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Author : Bergounioux Maitine
Publisher :
ISBN 13 : 9783110439267
Total Pages : 300 pages
Book Rating : 4.4/5 (392 download)
Download or read book Topological Optimization written by Bergounioux Maitine and published by . This book was released on 2016-03-01 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Maïtine Bergounioux
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110430509
Total Pages : 514 pages
Book Rating : 4.1/5 (14 download)
Download or read book Topological Optimization and Optimal Transport written by Maïtine Bergounioux and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-08-07 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: By discussing topics such as shape representations, relaxation theory and optimal transport, trends and synergies of mathematical tools required for optimization of geometry and topology of shapes are explored. Furthermore, applications in science and engineering, including economics, social sciences, biology, physics and image processing are covered. Contents Part I Geometric issues in PDE problems related to the infinity Laplace operator Solution of free boundary problems in the presence of geometric uncertainties Distributed and boundary control problems for the semidiscrete Cahn–Hilliard/Navier–Stokes system with nonsmooth Ginzburg–Landau energies High-order topological expansions for Helmholtz problems in 2D On a new phase field model for the approximation of interfacial energies of multiphase systems Optimization of eigenvalues and eigenmodes by using the adjoint method Discrete varifolds and surface approximation Part II Weak Monge–Ampere solutions of the semi-discrete optimal transportation problem Optimal transportation theory with repulsive costs Wardrop equilibria: long-term variant, degenerate anisotropic PDEs and numerical approximations On the Lagrangian branched transport model and the equivalence with its Eulerian formulation On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows Pressureless Euler equations with maximal density constraint: a time-splitting scheme Convergence of a fully discrete variational scheme for a thin-film equatio Interpretation of finite volume discretization schemes for the Fokker–Planck equation as gradient flows for the discrete Wasserstein distance
Author : Yann Ollivier
Publisher : Cambridge University Press
ISBN 13 : 110768949X
Total Pages : 317 pages
Book Rating : 4.1/5 (76 download)
Download or read book Optimal Transportation 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: Lecture notes and research papers on optimal transportation, its applications, and interactions with other areas of mathematics.
Author : Giuseppe Buttazzo
Publisher : Springer Science & Business Media
ISBN 13 : 3540857982
Total Pages : 161 pages
Book Rating : 4.5/5 (48 download)
Download or read book Optimal Urban Networks via Mass Transportation written by Giuseppe Buttazzo and published by Springer Science & Business Media. This book was released on 2008-12-03 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently much attention has been devoted to the optimization of transportation networks in a given geographic area. One assumes the distributions of population and of services/workplaces (i.e. the network's sources and sinks) are known, as well as the costs of movement with/without the network, and the cost of constructing/maintaining it. Both the long-term optimization and the short-term, "who goes where," optimization are considered. These models can also be adapted for the optimization of other types of networks, such as telecommunications, pipeline or drainage networks. In the monograph we study the most general problem settings, namely, when neither the shape nor even the topology of the network to be constructed is known a priori.
Author : Cédric Villani
Publisher : Springer Science & Business Media
ISBN 13 : 3540710507
Total Pages : 970 pages
Book Rating : 4.5/5 (47 download)
Download or read book Optimal Transport written by Cédric Villani and published by Springer Science & Business Media. This book was released on 2008-10-26 with total page 970 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.
Author : Guido Philippis
Publisher : Springer Science & Business Media
ISBN 13 : 887642458X
Total Pages : 186 pages
Book Rating : 4.8/5 (764 download)
Download or read book Regularity of Optimal Transport Maps and Applications written by Guido Philippis and published by Springer Science & Business Media. This book was released on 2013-06-28 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we study the regularity of optimal transport maps and its applications to the semi-geostrophic system. The first two chapters survey the known theory, in particular there is a self-contained proof of Brenier’ theorem on existence of optimal transport maps and of Caffarelli’s Theorem on Holder continuity of optimal maps. In the third and fourth chapter we start investigating Sobolev regularity of optimal transport maps, while in Chapter 5 we show how the above mentioned results allows to prove the existence of Eulerian solution to the semi-geostrophic equation. In Chapter 6 we prove partial regularity of optimal maps with respect to a generic cost functions (it is well known that in this case global regularity can not be expected). More precisely we show that if the target and source measure have smooth densities the optimal map is always smooth outside a closed set of measure zero.
Author : Cédric Villani
Publisher :
ISBN 13 : 9781316005149
Total Pages : 318 pages
Book Rating : 4.0/5 (51 download)
Download or read book Optimal Transport written by Cédric Villani and published by . This book was released on 2014-09-02 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lecture notes and research papers on optimal transportation, its applications, and interactions with other areas of mathematics.
