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Geometric Flows on Planar Lattices

  • Book
  • © 2021

Overview

Authors:
  1. Andrea Braides

    1. Dipartimento di Matematica, Università di Roma Tor Vergata, Roma, Italy

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  2. Margherita Solci

    1. Dipartimento di Architettura, Università di Sassari, Alghero, Italy

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    You can also search for this author in PubMed   Google Scholar

  • Introduces important concepts in modern Applied Analysis through prototypical problems, discussed in a natural way
  • Advanced research topics are introduced in a stimulating and constructive fashion
  • Copious figures promote visual descriptions of concepts and methods

Part of the book series: Pathways in Mathematics (PATHMATH)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction: Motion on Lattices

    • Andrea Braides, Margherita Solci
    Pages 1-6

  3. Variational Evolution

    • Andrea Braides, Margherita Solci
    Pages 7-29

  4. Discrete-to-Continuum Limits of Planar Lattice Energies

    • Andrea Braides, Margherita Solci
    Pages 31-51

  5. Evolution of Planar Lattices

    • Andrea Braides, Margherita Solci
    Pages 53-101

  6. Perspectives: Evolutions with Microstructure

    • Andrea Braides, Margherita Solci
    Pages 103-118

  7. Back Matter

    Pages 119-134
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Keywords

About this book

This book introduces the reader to important concepts in modern applied analysis, such as homogenization, gradient flows on metric spaces, geometric evolution, Gamma-convergence tools, applications of geometric measure theory, properties of interfacial energies, etc. This is done by tackling a prototypical problem of interfacial evolution in heterogeneous media, where these concepts are introduced and elaborated in a natural and constructive way. At the same time, the analysis introduces open issues of a general and fundamental nature, at the core of important applications. The focus on two-dimensional lattices as a prototype of heterogeneous media allows visual descriptions of concepts and methods through a large amount of illustrations.

Reviews

“The book fairly self-contained. Many illuminating examples are worked out in detail, and a large number of extensions are included." (John Urbas, zbMATH 1486.53002, 2022)

Authors and Affiliations

  • Dipartimento di Matematica, Università di Roma Tor Vergata, Roma, Italy

    Andrea Braides

  • Dipartimento di Architettura, Università di Sassari, Alghero, Italy

    Margherita Solci

About the authors

Andrea Braides is professor of Mathematical Analysis at the University of Rome Tor Vergata. He is the author among others of the books Gamma-convergence for Beginners and (with A.Defranceschi) Homogenization of Multiple Integrals. He was an invited speaker at the 2014 International Congress of Mathematicians in Seoul in the section Mathematics in Science and Technology.

Margherita Solci is professor of Mathematical Analysis at the University of Sassari at Alghero. She works on various topics involving variational convergence; in particular, static and dynamic passages from discrete to continuum.



Bibliographic Information

  • Book Title: Geometric Flows on Planar Lattices

  • Authors: Andrea Braides, Margherita Solci

  • Series Title: Pathways in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-69917-8

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

  • Hardcover ISBN: 978-3-030-69916-1Published: 24 March 2021

  • Softcover ISBN: 978-3-030-69919-2Published: 25 March 2022

  • eBook ISBN: 978-3-030-69917-8Published: 23 March 2021

  • Series ISSN: 2367-3451

  • Series E-ISSN: 2367-346X

  • Edition Number: 1

  • Number of Pages: X, 134

  • Number of Illustrations: 62 b/w illustrations, 1 illustrations in colour

  • Topics: Differential Geometry, Optimization, Analysis

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