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© 2017

The Many Faces of Elastica

Benefits

  • Provides a deep overview of elastica theory with application to biological systems

  • Requires minimal prerequisites consisting of basic calculus and basic physics

  • Suitable for a mixed audience of students in mathematics, physics and engineering

Book
  • 3.6k Downloads

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

  1. 1.Institute of Biophysics and Biomedical EngineeringBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Institute of Biophysics and Biomedical EngineeringBulgarian Academy of SciencesSofiaBulgaria

Bibliographic information

Reviews

“This book provides a treatment of a beautiful area of mathematics and its applications which ties together aspects of classical differential geometry of surfaces and the calculus of variations. … The reader will find in this book a useful introduction to some of the relevant underlying mathematics; there is a nice introduction to the differential geometry of curves and surfaces and certain aspects of the calculus of variations.” (John MuCuan, Mathematical Reviews, April, 2018)