Modeling complex biological, chemical, and physical systems, in the context of spatially heterogeneous mediums, is a challenging task for scientists and engineers using traditional methods of analysis.

Modeling in Applied Sciences is a comprehensive survey of modeling large systems using kinetic equations, and in particular the Boltzmann equation and its generalizations. An interdisciplinary group of leading authorities carefully develop the foundations of kinetic models and discuss the connections and interactions between model theories, qualitative and computational analysis and real-world applications. This book provides a thoroughly accessible and lucid overview of the different aspects, models, computations, and methodology for the kinetic-theory modeling process.

Topics and Features:

* Integrated modeling perspective utilized in all chapters

* Fluid dynamics of reacting gases

* Self-contained introduction to kinetic models

* Becker Doring equations

* Nonlinear kinetic models with chemical reactions

* Kinetic traffic-flow models

* Models of granular media

* Large communication networks

* Thorough discussion of numerical simulations of Boltzmann equation

This new book is an essential resource for all scientists and engineers who use large-scale computations for studying the dynamics of complex systems of fluids and particles. Professionals, researchers, and postgraduates will find the book a modern and authoritative guide to the topic.

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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.

In recent years the interaction between dynamical systems theory and non-equilibrium statistical mechanics has been enormous. The discovery of fluctuation theorems as a fundamental structure common to almost all non-equilibrium systems, and the connections with the free energy calculation methods of Jarzynski and Crooks, have excited both theorists and experimentalists. This graduate level book charts the development and theoretical analysis of molecular dynamics as applied to equilibrium and non-equilibrium systems. Designed for both researchers in the field and graduate students of physics, it connects molecular dynamics simulation with the mathematical theory to understand non-equilibrium steady states. It also provides a link between the atomic, nano, and macro worlds. The book ends with an introduction to the use of non-equilibrium statistical mechanics to justify a thermodynamic treatment of non-equilibrium steady states, and gives a direction to further avenues of exploration.

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.

Ludwig Prandtl, with his fundamental contributions to hydrodynamics, ae- dynamics, and gas dynamics, greatly in?uenced the development of ?uid - chanics as a whole, and it was his pioneering research in the ?rst half of the last century that founded modern ?uid mechanics. His book Fu]hrer durch die Str]omungslehre, which appeared in 1942, originated from previous pub- cations in 1913, Lehre von der Flu]ssigkeit und Gasbewegung, and 1931, Abriss der Str]omungslehre. The title Fu]hrer durch die Str]omungslehre, or Essentials of Fluid Mechanics, is an indication of Prandtl's intentions to guide the reader on a carefully thought-out path through the di?erent areas of ?uid mech- ics. On his way, the author advances intuitively to the core of the physical problem, without extensive mathematical derivations. The description of the fundamental physical phenomena and concepts of ?uid mechanics that are needed to derive the simpli?ed models has priority over a formal treatment of the methods. This is in keeping with the spirit of Prandtl's research work. The ?rst edition of Prandtl's Fu]hrer durch die Str]omungslehre was the only book on ?uid mechanics of its time and, even today, counts as one of the most important books in this area. After Prandtl's death, his students Klaus Oswatitsch and Karl Wieghardt undertook to continue his work, and to add new ?ndings in ?uid mechanics in the same clear manner of presentation."

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.

This book was first published in 2005. When an oceanic tidal wave that is primarily active on the water surface passes an ocean shelf or a region with a seamount, it is split into a less energetic surface wave and other internal modes with different wavelengths and propagation speeds. This cascading process, from the barotropic tides to the baroclinic components, leads to the transformation of tidal energy into turbulence and heat, an important process for the dynamics of the lower ocean. Baroclinic Tides demonstrates the analytical and numerical methods used to study the generation and evolution of baroclinic tides and, by comparison with experiments and observational data, shows how to distinguish and interpret internal waves. Strongly non-linear solitary internal waves, which are generated by internal tidal waves at the final stage of their evolution, are investigated in detail. This book is intended for researchers and graduate students of physical oceanography, geophysical fluid dynamics and hydroacoustics.

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.

The primary goal of numerical simulation of compressible, inviscid time-dependent flow is to represent the time evolution of complex flow patterns. Developed by Matania Ben-Artzi and Joseph Falcovitz, the Generalized Riemann Problem (GRP) algorithm comprises some of the most commonly used numerical schemes of this process. This monograph presents the GRP methodology ranging from underlying mathematical principles through basic scheme analysis and scheme extensions. The book is intended for researchers and graduate students of applied mathematics, science and engineering.

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.

