The Many Faces of Elastica

Beschreibung

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.

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.


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 Includes supplementary material: sn.pub/extras

Autor*in

Ivaïlo M. Mladenov

Themen in »The Many Faces of Elastica«

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

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“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)
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