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Gradient Flows
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Download or read book Gradient Flows written by Luigi Ambrosio and published by Springer Science & Business Media. This book was released on 2008-10-29 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.
Download or read book Gradient Flows written by Luigi Ambrosio and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to a theory of gradient ?ows in spaces which are not nec- sarily endowed with a natural linear or di?erentiable structure. It is made of two parts, the ?rst one concerning gradient ?ows in metric spaces and the second one 2 1 devoted to gradient ?ows in the L -Wasserstein space of probability measures on p a separable Hilbert space X (we consider the L -Wasserstein distance, p? (1,?), as well). The two parts have some connections, due to the fact that the Wasserstein space of probability measures provides an important model to which the “metric” theory applies, but the book is conceived in such a way that the two parts can be read independently, the ?rst one by the reader more interested to Non-Smooth Analysis and Analysis in Metric Spaces, and the second one by the reader more oriented to theapplications in Partial Di?erential Equations, Measure Theory and Probability.
Book Synopsis The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces by : Karl-Theodor Sturm
Download or read book The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces written by Karl-Theodor Sturm and published by American Mathematical Society. This book was released on 2023-11-27 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis The Ricci Flow in Riemannian Geometry by : Ben Andrews
Download or read book The Ricci Flow in Riemannian Geometry written by Ben Andrews and published by Springer Science & Business Media. This book was released on 2011 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.
Book Synopsis An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows by : Alessio Figalli
Download or read book An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows written by Alessio Figalli and published by European Mathematical Society. This book was released on 2023-05-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to optimal transport, and it is intended as a starting point for any researcher who wants to enter into this beautiful subject. The presentation focuses on the essential topics of the theory: Kantorovich duality, existence and uniqueness of optimal transport maps, Wasserstein distances, the JKO scheme, Otto's calculus, and Wasserstein gradient flows. At the end, a presentation of some selected applications of optimal transport is given. Suitable for a course at the graduate level, the book also includes an appendix with a series of exercises along with their solutions. The second edition contains a number of additions, such as a new section on the Brunn–Minkowski inequality, new exercises, and various corrections throughout the text.
Book Synopsis Lectures on Optimal Transport by : Luigi Ambrosio
Download or read book Lectures on Optimal Transport written by Luigi Ambrosio and published by Springer Nature. This book was released on 2021-07-22 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport. It originated from the teaching experience of the first author in the Scuola Normale Superiore, where a course on optimal transport and its applications has been given many times during the last 20 years. The topics and the tools were chosen at a sufficiently general and advanced level so that the student or scholar interested in a more specific theme would gain from the book the necessary background to explore it. After a large and detailed introduction to classical theory, more specific attention is devoted to applications to geometric and functional inequalities and to partial differential equations.
Book Synopsis Optimal Transport for Applied Mathematicians by : Filippo Santambrogio
Download or read book Optimal Transport for Applied Mathematicians written by Filippo Santambrogio and published by Birkhäuser. This book was released on 2015-10-17 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current research in optimal transport and the tools which are most useful for its applications. Full proofs are used to illustrate mathematical concepts and each chapter includes a section that discusses applications of optimal transport to various areas, such as economics, finance, potential games, image processing and fluid dynamics. Several topics are covered that have never been previously in books on this subject, such as the Knothe transport, the properties of functionals on measures, the Dacorogna-Moser flow, the formulation through minimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods. Graduate students and researchers in both pure and applied mathematics interested in the problems and applications of optimal transport will find this to be an invaluable resource.
Book Synopsis Topics in Applied Analysis and Optimisation by : Michael Hintermüller
Download or read book Topics in Applied Analysis and Optimisation written by Michael Hintermüller and published by Springer Nature. This book was released on 2019-11-27 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises selected, revised papers from the Joint CIM-WIAS Workshop, TAAO 2017, held in Lisbon, Portugal, in December 2017. The workshop brought together experts from research groups at the Weierstrass Institute in Berlin and mathematics centres in Portugal to present and discuss current scientific topics and to promote existing and future collaborations. The papers include the following topics: PDEs with applications to material sciences, thermodynamics and laser dynamics, scientific computing, nonlinear optimization and stochastic analysis.
Book Synopsis Applications of Artificial Intelligence and Neural Systems to Data Science by : Anna Esposito
Download or read book Applications of Artificial Intelligence and Neural Systems to Data Science written by Anna Esposito and published by Springer Nature. This book was released on 2023-09-02 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview on the current progresses in artificial intelligence and neural nets in data science. The book is reporting on intelligent algorithms and applications modeling, prediction, and recognition tasks and many other application areas supporting complex multimodal systems to enhance and improve human–machine or human–human interactions. This field is broadly addressed by the scientific communities and has a strong commercial impact since investigates on the theoretical frameworks supporting the implementation of sophisticated computational intelligence tools. Such tools will support multidisciplinary aspects of data mining and data processing characterizing appropriate system reactions to human-machine interactional exchanges in interactive scenarios. The emotional issue has recently gained increasing attention for such complex systems due to its relevance in helping in the most common human tasks (like cognitive processes, perception, learning, communication, and even "rational" decision-making) and therefore improving the quality of life of the end users.
Book Synopsis Optimal Transport by : Yann Ollivier
Download or read book Optimal Transport written by Yann Ollivier and published by Cambridge University Press. This book was released on 2014-08-07 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of optimal transportation has its origins in the eighteenth century when the problem of transporting resources at a minimal cost was first formalised. Through subsequent developments, particularly in recent decades, it has become a powerful modern theory. This book contains the proceedings of the summer school 'Optimal Transportation: Theory and Applications' held at the Fourier Institute in Grenoble. The event brought together mathematicians from pure and applied mathematics, astrophysics, economics and computer science. Part I of this book is devoted to introductory lecture notes accessible to graduate students, while Part II contains research papers. Together, they represent a valuable resource on both fundamental and advanced aspects of optimal transportation, its applications, and its interactions with analysis, geometry, PDE and probability, urban planning and economics. Topics covered include Ricci flow, the Euler equations, functional inequalities, curvature-dimension conditions, and traffic congestion.
