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Curvature A Variational Approach
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Book Synopsis Curvature: A Variational Approach by : A. Agrachev
Download or read book Curvature: A Variational Approach written by A. Agrachev and published by American Mathematical Soc.. This book was released on 2019-01-08 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: The curvature discussed in this paper is a far reaching generalization of the Riemannian sectional curvature. The authors give a unified definition of curvature which applies to a wide class of geometric structures whose geodesics arise from optimal control problems, including Riemannian, sub-Riemannian, Finsler and sub-Finsler spaces. Special attention is paid to the sub-Riemannian (or Carnot–Carathéodory) metric spaces. The authors' construction of curvature is direct and naive, and similar to the original approach of Riemann. In particular, they extract geometric invariants from the asymptotics of the cost of optimal control problems. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces.
Book Synopsis A Variational Approach to Structural Analysis by : David V. Wallerstein
Download or read book A Variational Approach to Structural Analysis written by David V. Wallerstein and published by John Wiley & Sons. This book was released on 2002 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: An insightful examination of the numerical methods used to develop finite element methods A Variational Approach to Structural Analysis provides readers with the underpinnings of the finite element method (FEM) while highlighting the power and pitfalls of virtual methods. In an easy-to-follow, logical format, this book gives complete coverage of the principle of virtual work, complementary virtual work and energy methods, and static and dynamic stability concepts. The first two chapters prepare the reader with preliminary material, introducing in detail the variational approach used in the book as well as reviewing the equilibrium and compatibility equations of mechanics. The next chapter, on virtual work, teaches how to use kinematical formulations for the determination of the required strain relationships for straight, curved, and thin walled beams. The chapters on complementary virtual work and energy methods are problem-solving chapters that incorporate Castigliano's first theorem, the Engesser-Crotti theorem, and the Galerkin method. In the final chapter, the reader is introduced to various geometric measures of strain and revisits straight, curved, and thin walled beams by examining them in a deformed geometry. Based on nearly two decades of work on the development of the world's most used FEM code, A Variational Approach to Structural Analysis has been designed as a self-contained, single-source reference for mechanical, aerospace, and civil engineering professionals. The book's straightforward style also provides accessible instruction for graduate students in aeronautical, civil, mechanical, and engineering mechanics courses.
Book Synopsis Variational Approach to Pursuit-Evasion Game with Curvature Constraint by :
Download or read book Variational Approach to Pursuit-Evasion Game with Curvature Constraint written by and published by . This book was released on 2000 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Variational Methods with Applications in Science and Engineering by : Kevin W. Cassel
Download or read book Variational Methods with Applications in Science and Engineering written by Kevin W. Cassel and published by Cambridge University Press. This book was released on 2013-07-22 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is a resurgence of applications in which the calculus of variations has direct relevance. In addition to application to solid mechanics and dynamics, it is now being applied in a variety of numerical methods, numerical grid generation, modern physics, various optimization settings and fluid dynamics. Many applications, such as nonlinear optimal control theory applied to continuous systems, have only recently become tractable computationally, with the advent of advanced algorithms and large computer systems. This book reflects the strong connection between calculus of variations and the applications for which variational methods form the fundamental foundation. The mathematical fundamentals of calculus of variations (at least those necessary to pursue applications) is rather compact and is contained in a single chapter of the book. The majority of the text consists of applications of variational calculus for a variety of fields.
Book Synopsis Variational Methods for Discontinuous Structures by : Raul Serapioni
Download or read book Variational Methods for Discontinuous Structures written by Raul Serapioni and published by Birkhäuser. This book was released on 2012-12-06 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years many researchers in material science have focused their attention on the study of composite materials, equilibrium of crystals and crack distribution in continua subject to loads. At the same time several new issues in computer vision and image processing have been studied in depth. The understanding of many of these problems has made significant progress thanks to new methods developed in calculus of variations, geometric measure theory and partial differential equations. In particular, new technical tools have been introduced and successfully applied. For example, in order to describe the geometrical complexity of unknown patterns, a new class of problems in calculus of variations has been introduced together with a suitable functional setting: the free-discontinuity problems and the special BV and BH functions. The conference held at Villa Olmo on Lake Como in September 1994 spawned successful discussion of these topics among mathematicians, experts in computer science and material scientists.