Discusses the modeling and analysis of nanoparticles. Covers all fundamental aspects of particle and droplet flows. Includes heat and mass transfer processes. Features new and updated sections throughout the text. Includes chapter exercises.

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 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 provides an up-to-date overview of mathematical theories and research results in non-Newtonian fluid dynamics. Related mathematical models, solutions as well as numerical experiments are discussed. Fundamental theories and practical applications make it a handy reference for researchers and graduate students in mathematics, physics and engineering. Contents Non-Newtonian fluids and their mathematical model Global solutions to the equations of non-Newtonian fluids Global attractors of incompressible non-Newtonian fluids Global attractors of modified Boussinesq approximation Inertial manifolds of incompressible non-Newtonian fluids The regularity of solutions and related problems Global attractors and time-spatial chaos Non-Newtonian generalized fluid and their applications

Introduction to Fluid Mechanics, Second Edition, uses clear images and animations of flow patterns to help readers grasp the fundamental rules of fluid behavior. Everyday examples are provided for practical context, before tackling the more involved mathematic techniques that form the basis for computational fluid mechanics. This fully updated and expanded edition builds on the author's flair for flow visualization with new content. With basic introductions to all essential fluids theory, and exercises to test your progress, this is the ideal introduction to fluids for anyone involved in mechanical, civil, chemical, or biomedical engineering.

This is an introductory textbook on the geometrical theory of dynamical systems, fluid flows and certain integrable systems. The topics are interdisciplinary and extend from mathematics, mechanics and physics to mechanical engineering, and the approach is very fundamental. The main theme of this book is a unified formulation to understand dynamical evolutions of physical systems within mathematical ideas of Riemannian geometry and Lie groups by using well-known examples. Underlying mathematical concepts include transformation invariance, covariant derivative, geodesic equation and curvature tensors on the basis of differential geometry, theory of Lie groups and integrability. These mathematical theories are applied to physical systems such as free rotation of a top, surface wave of shallow water, action principle in mechanics, diffeomorphic flow of fluids, vortex motions and some integrable systems.In the latest edition, a new formulation of fluid flows is also presented in a unified fashion on the basis of the gauge principle of theoretical physics and principle of least action along with new type of Lagrangians. A great deal of effort has been directed toward making the description elementary, clear and concise, to provide beginners easy access to the topics.

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.

This textbook provides a concise introduction to the mathematical theory of fluid motion with the underlying physics. Different branches of fluid mechanics are developed from general to specific topics. At the end of each chapter carefully designed problems are assigned as homework, for which selected fully worked-out solutions are provided. This book can be used for self-study, as well as in conjunction with a course in fluid mechanics.

Modeling and Analysis of Modern Fluids helps researchers solve physical problems observed in fluid dynamics and related fields, such as heat and mass transfer, boundary layer phenomena, and numerical heat transfer. These problems are characterized by nonlinearity and large system dimensionality, and 'exact' solutions are impossible to provide using the conventional mixture of theoretical and analytical analysis with purely numerical methods. To solve these complex problems, this work provides a toolkit of established and novel methods drawn from the literature across nonlinear approximation theory. It covers Pade approximation theory, embedded-parameters perturbation, Adomian decomposition, homotopy analysis, modified differential transformation, fractal theory, fractional calculus, fractional differential equations, as well as classical numerical techniques for solving nonlinear partial differential equations. In addition, 3D modeling and analysis are also covered in-depth.

A comprehensive presentation of wicking models developed in academia and industry, Wicking in Porous Materials: Traditional and Modern Modeling Approaches contains some of the most important approaches and methods available, from the traditional Washburn-type models to the latest Lattice-Boltzmann approaches developed during the last few years. It provides a sound conceptual framework for learning the science behind different mathematical models while at the same time being aware of the practical issues of model validation as well as measurement of important properties and parameters associated with various models. Top experts in the field reveal the secrets of their wicking models. The chapters cover the following topics: Wetting and wettability Darcy's law for single- and multi-phase flows Traditional capillary models, such as the Washburn-equation based approaches Unsaturated-flow based methodologies (Richard's Equation) Sharp-front (plug-flow) type approaches using Darcy's law Pore network models for wicking after including various micro-scale fluid-flow phenomena Studying the effect of evaporation on wicking using pore network models Fractal-based methods Modeling methods based on mixture theory Lattice-Boltzmann method for modeling wicking in small scales Modeling wicking in swelling and non-rigid porous media This extensive look at the modeling of porous media compares various methods and treats traditional topics as well as modern technologies. It emphasizes experimental validation of modeling approaches as well as experimental determination of model parameters. Matching models to particular media, the book provides guidance on what models to use and how to use them.