Soap Bubble Clusters And Constant Mean Curvature Surfaces

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Soap Bubble Clusters And Constant Mean Curvature Surfaces

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Author : Société mathématique de France. Journées
language : en
Publisher:
Release Date : 1993

Soap Bubble Clusters And Constant Mean Curvature Surfaces written by Société mathématique de France. Journées and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Calculus of variations categories.

Geometric Measure Theory

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Author : Frank Morgan
language : en
Publisher: Academic Press
Release Date : 2008-09-09

Geometric Measure Theory written by Frank Morgan and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-09 with Mathematics categories.

Geometric Measure Theory, Fourth Edition, is an excellent text for introducing ideas from geometric measure theory and the calculus of variations to beginning graduate students and researchers.This updated edition contains abundant illustrations, examples, exercises, and solutions; and the latest results on soap bubble clusters, including a new chapter on Double Bubbles in Spheres, Gauss Space, and Tori. It also includes a new chapter on Manifolds with Density and Perelman's Proof of the Poincaré Conjecture.This text is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Morgan emphasizes geometry over proofs and technicalities providing a fast and efficient insight into many aspects of the subject.New to the 4th edition:* Abundant illustrations, examples, exercises, and solutions.* The latest results on soap bubble clusters, including a new chapter on "Double Bubbles in Spheres, Gauss Space, and Tori."* A new chapter on "Manifolds with Density and Perelman's Proof of the Poincaré Conjecture."* Contributions by undergraduates.

The Kelvin Problem

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Author : Denis Weaire
language : en
Publisher: CRC Press
Release Date : 1997-09-09

The Kelvin Problem written by Denis Weaire and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-09-09 with Science categories.

In 1887, Kelvin posed one of the most discussed scientific questions of the last 100 years - the problem of the division of three-dimensional space into cells of equal volume with minimal area. It has interested mathematicians, physical scientists and biologists ever since and the problem has scientific relevance to foams, emulsions and many other kinds of cells. In the 1990s, a more complex structure was discovered by Robert Phelan and Denis Weaire and it remains the best yet found. This text assesses the various merits of Kelvin's structure and of that discovered by Weaire and Phelan. It also looks at the problem of proof that Weaire's structure having minimal area remains open.

Six Themes On Variation

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Author : Steven James Cox
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Six Themes On Variation written by Steven James Cox and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Computers categories.

The calculus of variations is a beautiful subject with a rich history and with origins in the minimization problems of calculus. Although it is now at the core of many modern mathematical fields, it does not have a well-defined place in most undergraduate mathematics curricula. This volume should nevertheless give the undergraduate reader a sense of its great character and importance. Interesting functionals, such as area or energy, often give rise to problems whose most natural solution occurs by differentiating a one-parameter family of variations of some function. The critical points of the functional are related to the solutions of the associated Euler-Lagrange equation. These differential equations are at the heart of the calculus of variations and its applications to wave mechanics, minimal surfaces, soap bubbles, and modeling traffic flow. All are readily accessible to advanced undergraduates. This book is derived from a workshop sponsored by Rice University. It is suitable for advanced undergraduates, graduate students and research mathematicians interested in the calculus of variations and its applications to other subjects.

Selected Works Of Frederick J Almgren Jr

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Author : Frederick J. Almgren
language : en
Publisher: American Mathematical Soc.
Release Date : 1999

Selected Works Of Frederick J Almgren Jr written by Frederick J. Almgren and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

This volume offers a unique collection of some of the work of Frederick J. Almgren, Jr., the man most noted for defining the shape of geometric variational problems and for his role in founding The Geometry Center. Included in the volume are the following: a summary by Sheldon Chang of the famous 1700 page paper on singular sets of area-minimizing $m$-dimensional surfaces in $R^n$, a detailed summary by Brian White of Almgren's contributions to mathematics, his own announcements of several longer papers, important shorter papers, and memorable expository papers.Almgren's enthusiasm for the subject and his ability to locate mathematically beautiful problems that were 'ready to be solved' attracted many students who further expanded the subject into new areas. Many of these former students are now known for the clarity of their expositions and for the beauty of the problems that they work on. As Almgren's former graduate student, wife, and colleague, Professor Taylor has compiled an important volume on an extraordinary mathematician. This collection presents a fine comprehensive view of the man's mathematical legacy.