Book Synopsis A Variational Approach to Fracture and Other Inelastic Phenomena by : Gianpietro Del Piero
Download or read book A Variational Approach to Fracture and Other Inelastic Phenomena written by Gianpietro Del Piero and published by Springer Science & Business Media. This book was released on 2013-08-30 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book exposes a number of mathematical models for fracture of growing difficulty. All models are treated in a unified way, based on incremental energy minimization. They differ from each other by the assumptions made on the inelastic part of the total energy, here called the "cohesive energy". Each model describes a specific aspect of material response, and particular care is devoted to underline the correspondence of each model to the experiments. The content of the book is a re-elaboration of the lectures delivered at the First Sperlonga Summer School on Mechanics and Engineering Sciences in September 2011. In the year and a half elapsed after the course, the material has been revised and enriched with new and partially unpublished results. Significant additions have been introduced in the occasion of the course "The variational approach to fracture and other inelastic phenomena", delivered at SISSA, Trieste, in March 2013. The Notes reflect a research line carried on by the writer over the years, addressed to a comprehensive description of the many aspects of the phenomenon of fracture, and to its relations with other phenomena, such as the formation of microstructure and the changes in the material’s strength induced by plasticity and damage. Reprinted from the Journal of Elasticity, volume 112, issue 1, 2013.
Book Synopsis Handbook of Variational Methods for Nonlinear Geometric Data by : Philipp Grohs
Download or read book Handbook of Variational Methods for Nonlinear Geometric Data written by Philipp Grohs and published by Springer Nature. This book was released on 2020-04-03 with total page 701 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art. Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance. Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.
Book Synopsis Curvature and Variational Modeling in Physics and Biophysics by : Oscar J. Garay
Download or read book Curvature and Variational Modeling in Physics and Biophysics written by Oscar J. Garay and published by American Institute of Physics. This book was released on 2008-04-22 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The School was mainly addressed to young researchers coming from different disciplines with a common interest in variational problems defined by curvature energy functionals. Curves and surfaces obtained as critical points of these functionals are investigated from a theoretical and numerical point of view. Applications are shown in Geometry, Physics and Biophysics. An elementary background in Differential Geometry and Variational Calculus is assumed.
Book Synopsis Variational Methods in Nonlinear Analysis by : Antonio Ambrosetti
Download or read book Variational Methods in Nonlinear Analysis written by Antonio Ambrosetti and published by CRC Press. This book was released on 1995 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very Good,No Highlights or Markup,all pages are intact.
Book Synopsis Designing Fair Curves and Surfaces by : Nickolas S. Sapidis
Download or read book Designing Fair Curves and Surfaces written by Nickolas S. Sapidis and published by SIAM. This book was released on 1994-01-01 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This state-of-the-art study of the techniques used for designing curves and surfaces for computer-aided design applications focuses on the principle that fair shapes are always free of unessential features and are simple in design. The authors define fairness mathematically, demonstrate how newly developed curve and surface schemes guarantee fairness, and assist the user in identifying and removing shape aberrations in a surface model without destroying the principal shape characteristics of the model. Aesthetic aspects of geometric modeling are of vital importance in industrial design and modeling, particularly in the automobile and aerospace industries. Any engineer working in computer-aided design, computer-aided manufacturing, or computer-aided engineering will want to add this volume to his or her library. Researchers who have a familiarity with basic techniques in computer-aided graphic design and some knowledge of differential geometry will find this book a helpful reference. It is essential reading for statisticians working on approximation or smoothing of data with mathematical curves or surfaces.
Author :R. Tyrrell Rockafellar Publisher :Springer Science & Business Media ISBN 13 :3642024319 Total Pages :747 pages Book Rating :4.6/5 (42 download)
Book Synopsis Variational Analysis by : R. Tyrrell Rockafellar
Download or read book Variational Analysis written by R. Tyrrell Rockafellar and published by Springer Science & Business Media. This book was released on 2009-06-26 with total page 747 pages. Available in PDF, EPUB and Kindle. Book excerpt: From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.
Book Synopsis Variational Methods by : Michael Struwe
Download or read book Variational Methods written by Michael Struwe and published by Springer Science & Business Media. This book was released on 2008-11-05 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This, the fourth edition of Stuwe’s book on the calculus of variations, surveys new developments in this exciting field. It also gives a concise introduction to variational methods. In particular it includes the proof for the convergence of the Yamabe flow and a detailed treatment of the phenomenon of blow-up. Recently discovered results for backward bubbling in the heat flow for harmonic maps or surfaces are discussed. A number of changes have been made throughout the text.
