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The Many Faces of Elastica

  • Ivaïlo M. Mladenov
  • Mariana Hadzhilazova

Part of the Forum for Interdisciplinary Mathematics book series (FFIM)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Ivaïlo M. Mladenov, Mariana Hadzhilazova
    Pages 1-46
  3. Ivaïlo M. Mladenov, Mariana Hadzhilazova
    Pages 47-68
  4. Ivaïlo M. Mladenov, Mariana Hadzhilazova
    Pages 69-82
  5. Ivaïlo M. Mladenov, Mariana Hadzhilazova
    Pages 83-149
  6. Ivaïlo M. Mladenov, Mariana Hadzhilazova
    Pages 151-166
  7. Ivaïlo M. Mladenov, Mariana Hadzhilazova
    Pages 167-199
  8. Back Matter
    Pages 201-212

About this book

Introduction

This book provides an introduction to the mathematical aspects of Euler's elastic theory and its application. The approach is rigorous, as well as visually depicted, and can be easily digested. The first few chapters introduce the needed mathematical concepts from geometry and variational calculus. The formal definitions and proofs are always illustrated through complete derivations and concrete examples. In this way, the reader becomes acquainted with Cassinian ovals, Sturmian spirals, co-Lemniscates, the nodary and the undulary, Delaunay surfaces, and their generalizations. The remaining chapters discuss the modeling of membranes, mylar balloons, rotating liquid drops, Hele-Shaw cells, nerve fibers, Cole's experiments, and membrane fusion. The book is geared towards applied mathematicians, physicists and engineers interested in Elastica Theory and its applications.

Keywords

Bernoulli’s lemniscates Biological membranes Canham model Cassinian ovals Cole model Delaunay surfaces Deuling model Frenet-Serret equations Hele-Shaw cells Helfrich model Laplace-Young equation Whewell parameterization Yoneda method rotating liquid drop local theory of curves Sturmian spirals nodoid unduloid mylar balloon Stalk model

Authors and affiliations

  • Ivaïlo M. Mladenov
    • 1
  • Mariana Hadzhilazova
    • 2
  1. 1.Institute of Biophysics and Biomedical EngineeringBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Institute of Biophysics and Biomedical EngineeringBulgarian Academy of SciencesSofiaBulgaria

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-61244-7
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-61242-3
  • Online ISBN 978-3-319-61244-7
  • Series Print ISSN 2364-6748
  • Series Online ISSN 2364-6756
  • Buy this book on publisher's site