Author : Martin Philip Bendsoe
Publisher : Springer Science & Business Media
ISBN 13 : 3662050862
Total Pages : 381 pages
Book Rating : 4.6/5 (62 download)
Download or read book Topology Optimization written by Martin Philip Bendsoe and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topology optimization method solves the basic enginee- ring problem of distributing a limited amount of material in a design space. The first edition of this book has become the standard text on optimal design which is concerned with the optimization of structural topology, shape and material. This edition, has been substantially revised and updated to reflect progress made in modelling and computational procedures. It also encompasses a comprehensive and unified description of the state-of-the-art of the so-called material distribution method, based on the use of mathematical programming and finite elements. Applications treated include not only structures but also materials and MEMS.
Author : Filippo Santambrogio
Publisher : Birkhäuser
ISBN 13 : 3319208284
Total Pages : 376 pages
Book Rating : 4.3/5 (192 download)
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.
Author : George I. N. Rozvany
Publisher : Springer Science & Business Media
ISBN 13 : 3709116430
Total Pages : 471 pages
Book Rating : 4.7/5 (91 download)
Download or read book Topology Optimization in Structural and Continuum Mechanics written by George I. N. Rozvany and published by Springer Science & Business Media. This book was released on 2013-09-20 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers new developments in structural topology optimization. Basic features and limitations of Michell’s truss theory, its extension to a broader class of support conditions, generalizations of truss topology optimization, and Michell continua are reviewed. For elastic bodies, the layout problems in linear elasticity are discussed and the method of relaxation by homogenization is outlined. The classical problem of free material design is shown to be reducible to a locking material problem, even in the multiload case. For structures subjected to dynamic loads, it is explained how they can be designed so that the structural eigenfrequencies of vibration are as far away as possible from a prescribed external excitation frequency (or a band of excitation frequencies) in order to avoid resonance phenomena with high vibration and noise levels. For diffusive and convective transport processes and multiphysics problems, applications of the density method are discussed. In order to take uncertainty in material parameters, geometry, and operating conditions into account, techniques of reliability-based design optimization are introduced and reviewed for their applicability to topology optimization.
Author : Cédric Villani
Publisher : American Mathematical Soc.
ISBN 13 : 1470467267
Total Pages : 370 pages
Book Rating : 4.4/5 (74 download)
Download or read book Topics in Optimal Transportation written by Cédric Villani and published by American Mathematical Soc.. This book was released on 2021-08-25 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive introduction to the theory of mass transportation with its many—and sometimes unexpected—applications. In a novel approach to the subject, the book both surveys the topic and includes a chapter of problems, making it a particularly useful graduate textbook. In 1781, Gaspard Monge defined the problem of “optimal transportation” (or the transferring of mass with the least possible amount of work), with applications to engineering in mind. In 1942, Leonid Kantorovich applied the newborn machinery of linear programming to Monge's problem, with applications to economics in mind. In 1987, Yann Brenier used optimal transportation to prove a new projection theorem on the set of measure preserving maps, with applications to fluid mechanics in mind. Each of these contributions marked the beginning of a whole mathematical theory, with many unexpected ramifications. Nowadays, the Monge-Kantorovich problem is used and studied by researchers from extremely diverse horizons, including probability theory, functional analysis, isoperimetry, partial differential equations, and even meteorology. Originating from a graduate course, the present volume is intended for graduate students and researchers, covering both theory and applications. Readers are only assumed to be familiar with the basics of measure theory and functional analysis.
Author : Gabriel Peyre
Publisher : Foundations and Trends(r) in M
ISBN 13 : 9781680835502
Total Pages : 272 pages
Book Rating : 4.8/5 (355 download)
Download or read book Computational Optimal Transport written by Gabriel Peyre and published by Foundations and Trends(r) in M. This book was released on 2019-02-12 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of Optimal Transport (OT) is to define geometric tools that are useful to compare probability distributions. Their use dates back to 1781. Recent years have witnessed a new revolution in the spread of OT, thanks to the emergence of approximate solvers that can scale to sizes and dimensions that are relevant to data sciences. Thanks to this newfound scalability, OT is being increasingly used to unlock various problems in imaging sciences (such as color or texture processing), computer vision and graphics (for shape manipulation) or machine learning (for regression, classification and density fitting). This monograph reviews OT with a bias toward numerical methods and their applications in data sciences, and sheds lights on the theoretical properties of OT that make it particularly useful for some of these applications. Computational Optimal Transport presents an overview of the main theoretical insights that support the practical effectiveness of OT before explaining how to turn these insights into fast computational schemes. Written for readers at all levels, the authors provide descriptions of foundational theory at two-levels. Generally accessible to all readers, more advanced readers can read the specially identified more general mathematical expositions of optimal transport tailored for discrete measures. Furthermore, several chapters deal with the interplay between continuous and discrete measures, and are thus targeting a more mathematically-inclined audience. This monograph will be a valuable reference for researchers and students wishing to get a thorough understanding of Computational Optimal Transport, a mathematical gem at the interface of probability, analysis and optimization.
