Download or read book Some Contributions to Geometric Variational Problems Involving Nonlocal Energies written by Marc Pegon and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is dedicated to the study of two separate geometric variational problems involving nonlocal energies: firstly, the geometry and singularities of fractional harmonic maps,and secondly, an iso perimetric problem with a repulsive integrable potential inspired by Gamow's liquid drop model for the atomic nucleus. On the first topic, we improve already-known results for minimizing 1/2-harmonic maps when the target manifold is a sphere by reducing the upperbound on the Haudorff dimension of the singular set, i.e., the set of points of discontinuity. Wealso characterize so-called minimizing 1/2-harmonic tangent maps from the plane into the unit circle S1, shedding light on the behavior of minimizing 1/2-harmonic maps from R2into S1 near singularities. Finally, when s ∈ (0, 1), we prove partial regularity results for s-harmonic maps into spheres in the stationary and minimizing case, obtaining sharp estimates on the Hausdorffd imension of the set of singularities, depending on the value of s. As for the second topic of the thesis, we study a minimization problem on sets of finite perimeter under a volume constraint, where the functional is the sum of a cohesive perimeter term and a repulsive term given by a general integrable symmetric kernel on Rn. We show that under reasonable assumptions on the behavior near the origin and on some of the moments of this kernel - which include physically relevant Bessel potentials - the problem admits large mass (or volume) minimizers. In addition,after normalization, those minimizers converge to the unit ball as the mass goes to infinity. By studying the stability of the ball, we show that without these assumptions, symmetry breaking can occur, that is, there are cases when the problem admits minimizers which cannot be the ball.
Download or read book Geometric Properties for Parabolic and Elliptic PDE s written by Rolando Magnanini and published by Springer Science & Business Media. This book was released on 2012-11-27 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of qualitative aspects of PDE's has always attracted much attention from the early beginnings. More recently, once basic issues about PDE's, such as existence, uniqueness and stability of solutions, have been understood quite well, research on topological and/or geometric properties of their solutions has become more intense. The study of these issues is attracting the interest of an increasing number of researchers and is now a broad and well-established research area, with contributions that often come from experts from disparate areas of mathematics, such as differential and convex geometry, functional analysis, calculus of variations, mathematical physics, to name a few. This volume collects a selection of original results and informative surveys by a group of international specialists in the field, analyzes new trends and techniques and aims at promoting scientific collaboration and stimulating future developments and perspectives in this very active area of research.
Download or read book Sets of Finite Perimeter and Geometric Variational Problems written by Francesco Maggi and published by Cambridge University Press. This book was released on 2012-08-09 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: The marriage of analytic power to geometric intuition drives many of today's mathematical advances, yet books that build the connection from an elementary level remain scarce. This engaging introduction to geometric measure theory bridges analysis and geometry, taking readers from basic theory to some of the most celebrated results in modern analysis. The theory of sets of finite perimeter provides a simple and effective framework. Topics covered include existence, regularity, analysis of singularities, characterization and symmetry results for minimizers in geometric variational problems, starting from the basics about Hausdorff measures in Euclidean spaces and ending with complete proofs of the regularity of area-minimizing hypersurfaces up to singular sets of codimension 8. Explanatory pictures, detailed proofs, exercises and remarks providing heuristic motivation and summarizing difficult arguments make this graduate-level textbook suitable for self-study and also a useful reference for researchers. Readers require only undergraduate analysis and basic measure theory.
Download or read book Introduction to Computational Chemistry written by Frank Jensen and published by John Wiley & Sons. This book was released on 2013-03-22 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Computational Chemistry, Second Edition provides a comprehensive account of the fundamental principles underlying different methods, ranging from classical to the sophisticated. Although comprehensive in its coverage, this textbook focuses on calculating molecular structures and (relative) energies and less on molecular properties or dynamical aspects. No prior knowledge of concepts specific to computational chemistry are assumed, but the reader will need some understanding of introductory quantum mechanics, linear algebra, and vector, differential and integral calculus.
Download or read book Analysis and Geometry in Control Theory and its Applications written by Piernicola Bettiol and published by Springer. This book was released on 2015-09-01 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the 1950s control theory has established itself as a major mathematical discipline, particularly suitable for application in a number of research fields, including advanced engineering design, economics and the medical sciences. However, since its emergence, there has been a need to rethink and extend fields such as calculus of variations, differential geometry and nonsmooth analysis, which are closely tied to research on applications. Today control theory is a rich source of basic abstract problems arising from applications, and provides an important frame of reference for investigating purely mathematical issues. In many fields of mathematics, the huge and growing scope of activity has been accompanied by fragmentation into a multitude of narrow specialties. However, outstanding advances are often the result of the quest for unifying themes and a synthesis of different approaches. Control theory and its applications are no exception. Here, the interaction between analysis and geometry has played a crucial role in the evolution of the field. This book collects some recent results, highlighting geometrical and analytical aspects and the possible connections between them. Applications provide the background, in the classical spirit of mutual interplay between abstract theory and problem-solving practice.
