The Many Faces of Elastica: Forum for Interdisciplinary Mathematics, cartea 3
Autor Ivaïlo M. Mladenov, Mariana Hadzhilazovaen Limba Engleză Hardback – 29 aug 2017
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.
| Toate formatele și edițiile | Preț | Express |
|---|---|---|
| Paperback (1) | 360.64 lei 38-44 zile | |
| Springer International Publishing – 7 aug 2018 | 360.64 lei 38-44 zile | |
| Hardback (1) | 391.61 lei 6-8 săpt. | |
| Springer International Publishing – 29 aug 2017 | 391.61 lei 6-8 săpt. |
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Specificații
ISBN-13: 9783319612423
ISBN-10: 3319612425
Pagini: 212
Ilustrații: XV, 212 p. 85 illus., 6 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 0.5 kg
Ediția:1st ed. 2017
Editura: Springer International Publishing
Colecția Springer
Seria Forum for Interdisciplinary Mathematics
Locul publicării:Cham, Switzerland
ISBN-10: 3319612425
Pagini: 212
Ilustrații: XV, 212 p. 85 illus., 6 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 0.5 kg
Ediția:1st ed. 2017
Editura: Springer International Publishing
Colecția Springer
Seria Forum for Interdisciplinary Mathematics
Locul publicării:Cham, Switzerland
Cuprins
Preface.- List of Symbols.- Geometry and Variational Calculus.- Plane Curves.- Space Curves.- Surfaces.- Variational Calculus.- Planar Curves Whose Curvature Depends Only on the Distance from a Fixed Point.- The Moving Frame Associated With a Plane Curve.- Integration.- Bernoulli's Lemniscates.- Relationship Between the Lemniscate and the Elastica.- Spirals.- Sturmian Spirals.- Generalized Sturm Spirals.- Serret Curves.- Cassinian Ovals.- Biological Membranes.- Subject Matter and Biological Membranes.- Types of Membranes.- Functions of Biomembranes.- Chemical Composition and Physical Properties of Biomembranes.- Membrane Models and Methods for the Study of Biomembranes.- Model Membrane Structures.- Surface Tension and Equilibrium.- Mechanical Equilibrium.- Tensions and Geometry.- Delaunay Surfaces.- Mylar Balloon and Elastic Curves.- Whewell Parameterization.- Elastic Sturmian Spirals.- Alternative Parametrization of Elastic Spirals.- Zero Tension.- Geometry of the Rotating Liquid Drop.- Introduction.- Geometry and Surface Invariants.- Parametrization via Legendre's Integrals.- Parameterization via Weierstrass's Functions.- Geodesics on the Drop.- Questions for Future Work.- Equations of Equilibrium States of Membranes.- Canham Model.- Key Assumptions in the Model.- Helfrich and Deuling Model.- Ou-Yang and Helfrich Model.- Symmetries of the Shape Equation.- Exact Solutions and Applications.- Unduloids and Nerve Fibers.- Mathematical Model of the Cole Experiment.- Fusion of Membranes.- Cylindrical Membranes.- Beyond Delaunay Surfaces.- Epilogue.- A Elliptical Integrals and Functions.- A.1 Jacobian Elliptic Functions.- A.2 Weierstrassian Elliptic Functions.- References.- Index.
Recenzii
“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)
Textul de pe ultima copertă
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.
Caracteristici
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