Download or read book Surface Evolution Equations written by Yoshikazu Giga and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a self-contained introduction to the analytic foundation of a level set approach for various surface evolution equations including curvature flow equations. These equations are important in many applications, such as material sciences, image processing and differential geometry. The goal is to introduce a generalized notion of solutions allowing singularities, and to solve the initial-value problem globally-in-time in a generalized sense. Various equivalent definitions of solutions are studied. Several new results on equivalence are also presented. Moreover, structures of level set equations are studied in detail. Further, a rather complete introduction to the theory of viscosity solutions is contained, which is a key tool for the level set approach. Although most of the results in this book are more or less known, they are scattered in several references, sometimes without proofs. This book presents these results in a synthetic way with full proofs. The intended audience are graduate students and researchers in various disciplines who would like to know the applicability and detail of the theory as well as its flavour. No familiarity with differential geometry or the theory of viscosity solutions is required. Only prerequisites are calculus, linear algebra and some basic knowledge about semicontinuous functions.
Download or read book Surface Evolution Equations written by Yoshikazu Giga and published by . This book was released on 2006 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Surface Evolution Equations written by Yoshikazu Giga and published by . This book was released on 2002 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric Evolution Equations written by Shu-Cheng Chang and published by American Mathematical Soc.. This book was released on 2005 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Workshop on Geometric Evolution Equations was a gathering of experts that produced this comprehensive collection of articles. Many of the papers relate to the Ricci flow and Hamilton's program for understanding the geometry and topology of 3-manifolds. The use of evolution equations in geometry can lead to remarkable results. Of particular interest is the potential solution of Thurston's Geometrization Conjecture and the Poincare Conjecture. Yet applying the method poses serious technical problems. Contributors to this volume explain some of these issues and demonstrate a noteworthy deftness in the handling of technical areas. Various topics in geometric evolution equations and related fields are presented. Among other topics covered are minimal surface equations, mean curvature flow, harmonic map flow, Calabi flow, Ricci flow (including a numerical study), Kahler-Ricci flow, function theory on Kahler manifolds, flows of plane curves, convexity estimates, and the Christoffel-Minkowski problem. The material is suitable for graduate students and researchers interested in geometric analysis and connections to topology. Related titles of interest include The Ricci Flow: An Introduction.
Download or read book Invariant Manifolds and Dispersive Hamiltonian Evolution Equations written by Kenji Nakanishi and published by European Mathematical Society. This book was released on 2011 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of an invariant manifold arises naturally in the asymptotic stability analysis of stationary or standing wave solutions of unstable dispersive Hamiltonian evolution equations such as the focusing semilinear Klein-Gordon and Schrodinger equations. This is due to the fact that the linearized operators about such special solutions typically exhibit negative eigenvalues (a single one for the ground state), which lead to exponential instability of the linearized flow and allows for ideas from hyperbolic dynamics to enter. One of the main results proved here for energy subcritical equations is that the center-stable manifold associated with the ground state appears as a hyper-surface which separates a region of finite-time blowup in forward time from one which exhibits global existence and scattering to zero in forward time. The authors' entire analysis takes place in the energy topology, and the conserved energy can exceed the ground state energy only by a small amount. This monograph is based on recent research by the authors. The proofs rely on an interplay between the variational structure of the ground states and the nonlinear hyperbolic dynamics near these states. A key element in the proof is a virial-type argument excluding almost homoclinic orbits originating near the ground states, and returning to them, possibly after a long excursion. These lectures are suitable for graduate students and researchers in partial differential equations and mathematical physics. For the cubic Klein-Gordon equation in three dimensions all details are provided, including the derivation of Strichartz estimates for the free equation and the concentration-compactness argument leading to scattering due to Kenig and Merle.
Download or read book Calculus of Variations and Geometric Evolution Problems written by F. Bethuel and published by Springer. This book was released on 2006-11-14 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro which have provided an image of a fairly broad field in analysis where in recent years we have seen many important contributions. Among the topics treated in the courses were variational methods for Ginzburg-Landau equations, variational models for microstructure and phase transitions, a variational treatment of the Plateau problem for surfaces of prescribed mean curvature in Riemannian manifolds - both from the classical point of view and in the setting of geometric measure theory.
Download or read book Nonlinear Evolution Equations And Dynamical Systems Proceedings Of The Workshop Needs 91 written by M Boiti and published by World Scientific. This book was released on 1992-08-26 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Workshop NEEDS '91 brought together, from all over the world, scientists engaged in research on nonlinear systems, either their underlying mathematical properties or their physical applications. Accordingly, many talks were devoted to present methods of solution (like spectral transform) and to the investigation of structural (geometrical and/or algebraic) properties of (continuous and discrete) nonlinear evolution equations. Peculiar nonlinear systems, such as cellular automata, were also discussed. Applications to various fields of physics, namely, quantum field theory, fluid dynamics, general relativity and plasma physics were considered.