Author : Gershon Wolansky
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110633175
Total Pages : 235 pages
Book Rating : 4.1/5 (16 download)
Download or read book Optimal Transport written by Gershon Wolansky and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-01-18 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-Chief J rgen Appell, W rzburg, Germany Honorary and Advisory Editors Catherine Bandle, Basel, Switzerland Alain Bensoussan, Richardson, Texas, USA Avner Friedman, Columbus, Ohio, USA Umberto Mosco, Worcester, Massachusetts, USA Louis Nirenberg, New York, USA Alfonso Vignoli, Rome, Italy Editorial Board Manuel del Pino, Bath, UK, and Santiago, Chile Mikio Kato, Nagano, Japan Wojciech Kryszewski, Toruń, Poland Vicenţiu D. Rădulescu, Krak w, Poland Simeon Reich, Haifa, Israel Please submit book proposals to J rgen Appell. Titles in planning include Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019) Tomasz W. Dlotko and Yejuan Wang, Critical Parabolic-Type Problems (2019) Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective (2019) Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy-Leray Potential (2020) Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020) Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)
Author : Natalya Kizilova
Publisher : World Scientific Publishing Company
ISBN 13 : 9789812838735
Total Pages : 200 pages
Book Rating : 4.8/5 (387 download)
Download or read book Optimal Transport Networks in Nature written by Natalya Kizilova and published by World Scientific Publishing Company. This book was released on 2010 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book presents a broad range of data on geometry and topology of long-distance liquid transport networks in nature including circulatory and respiratory systems of mammals, trophic fluid transport systems of animals, and conducting systems of higher plants. It is the very first book where evidence of the common design principles and optimal properties of the transportation networks of vascular plants and animals is provided. The book also provides a comprehensive comparative study of the recent measurement results and data analysis, including unique data obtained by the author to conduct systems of plant leaves of different shapes, sizes, venation types and evolutionary ages. It was shown that the mathematical solutions of the optimization problem for the animal and plant conducting systems lead to the same design principles, despite different physical conditions of the fluid transport.
Author : Jihong Zhu
Publisher : Elsevier
ISBN 13 : 0081021194
Total Pages : 296 pages
Book Rating : 4.0/5 (81 download)
Download or read book Topology Optimization in Engineering Structure Design written by Jihong Zhu and published by Elsevier. This book was released on 2016-11-08 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology Optimization in Engineering Structure Design explores the recent advances and applications of topology optimization in engineering structures design, with a particular focus on aircraft and aerospace structural systems.To meet the increasingly complex engineering challenges provided by rapid developments in these industries, structural optimization techniques have developed in conjunction with them over the past two decades. The latest methods and theories to improve mechanical performances and save structural weight under static, dynamic and thermal loads are summarized and explained in detail here, in addition to potential applications of topology optimization techniques such as shape preserving design, smart structure design and additive manufacturing.These new design strategies are illustrated by a host of worked examples, which are inspired by real engineering situations, some of which have been applied to practical structure design with significant effects. Written from a forward-looking applied engineering perspective, the authors not only summarize the latest developments in this field of structure design but also provide both theoretical knowledge and a practical guideline. This book should appeal to graduate students, researchers and engineers, in detailing how to use topology optimization methods to improve product design. Combines practical applications and topology optimization methodologies Provides problems inspired by real engineering difficulties Designed to help researchers in universities acquire more engineering requirements
Author : Nikolay V. Banichuk
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110531186
Total Pages : 206 pages
Book Rating : 4.1/5 (15 download)
Download or read book Optimal Structural Design written by Nikolay V. Banichuk and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-09-11 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph studies optimization problems for rigid punches in elastic media and for high-speed penetration of rigid strikers into deformed elastoplastic, concrete, and composite media using variational calculations, tools from functional analysis, and stochastic and min-max (guaranteed) optimization approaches with incomplete data. The book presents analytical and numerical results developed by the authors during the last ten years.
Author : Eric Cancès
Publisher : Springer Nature
ISBN 13 : 3031223403
Total Pages : 595 pages
Book Rating : 4.0/5 (312 download)
Download or read book Density Functional Theory written by Eric Cancès and published by Springer Nature. This book was released on 2023-07-18 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: Density functional theory (DFT) provides the most widely used models for simulating molecules and materials based on the fundamental laws of quantum mechanics. It plays a central role in a huge spectrum of applications in chemistry, physics, and materials science.Quantum mechanics describes a system of N interacting particles in the physical 3-dimensional space by a partial differential equation in 3N spatial variables. The standard numerical methods thus incur an exponential increase of computational effort with N, a phenomenon known as the curse of dimensionality; in practice these methods already fail beyond N=2. DFT overcomes this problem by 1) reformulating the N-body problem involving functions of 3N variables in terms of the density, a function of 3 variables, 2) approximating it by a pioneering hybrid approach which keeps important ab initio contributions and re-models the remainder in a data-driven way. This book intends to be an accessible, yet state-of-art text on DFT for graduate students and researchers in applied and computational mathematics, physics, chemistry, and materials science. It introduces and reviews the main models of DFT, covering their derivation and mathematical properties, numerical treatment, and applications.