Book Synopsis Analysis of Turbulent Flows with Computer Programs by : Tuncer Cebeci
Download or read book Analysis of Turbulent Flows with Computer Programs written by Tuncer Cebeci and published by Butterworth-Heinemann. This book was released on 2013-02-26 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis of Turbulent Flows is written by one of the most prolific authors in the field of CFD. Professor of Aerodynamics at SUPAERO and Director of DMAE at ONERA, Professor Tuncer Cebeci calls on both his academic and industrial experience when presenting this work. Each chapter has been specifically constructed to provide a comprehensive overview of turbulent flow and its measurement. Analysis of Turbulent Flows serves as an advanced textbook for PhD candidates working in the field of CFD and is essential reading for researchers, practitioners in industry and MSc and MEng students. The field of CFD is strongly represented by the following corporate organizations: Boeing, Airbus, Thales, United Technologies and General Electric. Government bodies and academic institutions also have a strong interest in this exciting field. - An overview of the development and application of computational fluid dynamics (CFD), with real applications to industry - Contains a unique section on short-cut methods – simple approaches to practical engineering problems
Book Synopsis Modelling and Optimisation of Flows on Networks by : Luigi Ambrosio
Download or read book Modelling and Optimisation of Flows on Networks written by Luigi Ambrosio and published by Springer. This book was released on 2012-12-14 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years flows in networks have attracted the interest of many researchers from different areas, e.g. applied mathematicians, engineers, physicists, economists. The main reason for this ubiquity is the wide and diverse range of applications, such as vehicular traffic, supply chains, blood flow, irrigation channels, data networks and others. This book presents an extensive set of notes by world leaders on the main mathematical techniques used to address such problems, together with investigations into specific applications. The main focus is on partial differential equations in networks, but ordinary differential equations and optimal transport are also included. Moreover, the modeling is completed by analysis, numerics, control and optimization of flows in networks. The book will be a valuable resource for every researcher or student interested in the subject.
Book Synopsis Analysis and Numerics of Partial Differential Equations by : Franco Brezzi
Download or read book Analysis and Numerics of Partial Differential Equations written by Franco Brezzi and published by Springer Science & Business Media. This book was released on 2012-12-22 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a selection of contributions offered by friends, collaborators, past students in memory of Enrico Magenes. The first part gives a wide historical perspective of Magenes' work in his 50-year mathematical career; the second part contains original research papers, and shows how ideas, methods, and techniques introduced by Magenes and his collaborators still have an impact on the current research in Mathematics.
Book Synopsis Flows on 2-dimensional Manifolds by : Igor Nikolaev
Download or read book Flows on 2-dimensional Manifolds written by Igor Nikolaev and published by Springer. This book was released on 2006-11-14 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time-evolution in low-dimensional topological spaces is a subject of puzzling vitality. This book is a state-of-the-art account, covering classical and new results. The volume comprises Poincaré-Bendixson, local and Morse-Smale theories, as well as a carefully written chapter on the invariants of surface flows. Of particular interest are chapters on the Anosov-Weil problem, C*-algebras and non-compact surfaces. The book invites graduate students and non-specialists to a fascinating realm of research. It is a valuable source of reference to the specialists.
Book Synopsis From Particle Systems to Partial Differential Equations III by : Patrícia Gonçalves
Download or read book From Particle Systems to Partial Differential Equations III written by Patrícia Gonçalves and published by Springer. This book was released on 2016-07-16 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main focus of this book is on different topics in probability theory, partial differential equations and kinetic theory, presenting some of the latest developments in these fields. It addresses mathematical problems concerning applications in physics, engineering, chemistry and biology that were presented at the Third International Conference on Particle Systems and Partial Differential Equations, held at the University of Minho, Braga, Portugal in December 2014. The purpose of the conference was to bring together prominent researchers working in the fields of particle systems and partial differential equations, providing a venue for them to present their latest findings and discuss their areas of expertise. Further, it was intended to introduce a vast and varied public, including young researchers, to the subject of interacting particle systems, its underlying motivation, and its relation to partial differential equations. This book will appeal to probabilists, analysts and those mathematicians whose work involves topics in mathematical physics, stochastic processes and differential equations in general, as well as those physicists whose work centers on statistical mechanics and kinetic theory.
Book Synopsis Interfaces: Modeling, Analysis, Numerics by : Eberhard Bänsch
Download or read book Interfaces: Modeling, Analysis, Numerics written by Eberhard Bänsch and published by Springer Nature. This book was released on 2023-11-11 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems appearing in geometry and in various applications, ranging from crystal growth, tumour growth, biological membranes to porous media, two-phase flows, fluid-structure interactions, and shape optimization. We first give an introduction to classical methods from differential geometry and systematically derive the governing equations from physical principles. Then we will analyse parametric approaches to interface evolution problems and derive numerical methods which will be thoroughly analysed. In addition, implicit descriptions of interfaces such as phase field and level set methods will be analysed. Finally, we will discuss numerical methods for complex interface evolutions and will focus on two phase flow problems as an important example of such evolutions.
Book Synopsis Introduction to the Modern Theory of Dynamical Systems by : Anatole Katok
Download or read book Introduction to the Modern Theory of Dynamical Systems written by Anatole Katok and published by Cambridge University Press. This book was released on 1995 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up.