Download or read book Energy Research Abstracts written by and published by . This book was released on 1992-02 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlocal Diffusion and Applications written by Claudia Bucur and published by Springer. This book was released on 2016-04-08 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: Working in the fractional Laplace framework, this book provides models and theorems related to nonlocal diffusion phenomena. In addition to a simple probabilistic interpretation, some applications to water waves, crystal dislocations, nonlocal phase transitions, nonlocal minimal surfaces and Schrödinger equations are given. Furthermore, an example of an s-harmonic function, its harmonic extension and some insight into a fractional version of a classical conjecture due to De Giorgi are presented. Although the aim is primarily to gather some introductory material concerning applications of the fractional Laplacian, some of the proofs and results are new. The work is entirely self-contained, and readers who wish to pursue related subjects of interest are invited to consult the rich bibliography for guidance.
Download or read book Energy Minimization Methods in Computer Vision and Pattern Recognition written by Daniel Cremers and published by Springer. This book was released on 2009-08-17 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.
Download or read book Contemporary Research in Elliptic PDEs and Related Topics written by Serena Dipierro and published by Springer. This book was released on 2019-07-12 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects contributions from the speakers at an INdAM Intensive period held at the University of Bari in 2017. The contributions cover several aspects of partial differential equations whose development in recent years has experienced major breakthroughs in terms of both theory and applications. The topics covered include nonlocal equations, elliptic equations and systems, fully nonlinear equations, nonlinear parabolic equations, overdetermined boundary value problems, maximum principles, geometric analysis, control theory, mean field games, and bio-mathematics. The authors are trailblazers in these topics and present their work in a way that is exhaustive and clearly accessible to PhD students and early career researcher. As such, the book offers an excellent introduction to a variety of fundamental topics of contemporary investigation and inspires novel and high-quality research.
Download or read book Morphology of Condensed Matter written by Klaus R. Mecke and published by Springer. This book was released on 2008-01-11 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: The morphology of spatially stuctured materials is a rapidly growing field of research at the interface of statistical physics, applied mathematics and materials science. A wide spectrum of applications encompasses the flow through porous and composite materials as well as microemulsions and foams. Written as a set of lectures and tutorial reviews leading up to the forefront of research, this book will be both a compendium for the experienced researcher as well as a high level introductory text for postgraduate students and nonspecialist researchers working in related areas.
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1974 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied mechanics reviews written by and published by . This book was released on 1948 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Journal of Applied Mechanics written by and published by . This book was released on 1991 with total page 1158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1992 with total page 1572 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Encyclopedia of Physical Organic Chemistry 6 Volume Set written by Zerong Wang and published by John Wiley & Sons. This book was released on 2017-04-17 with total page 4542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner of 2018 PROSE Award for MULTIVOLUME REFERENCE/SCIENCE This encyclopedia offers a comprehensive and easy reference to physical organic chemistry (POC) methodology and techniques. It puts POC, a classical and fundamental discipline of chemistry, into the context of modern and dynamic fields like biochemical processes, materials science, and molecular electronics. Covers basic terms and theories into organic reactions and mechanisms, molecular designs and syntheses, tools and experimental techniques, and applications and future directions Includes coverage of green chemistry and polymerization reactions Reviews different strategies for molecular design and synthesis of functional molecules Discusses computational methods, software packages, and more than 34 kinds of spectroscopies and techniques for studying structures and mechanisms Explores applications in areas from biology to materials science The Encyclopedia of Physical Organic Chemistry has won the 2018 PROSE Award for MULTIVOLUME REFERENCE/SCIENCE. The PROSE Awards recognize the best books, journals and digital content produced by professional and scholarly publishers. Submissions are reviewed by a panel of 18 judges that includes editors, academics, publishers and research librarians who evaluate each work for its contribution to professional and scholarly publishing. You can find out more at: proseawards.com Also available as an online edition for your library, for more details visit Wiley Online Library
Download or read book Physical Review written by and published by . This book was released on 2000-04 with total page 1432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publishes papers that report results of research in statistical physics, plasmas, fluids, and related interdisciplinary topics. There are sections on (1) methods of statistical physics, (2) classical fluids, (3) liquid crystals, (4) diffusion-limited aggregation, and dendritic growth, (5) biological physics, (6) plasma physics, (7) physics of beams, (8) classical physics, including nonlinear media, and (9) computational physics.
Download or read book Condensed Matter Field Theory written by Alexander Altland and published by Cambridge University Press. This book was released on 2010-03-11 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.