Download or read book An Integral Solution to Surface Evolution PDEs Via Geo Cuts written by Yuri Boykov and published by London : Department of Computer Science, University of Western Ontario. This book was released on 2006 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Research in Materials Science written by National Research Council and published by National Academies Press. This book was released on 1993-02-01 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes fruitful past collaborations between the mathematical and materials sciences and indicates future challenges. It seeks both to encourage mathematical sciences research that will complement vital research in materials science and to raise awareness of the value of quantitative methods. The volume encourages both communities to increase cross-disciplinary collaborations, emphasizing that each has much to gain from such an increase, and it presents recommendations for facilitating such work. This book is written for both mathematical and materials science researchers interested in advancing research at this interface; for federal and state agency representatives interested in encouraging such collaborations; and for anyone wanting information on how such cross-disciplinary, collaborative efforts can be accomplished successfully.
Download or read book Surface and Interface Science Volumes 9 and 10 written by Klaus Wandelt and published by John Wiley & Sons. This book was released on 2020-03-30 with total page 990 pages. Available in PDF, EPUB and Kindle. Book excerpt: In ten volumes, this unique handbook covers all fundamental aspects of surface and interface science and offers a comprehensive overview of this research area for scientists working in the field, as well as an introduction for newcomers. Volume 1: Concepts and Methods Volume 2: Properties of Elemental Surfaces Volume 3: Properties of Composite Surfaces: Alloys, Compounds, Semiconductors Volume 4: Solid-Solid Interfaces and Thin Films Volume 5: Solid-Gas Interfaces I Volume 6: Solid-Gas Interfaces II Volume 7: Liquid and Biological Interfaces Volume 8: Interfacial Electrochemistry Volume 9: Applications of Surface Science I Volume 10: Applications of Surface Science II Content of Volumes 8 & 9: * Surface Analytics with X-Ray Photoelectron and Auger Electron Spectroscopy on Coated Steel Sheets * Applications of Graphene * Industrial Heterogeneous Catalysis * Automotive Catalysis * High-Throughput Heterogeneous Catalyst Research, Development, Scale-Up, and Production Support * Industrial Separation of Insulating Particles: Triboelectric Charging * Friction: Friend and Foe * Surface Science and Flotation * Application of Surface Science to Corrosion * Electrons, Electrodes, and the Transformation of Organic Molecules * Self-Cleaning Surfaces: From Fundamental Aspect to Real Technical Applications * Thin Films: Sputtering, PVD Methods and Applications * Wafer Bonding * Superconformal Deposition * Spintronics: Surface and Interface Aspects * Device Efficiency of Organic Light-Emitting Diodes * Dye-Sensitized Solar Cells * Electronic Nose: Current Status and Future Trends * Surface Science in Batteries * Surface and Interface Science in Fuel Cells Research
Download or read book Theory And Applications Of Ocean Surface Waves Third Edition In 2 Volumes written by Chiang C Mei and published by World Scientific Publishing Company. This book was released on 2018-03-15 with total page 1240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book set is a revised version of the 2005 edition of Theory and Applications of Ocean Surface Waves. It presents theoretical topics on ocean wave dynamics, including basic principles and applications in coastal and offshore engineering as well as coastal oceanography. Advanced analytical and numerical techniques are demonstrated. In this revised version, five chapters on recent developments in linear and nonlinear aspects have been added. The first is on detailed analyses in Wave/Structure Interactions. The second is a new section on Waves through a Marine Forest, a topic motivated by its possible relevance to tsunami reduction. The third is on Long Waves in Shallow Water and the fourth is an update on Broad-Banded Nonlinear Surface Waves in the Open Sea to include new findings in this topic. The fifth is an expanded chapter on Numerical Simulation of Nonlinear Wave Dynamics to include predictions of nonlinear spectral evolution and rogue wave occurrence and dynamics using large-scale phase-resolved simulations. This revised version also includes recent developments in precorrected-FFT accelerated O(N log N) low- and high-order boundary element methods for the computation of fully nonlinear wave-wave and wave-body interactions.Theory and Applications of Ocean Surface Waves (2016) will be invaluable for graduate students and researchers in coastal and ocean engineering, geophysical fluid dynamicists interested in water waves, and theoretical scientists and applied mathematicians wishing to develop new techniques for challenging problems or to apply techniques existing elsewhere.
