Anisotropic Isoperimetric Problems And Related Topics

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Anisotropic Isoperimetric Problems And Related Topics

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Author : Valentina Franceschi
language : en
Publisher: Springer Nature
Release Date : 2024-12-18

Anisotropic Isoperimetric Problems And Related Topics written by Valentina Franceschi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-18 with Mathematics categories.

This book contains contributions from speakers at the "Anisotropic Isoperimetric Problems & Related Topics" conference in Rome, held from Sep 5 to 9, 2022. The classic isoperimetric problem has fascinated mathematicians of all eras, starting from the ancient Greeks, due to its simple statement: what are the sets of a given volume with minimal perimeter? The problem is mathematically well understood, and it plays a crucial role in explaining physical phenomena such as soap bubble shapes. Variations of the problem, including weighted counterparts with density dependencies, representing inhomogeneity and anisotropy of the medium, broaden its applicability, even in non-Euclidean environments, and they allow for descriptions, e.g., of crystal shapes. At large, the perimeter's physical interpretation is that of an attractive force; hence, it also appears in describing systems of particles where a balance between attractive and repulsive forces appears. A prominent example is that of Gamow's liquid drop model for atomic nuclei, where protons are subject to the strong nuclear attractive force (represented by the perimeter) and the electromagnetic repulsive force (represented by a nonlocal term). Such a model has been shown to be sound, as it explains the basic characteristics of the nuclei, and it successfully predicts nuclear fission for nuclei with a large atomic number. Similar energy functionals model various physical and biological systems, showcasing the competition between short-range interfacial and long-range nonlocal terms, leading to pattern formation. The authors mention, e.g., the Ohta–Kawasaki model for microphase separation of diblock copolymers and the Yukawa potential for colloidal systems. Despite diverse systems, the emergence of microphases follows similar patterns, although rigorously proving this phenomenon remains a challenge. The book collects several contributions within these topics, shedding light on the current state of the art.

Fundamentals Of Structural Optimization Ii

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Author : Vladimir Kobelev
language : en
Publisher: Springer Nature
Release Date : 2024-09-14

Fundamentals Of Structural Optimization Ii written by Vladimir Kobelev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-14 with Mathematics categories.

This book provides a comprehensive overview of analytical methods for solving optimization problems, covering principles and mathematical techniques alongside numerical solution routines, including MAPLE and MAXIMA optimization routines. Each method is explained with practical applications and ANSYS APDL scripts for select problems. Chapters delve into topics such as scaling methods, torsion compliance, shape variation, topological optimization, anisotropic material properties, and differential geometry. Specific optimization problems, including stress minimization and mass reduction under constraints, are addressed. The book also explores isoperimetric inequalities and optimal material selection principles. Appendices offer insights into tensors, differential geometry, integral equations, and computer algebra codes. Overall, it's a comprehensive guide for engineers and researchers in structural optimization.

Geometric And Functional Inequalities And Recent Topics In Nonlinear Pdes

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Author : Emanuel Indrei
language : en
Publisher: American Mathematical Society
Release Date : 2023-01-09

Geometric And Functional Inequalities And Recent Topics In Nonlinear Pdes written by Emanuel Indrei and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-09 with Mathematics categories.

This volume contains the proceedings of the virtual conference on Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs, held from February 28–March 1, 2021, and hosted by Purdue University, West Lafayette, IN. The mathematical content of this volume is at the intersection of viscosity theory, Fourier analysis, mass transport theory, fractional elliptic theory, and geometric analysis. The reader will encounter, among others, the following topics: the principal-agent problem; Maxwell's equations; Liouville-type theorems for fully nonlinear elliptic equations; a doubly monotone flow for constant width bodies; and the edge dislocations problem for crystals that describes the equilibrium configurations by a nonlocal fractional Laplacian equation.

Vector Valued Partial Differential Equations And Applications

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Author : Bernard Dacorogna
language : en
Publisher: Springer
Release Date : 2017-05-29

Vector Valued Partial Differential Equations And Applications written by Bernard Dacorogna and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-29 with Mathematics categories.

Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini. It contains the following contributions: The pullback equation (Bernard Dacorogna), The stability of the isoperimetric inequality (Nicola Fusco), Mathematical problems in thin elastic sheets: scaling limits, packing, crumpling and singularities (Stefan Müller), and Aspects of PDEs related to fluid flows (Vladimir Sverák). These lectures are addressed to graduate students and researchers in the field.

Curvature Flows And Related Topics

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Author : A.. Damlamian
language : en
Publisher:
Release Date : 1995

Curvature Flows And Related Topics written by A.. Damlamian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Curvature categories.

Convex Bodies The Brunn Minkowski Theory

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Author : Rolf Schneider
language : en
Publisher: Cambridge University Press
Release Date : 2013-10-31

Convex Bodies The Brunn Minkowski Theory written by Rolf Schneider and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-31 with Mathematics categories.

At the heart of this monograph is the Brunn–Minkowski theory, which can be used to great effect in studying such ideas as volume and surface area and their generalizations. In particular, the notions of mixed volume and mixed area measure arise naturally and the fundamental inequalities that are satisfied by mixed volumes are considered here in detail. The author presents a comprehensive introduction to convex bodies, including full proofs for some deeper theorems. The book provides hints and pointers to connections with other fields and an exhaustive reference list. This second edition has been considerably expanded to reflect the rapid developments of the past two decades. It includes new chapters on valuations on convex bodies, on extensions like the Lp Brunn–Minkowski theory, and on affine constructions and inequalities. There are also many supplements and updates to the original chapters, and a substantial expansion of chapter notes and references.

Topics In Modern Differential Geometry

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Author : Stefan Haesen
language : en
Publisher: Springer
Release Date : 2016-12-21

Topics In Modern Differential Geometry written by Stefan Haesen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-21 with Mathematics categories.

A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.

Convexity From The Geometric Point Of View

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Author : Vitor Balestro
language : en
Publisher: Springer Nature
Release Date : 2024-07-14

Convexity From The Geometric Point Of View written by Vitor Balestro and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-14 with Mathematics categories.

This text gives a comprehensive introduction to the “common core” of convex geometry. Basic concepts and tools which are present in all branches of that field are presented with a highly didactic approach. Mainly directed to graduate and advanced undergraduates, the book is self-contained in such a way that it can be read by anyone who has standard undergraduate knowledge of analysis and of linear algebra. Additionally, it can be used as a single reference for a complete introduction to convex geometry, and the content coverage is sufficiently broad that the reader may gain a glimpse of the entire breadth of the field and various subfields. The book is suitable as a primary text for courses in convex geometry and also in discrete geometry (including polytopes). It is also appropriate for survey type courses in Banach space theory, convex analysis, differential geometry, and applications of measure theory. Solutions to all exercises are available to instructors who adopt the text for coursework. Most chapters use the same structure with the first part presenting theory and the next containing a healthy range of exercises. Some of the exercises may even be considered as short introductions to ideas which are not covered in the theory portion. Each chapter has a notes section offering a rich narrative to accompany the theory, illuminating the development of ideas, and providing overviews to the literature concerning the covered topics. In most cases, these notes bring the reader to the research front. The text includes many figures that illustrate concepts and some parts of the proofs, enabling the reader to have a better understanding of the geometric meaning of the ideas. An appendix containing basic (and geometric) measure theory collects useful information for convex geometers.

Issues In General And Specialized Mathematics Research 2013 Edition

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Author :
language : en
Publisher: ScholarlyEditions
Release Date : 2013-05-01

Issues In General And Specialized Mathematics Research 2013 Edition written by and has been published by ScholarlyEditions this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-01 with Mathematics categories.

Issues in General and Specialized Mathematics Research: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about General Mathematics. The editors have built Issues in General and Specialized Mathematics Research: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General Mathematics in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General and Specialized Mathematics Research: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Mathematical Reviews

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Author :
language : en
Publisher:
Release Date : 2007

Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.