Preface 1. Introduction: a computational approach to multiphase flow A. Prosperetti and G. Tryggvason 2. Direct numerical simulations of finite Reynolds number flows G. Tryggvason and S. Balachandar 3. Immersed boundary methods for fluid interfaces G. Tryggvason, M. Sussman and M. Y. Hussaini 4. Structured grid methods for solid particles S. Balachandar 5. Finite element methods for particulate flows H. Hu 6. Lattice Boltzmann methods for multiphase flows S. Chen, X. He and L. S. Luo 7. Boundary integral methods for Stokes flows J. Blawzdziewic 8. Averaged equations for multiphase flows A. Prosperetti 9. Point particle methods for disperse flows K. Squires 10. Segregated methods for two-fluid models A. Prosperetti, S. Sundaresan, S. Pannala and D. Z. Zhang 11. Coupled methods for multi-fluid models A. Prosperetti References Index.
The book provides an introduction to the theory of cluster sets, a branch of topological analysis which has made great strides in recent years. The cluster set of a function at a particular point is the set of limit values of the function at that point which may be either a boundary point or (in the case of a non-analytic function) an interior point of the function's domain. In topological analysis, its main application is to problems arising in the theory of functions of a complex variable, with particular reference to boundary behaviour such as the theory of prime ends under conformal mapping. An important and novel feature of the book is the discussion of more general applications to non-analytic functions, including arbitrary functions. The authors assume a general familiarity with classical function theory but include the more specialised material required for the development of the theory of cluster sets, so making the treatment accessible to graduate students.
1. Existence and uniqueness for diffusion processes 2. The basic properties of diffusion processes 3. The spectral theory of elliptic operators on smooth bounded domains 4. Generalized spectral theory for operators on arbitrary domains 5. Applications to the one-dimensional case and the radially symmetric multi-dimensional case 6. Criteria for transience or recurrence and explosion or non-explosion of diffusion processes 7. Positive harmonic functions and the Martin boundary: general theory 8. Positive harmonic functions and the Martin boundary: applications to certain classes of operators 9. Bounded harmonic functions and applications to Brownian motion and the Laplacian on a manifold of non-positive curvature.
The book Vortex Methods: Theory and Practice presents a comprehensive account of the numerical technique for solving fluid flow problems. It provides a very nice balance between the theoretical development and analysis of the various techniques and their practical implementation. In fact, the presentation of the rigorous mathematical analysis of these methods instills confidence in their implementation. The book goes into some detail on the more recent developments that attempt to account for viscous effects, in particular the presence of viscous boundary layers in some flows of interest. The presentation is very readable, with most points illustrated with well-chosen examples, some quite sophisticated. It is a very worthy reference book that should appeal to a large body of readers, from those interested in the mathematical analysis of the methods to practitioners of computational fluid dynamics. The use of the book as a text is compromised by its lack of exercises for students, but it could form the basis of a graduate special topics course. Juan Lopez
The Dirichlet space is one of the three fundamental Hilbert spaces of holomorphic functions on the unit disk. It boasts a rich and beautiful theory, yet at the same time remains a source of challenging open problems and a subject of active mathematical research. This book is the first systematic account of the Dirichlet space, assembling results previously only found in scattered research articles, and improving upon many of the proofs. Topics treated include: the Douglas and Carleson formulas for the Dirichlet integral, reproducing kernels, boundary behaviour and capacity, zero sets and uniqueness sets, multipliers, interpolation, Carleson measures, composition operators, local Dirichlet spaces, shift-invariant subspaces, and cyclicity. Special features include a self-contained treatment of capacity, including the strong-type inequality. The book will be valuable to researchers in function theory, and with over 100 exercises it is also suitable for self-study by graduate students.
Green's Function and Boundary Elements of Multifield Materials contains a comprehensive treatment of multifield materials under coupled thermal, magnetic, electric, and mechanical loads. Its easy-to-understand text clarifies some of the most advanced techniques for deriving Green's function and the related boundary element formulation of magnetoelectroelastic materials: Radon transform, potential function approach, Fourier transform. Our hope in preparing this book is to attract interested readers and researchers to a new field that continues to provide fascinating and technologically important challenges. You will benefit from the authors' thorough coverage of general principles for each topic, followed by detailed mathematical derivation and worked examples as well as tables and figures where appropriate.In-depth explanations of the concept of Green's functionCoupled thermo-magneto-electro-elastic analysisDetailed mathematical derivation for Green's functions
Plates are integral parts of most engineering structures and their vibration analysis is required for safe design. Vibration of Plates provides a comprehensive, self-contained introduction to vibration theory and analysis of two-dimensional plates. Reflecting the author's more than 15 years of original research on plate vibration, this book presents new methodologies and demonstrates their effectiveness by providing comprehensive results. The text also offers background information on vibration problems along with a discussion of various plate geometries and boundary conditions, including the new concepts of Boundary Characteristic Orthogonal Polynomials (BCOPs).
Preliminaries from Differential Geometry Linear Connections, Differential of Tensor Fields, and Curvature Distance Functions A Basic Computational Technique Sobolev Spaces of Tensor Field and Some Basic Differential Operators Control of the Wave Equation with Variable Coefficients in Space How to Understand Riemannian Geometry as a Necessary Tool for Control of the Wave Equation with Variable Coefficients Geometric Multiplier Identities Escape Vector Fields and Escape Regions for Metrics Exact Controllability. Dirichlet/Neumann Action Smooth Controls A Counterexample without Exact Controllability Stabilization Transmission Stabilization Control of the Plate with Variable Coefficients in Space Multiplier Identities Escape Vector Fields for the Plate Exact Controllability from Boundary Controllability for Transmission of Plate Stabilization from Boundary for the Plate with a Curved Middle Surface Linear Shallow Shells: Modeling and Control Equations in Equilibrium. Green's Formulas Ellipticity of the Strain Energy of Shallow Shells Equations of Motion Multiplier Identities Escape Vector Field and Escape Region for the Shallow Shell Observability Inequalities. Exact Controllability Exact Controllability for Transmission Stabilization by Linear Boundary Feedbacks Stabilization by Nonlinear Boundary Feedbacks Naghdi's Shells: Modeling and Control Equations of Equilibrium. Green's Formulas. Ellipticity of the Strain Energy. Equations of Motion Observability Estimates from Boundary Stabilization by Boundary Feedback Stabilization of Transmission Koiter's Shells: Modeling and Controllability Equations of Equilibria. Equations of Motion Uniqueness for the Koiter Shell Multiplier Identities Observability Estimates from Boundary Control of the Quasilinear Wave Equation in Higher Dimensions Boundary Traces and Energy Estimates Locally and Globally Boundary Exact Controllability Boundary Feedback Stabilization Structure of Control Regions for Internal Feedbacks References Bibliography Index Notes and References appear at the end of each chapter.
Written for researchers and developers of three-dimensional modeling programs, this book examines the variety of existing systems while investigating the practical limitations of available software. From the table of contents: - Polyhedra - Boundary Models - A Small Language Modeler - The Algebraic Model - Computation of Algebraic Manifolds - Topological Specification of Forms and Shapes - The Modeling Principle - The GECO Language - Coefficients of a Projected Curve
Classical logic has been attacked by adherents of rival, anti-realist logical systems: Ian Rumfitt comes to its defence. He considers the nature of logic, and how to arbitrate between different logics. He argues that classical logic may dispense with the principle of bivalence, and may thus be liberated from the dead hand of classical semantics.
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