Download or read book Asymptotic Analysis and the Numerical Solution of Partial Differential Equations written by Hans G. Kaper and published by CRC Press. This book was released on 1991-02-25 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per
Download or read book Dynamical Issues in Combustion Theory written by Paul C. Fife and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications DYNAMICAL ISSUES IN COMBUSTION THEORY is based on the proceedings of a workshop which was an integral part of the 1989-90 IMA program on "Dynamical Systems and their Applications." The aim of this workshop was to cross-fertilize research groups working in topics of current interest in combustion dynamics and mathematical methods applicable thereto. We thank Shui-Nee Chow, Martin Golubitsky, Richard McGehee, George R. Sell, Paul Fife, Amable Liiian and Foreman Williams for organizing the meeting. We especially thank Paul Fife, Amable Liiilin and Foreman Williams for editing the proceedings. We also take this opportunity to thank those agencies whose financial support made the workshop possible: the Army Research Office, the National Science Foundation and the Office of Naval Research. Avner Friedman Willard Miller, Jr. ix PREFACE The world ofcombustion phenomena is rich in problems intriguing to the math ematical scientist. They offer challenges on several fronts: (1) modeling, which involves the elucidation of the essential features of a given phenomenon through physical insight and knowledge of experimental results, (2) devising appropriate asymptotic and computational methods, and (3) developing sound mathematical theories. Papers in the present volume, which are based on talks given at the Workshop on Dynamical Issues in Combustion Theory in November, 1989, describe how all of these challenges have been met for particular examples within a number of common combustion scenarios: reactiveshocks, low Mach number premixed reactive flow, nonpremixed phenomena, and solid propellants.
Download or read book 3 D Surface Geometry and Reconstruction Developing Concepts and Applications written by Chandra Pati, Umesh and published by IGI Global. This book was released on 2012-02-29 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book provides developers and scholars with an extensive collection of research articles in the expanding field of 3D reconstruction, investigating the concepts, methodologies, applications and recent developments in the field of 3D reconstruction"--
Download or read book Echocardiography written by Gani Bajraktari and published by BoD – Books on Demand. This book was released on 2012-01-18 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book "Echocardiography - New Techniques" brings worldwide contributions from highly acclaimed clinical and imaging science investigators, and representatives from academic medical centers. Each chapter is designed and written to be accessible to those with a basic knowledge of echocardiography. Additionally, the chapters are meant to be stimulating and educational to the experts and investigators in the field of echocardiography. This book is aimed primarily at cardiology fellows on their basic echocardiography rotation, fellows in general internal medicine, radiology and emergency medicine, and experts in the arena of echocardiography. Over the last few decades, the rate of technological advancements has developed dramatically, resulting in new techniques and improved echocardiographic imaging. The authors of this book focused on presenting the most advanced techniques useful in today's research and in daily clinical practice. These advanced techniques are utilized in the detection of different cardiac pathologies in patients, in contributing to their clinical decision, as well as follow-up and outcome predictions. In addition to the advanced techniques covered, this book expounds upon several special pathologies with respect to the functions of echocardiography.
Download or read book A Basic Guide to Uniqueness Problems for Evolutionary Differential Equations written by Mi-Ho Giga and published by Springer Nature. This book was released on 2023-10-16 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the issue of uniqueness of a solution to a problem – a very important topic in science and technology, particularly in the field of partial differential equations, where uniqueness guarantees that certain partial differential equations are sufficient to model a given phenomenon. This book is intended to be a short introduction to uniqueness questions for initial value problems. One often weakens the notion of a solution to include non-differentiable solutions. Such a solution is called a weak solution. It is easier to find a weak solution, but it is more difficult to establish its uniqueness. This book examines three very fundamental equations: ordinary differential equations, scalar conservation laws, and Hamilton-Jacobi equations. Starting from the standard Gronwall inequality, this book discusses less regular ordinary differential equations. It includes an introduction of advanced topics like the theory of maximal monotone operators as well as what is called DiPerna-Lions theory, which is still an active research area. For conservation laws, the uniqueness of entropy solution, a special (discontinuous) weak solution is explained. For Hamilton-Jacobi equations, several uniqueness results are established for a viscosity solution, a kind of a non-differentiable weak solution. The uniqueness of discontinuous viscosity solution is also discussed. A detailed proof is given for each uniqueness statement. The reader is expected to learn various fundamental ideas and techniques in mathematical analysis for partial differential equations by establishing uniqueness. No prerequisite other than simple calculus and linear algebra is necessary. For the reader’s convenience, a list of basic terminology is given at the end of this book.
Download or read book Calculus of Variations and Partial Differential Equations written by Luigi Ambrosio and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.