Mean Curvature Flow And Isoperimetric Inequalities

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Author : Manuel Ritoré
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-19

Mean Curvature Flow And Isoperimetric Inequalities written by Manuel Ritoré and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-19 with Mathematics categories.

Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is the gradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized. The mean curvature flow also has many geometric applications, in analogy with the Ricci flow of metrics on abstract riemannian manifolds. One can use this flow as a tool to obtain classification results for surfaces satisfying certain curvature conditions, as well as to construct minimal surfaces. Geometric flows, obtained from solutions of geometric parabolic equations, can be considered as an alternative tool to prove isoperimetric inequalities. On the other hand, isoperimetric inequalities can help in treating several aspects of convergence of these flows. Isoperimetric inequalities have many applications in other fields of geometry, like hyperbolic manifolds.

Foams And Emulsions

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Author : J.F. Sadoc
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Foams And Emulsions written by J.F. Sadoc and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Technology & Engineering categories.

A general and introductory survey of foams, emulsions and cellular materials. Foams and emulsions are illustrations of some fundamental concepts in statistical thermodynamics, rheology, elasticity and the physics and chemistry of divided media and interfaces. They also give rise to some of the most beautiful geometrical shapes and tilings, ordered or disordered. The chapters are grouped into sections having fairly loose boundaries. Each chapter is intelligible alone, but cross referencing means that the few concepts that may not be familiar to the reader can be found in other chapters in the book. Audience: Research students, researchers and teachers in physics, physical chemistry, materials science, mechanical engineering and geometry.

Boundaries Of A Complex World

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Author : Andrei Ludu
language : en
Publisher: Springer Nature
Release Date : 2022-09-24

Boundaries Of A Complex World written by Andrei Ludu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-24 with Science categories.

The 2nd edition of this book provides novel topics and studyies in boundaries of networks and Big Data Systems.The central theme of this book is the extent to which the structure of the free dynamical boundaries of a system controls the evolution of the system as a whole. Applying three orthogonal types of thinking - mathematical, constructivist and morphological, it illustrates these concepts using applications to selected problems from the social and life sciences, as well as economics. In a broader context, it introduces and reviews some modern mathematical approaches to the science of complex systems. Standard modeling approaches (based on non-linear differential equations, dynamic systems, graph theory, cellular automata, stochastic processes, or information theory) are suitable for studying local problems. However they cannot simultaneously take into account all the different facets and phenomena of a complex system, and new approaches are required to solve the challenging problem of correlations between phenomena at different levels and hierarchies, their self-organization and memory-evolutive aspects, the growth of additional structures and are ultimately required to explain why and how such complex systems can display both robustness and flexibility. This graduate-level text addresses a broader interdisciplinary audience, keeping the mathematical level essentially uniform throughout the book, and involving only basic elements from calculus, algebra, geometry and systems theory.

Imagine Math 6

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Author : Michele Emmer
language : en
Publisher: Springer
Release Date : 2018-11-06

Imagine Math 6 written by Michele Emmer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-06 with Mathematics categories.

Imagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. Imagine building mathematical models that make it possible to manage our world better, imagine combining music, art, poetry, literature, architecture and cinema with mathematics. Imagine the unpredictable and sometimes counterintuitive applications of mathematics in all areas of human endeavour. Imagination and mathematics, imagination and culture, culture and mathematics. This sixth volume in the series begins with a homage to the architect Zaha Hadid, who died on March 31st, 2016, a few weeks before the opening of a large exhibition of her works in Palazzo Franchetti in Venice, where all the Mathematics and Culture conferences have taken place in the last years. A large section of the book is dedicated to literature, narrative and mathematics including a contribution from Simon Singh. It discusses the role of media in mathematics, including museums of science, journals and movies. Mathematics and applications, including blood circulation and preventing crimes using earthquakes, is also addressed, while a section on mathematics and art examines the role of math in design. A large selection presents photos of mathematicians and mathematical objects by Vincent Moncorge. Discussing all topics in a way that is rigorous but captivating, detailed but full of evocations, it offers an all-embracing look at the world of mathematics and culture.

Geometry And Global Analysis

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Author : Takeshi Kotake
language : en
Publisher:
Release Date : 1993

Geometry And Global Analysis written by Takeshi Kotake and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Gauge fields (Physics) categories.