate findings that are nearly impossible by using ground-based experimental facilities. Plasma Dynamics for Aerospace Engineering will allow readers to reach an incisive understanding of plasma physics.

Gives comprehensive treatment on fluid dynamics and fluvial process from fundamentals to advanced level applications in one volume Present knowledge on sediment transport and its interaction with turbulence Covers recent methodologies on the study of turbulent flow theories with verification of data collected by ADV, PIV, LDA, and imaging techniques Explores latest empirical formulae for estimation of bed load, saltation and suspension Contains theory to experimentations with field practices with comprehensive explanations and illustrations with introduction of environmental fluid mechanics

Based on his over forty years of research and teaching, John C. Wyngaard's textbook is an excellent up-to-date introduction to turbulence in the atmosphere and in engineering flows for advanced students, and a reference work for researchers in the atmospheric sciences. Part I introduces the concepts and equations of turbulence. It includes a rigorous introduction to the principal types of numerical modeling of turbulent flows. Part II describes turbulence in the atmospheric boundary layer. Part III covers the foundations of the statistical representation of turbulence and includes illustrative examples of stochastic problems that can be solved analytically. The book treats atmospheric and engineering turbulence in a unified way, gives clear explanation of the fundamental concepts of modeling turbulence, and has an up-to-date treatment of turbulence in the atmospheric boundary layer. Student exercises are included at the ends of chapters, and worked solutions are available online for use by course instructors.

Rotary Drum: Fluid Dynamics, Dimensioning Criteria, and Industrial Applications provides in-depth analysis of fluid dynamics in rotary drums. In addition, it provides analysis on the different configurations, including nonconventional ones, diverse industrial applications, and comparison with competing dryer types, as well as the modeling of these devices. Covering important aspects of fluid dynamics in rotary drums, which directly influence the drying performance, the book also considers the significant cost of conventional rotary dryers. It takes into account the scale-up of rotary dryers and the control of product quality during processing, which can leave the final product overdried and overheated, wasting thermal energy. The book serves as a useful reference for researchers, graduate students, and engineers in the field of drying technology.

Detailing the major developments of the last decade, the Handbook of Hydraulic Fluid Technology, Second Edition updates the original and remains the most comprehensive and authoritative book on the subject. With all chapters either revised (in some cases, completely) or expanded to account for new developments, this book sets itself apart by approaching hydraulic fluids as a component of a system and focusing on key technological aspects. Written by experts from around the world, the handbook covers all major classes of hydraulic fluids in detail, delving into chemistry, design, fluid maintenance and selection, and other key concepts. It also offers a rigorous overview of hydraulic fluid technology and evaluates the ecological benefits of water and its use as an important alternative technology. This complete overview discusses pumps and motors, valves, and reservoir design, as well as fluid properties and associated topics. These include air entrainment, modulus, lubrication and wear assessment by bench and pump testing, biodegradability, and fire resistance. Contributors also present particularly important material on biodegradable fluids and the use of water as a hydraulic fluid. As the foremost resource on the design, selection, and testing of hydraulic systems and fluids used in engineering applications, this book contains new illustrations, data tables, and practical examples, all updated with essential information on the latest methods. To streamline presentation, relevant content from the first edition has been integrated into this new version, where appropriate. The result is a reference that helps readers develop an unparalleled understanding of the total hydraulic system, including essential hardware, fluid properties, and hydraulic lubricants.

Thermal-hydraulic instability can potentially impair thermal reliability of reactor cores or other power equipment components. Thus it is important to address stability issues in power equipment associated with thermal and nuclear installations, particularly in thermal nuclear power plants, chemical and petroleum industries, space technology, and radio, electronic, and computer cooling systems. Coolant Flow Instabilities in Power Equipment synthesizes results from instability investigations around the world, presenting an analysis and generalization of the published technical literature. The authors include individual examples on flow stability in various types of equipment, including boilers, reactors, steam generators, condensers, heat exchangers, turbines, pumps, deaerators, bubblers, and pipelines. They also present information that has not been widely available until recently, such as thermal-acoustic instability, flow instability with supercritical parameters, and single-phase coolant flow static instability. The material described in this book is derived from vast amounts of experimental data from thermal-physical test facilities and full-scale installations. It is presented in a manner accessible to readers without advanced mathematical backgrounds. Particular attention has been paid to oscillatory (low-frequency and thermal-acoustic) and static thermal-hydraulic coolant flow instability. In addition, the physical mechanism of instability has been considered in detail. This book provides knowledge of the various types of flow instability, the equipment where this instability can manifest, and the ensuing consequences, as well as makes recommendations concerning possible removal or mitigation of these consequences. The authors provide this information as a useful reference for readers to facilitate the enhanced safety of modern power equipment through qualitative evaluation of design and flow parameters and subsequent selection of the optimal means for increasing flow stability.

This book is the first to present flow measurement as an independent branch of the measurement techniques, according to a new global and unitary approach for the measurement of fluid flow field, starting from finding its unitary fundamental bases. Furthermore, it elaborates the method of unitary analysis/synthesis and classification of compound gauging structures (CGS): the UASC - CGS method. These methods ensure, in a systematic and predictable way, both the analysis of the types of flow meters made until present (i.e. CGS) and the synthesis of new types of flowmeters. The book outlines new contributions in this field, including separately, for flow meters, and CGS: structural schemes and their unitary, unitary classification, unitary logical matrix, method of unitary analysis/synthesis and classification.