Book Synopsis Variational Methods in Molecular Modeling by : Jianzhong Wu
Download or read book Variational Methods in Molecular Modeling written by Jianzhong Wu and published by Springer. This book was released on 2016-12-17 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents tutorial overviews for many applications of variational methods to molecular modeling. Topics discussed include the Gibbs-Bogoliubov-Feynman variational principle, square-gradient models, classical density functional theories, self-consistent-field theories, phase-field methods, Ginzburg-Landau and Helfrich-type phenomenological models, dynamical density functional theory, and variational Monte Carlo methods. Illustrative examples are given to facilitate understanding of the basic concepts and quantitative prediction of the properties and rich behavior of diverse many-body systems ranging from inhomogeneous fluids, electrolytes and ionic liquids in micropores, colloidal dispersions, liquid crystals, polymer blends, lipid membranes, microemulsions, magnetic materials and high-temperature superconductors. All chapters are written by leading experts in the field and illustrated with tutorial examples for their practical applications to specific subjects. With emphasis placed on physical understanding rather than on rigorous mathematical derivations, the content is accessible to graduate students and researchers in the broad areas of materials science and engineering, chemistry, chemical and biomolecular engineering, applied mathematics, condensed-matter physics, without specific training in theoretical physics or calculus of variations.
Download or read book Variational Methods written by BERESTYCKI and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the framework of the "Annee non lineaire" (the special nonlinear year) sponsored by the C.N.R.S. (the French National Center for Scien tific Research), a meeting was held in Paris in June 1988. It took place in the Conference Hall of the Ministere de la Recherche and had as an organizing theme the topic of "Variational Problems." Nonlinear analysis has been one of the leading themes in mathemat ical research for the past decade. The use of direct variational methods has been particularly successful in understanding problems arising from physics and geometry. The growth of nonlinear analysis is largely due to the wealth of ap plications from various domains of sciences and industrial applica tions. Most of the papers gathered in this volume have their origin in applications: from mechanics, the study of Hamiltonian systems, from physics, from the recent mathematical theory of liquid crystals, from geometry, relativity, etc. Clearly, no single volume could pretend to cover the whole scope of nonlinear variational problems. We have chosen to concentrate on three main aspects of these problems, organizing them roughly around the following topics: 1. Variational methods in partial differential equations in mathemat ical physics 2. Variational problems in geometry 3. Hamiltonian systems and related topics.
Book Synopsis Variational Approach to Hyperbolic Free Boundary Problems by : Seiro Omata
Download or read book Variational Approach to Hyperbolic Free Boundary Problems written by Seiro Omata and published by Springer Nature. This book was released on 2022-11-28 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the study of hyperbolic free boundary problems possessing variational structure. Such problems can be used to model, among others, oscillatory motion of a droplet on a surface or bouncing of an elastic body against a rigid obstacle. In the case of the droplet, for example, the membrane surrounding the fluid in general forms a positive contact angle with the obstacle, and therefore the second derivative is only a measure at the contact free boundary set. We will show how to derive the mathematical problem for a few physical systems starting from the action functional, discuss the mathematical theory, and introduce methods for its numerical solution. The mathematical theory and numerical methods depart from the classical approaches in that they are based on semi-discretization in time, which facilitates the application of the modern theory of calculus of variations.
Book Synopsis Energy Minimization Methods in Computer Vision and Pattern Recognition by : Daniel Cremers
Download or read book Energy Minimization Methods in Computer Vision and Pattern Recognition written by Daniel Cremers and published by Springer Science & Business Media. This book was released on 2009-08-11 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2009, held in Bonn, Germany in August 2009. The 18 revised full papers, 18 poster papers and 3 keynote lectures presented were carefully reviewed and selected from 75 submissions. The papers are organized in topical sections on discrete optimization and Markov random fields, partial differential equations, segmentation and tracking, shape optimization and registration, inpainting and image denoising, color and texture and statistics and learning.
Book Synopsis Elliptic and Parabolic Methods in Geometry by : Ben Chow
Download or read book Elliptic and Parabolic Methods in Geometry written by Ben Chow and published by CRC Press. This book was released on 1996-10-15 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book documents the results of a workshop held at the Geometry Center (University of Minnesota, Minneapolis) and captures the excitement of the week.
