The Many Faces of Elastica
Springer International Publishing (Verlag)
978-3-319-61242-3 (ISBN)
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.
"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)
“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)
Erscheinungsdatum | 08.09.2017 |
---|---|
Reihe/Serie | Forum for Interdisciplinary Mathematics |
Zusatzinfo | XV, 212 p. 85 illus., 6 illus. in color. |
Verlagsort | Cham |
Sprache | englisch |
Maße | 155 x 235 mm |
Gewicht | 466 g |
Themenwelt | Informatik ► Weitere Themen ► Bioinformatik |
Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
Schlagworte | 0 (Null) • 1. • 1. FC Kaiserslautern • 1. FC Kaiserslautern; Kalender • 1. FC Kaiserslautern; Nonbooks • 1 (Jahr) • 1-Liter-Auto • Applied mathematics • Bernoulli's lemniscates • Bernoulli’s lemniscates • Biological and Medical Physics, Biophysics • Biological membranes • Biophysics • Canham model • Cassinian ovals • Cole model • Delaunay surfaces • Deuling model • Ein-Chip-Mikrocomputer • Frenet-Serret Equations • hele-shaw cells • Helfrich model • Laplace-Young equation • 'Lauschangriff' 2 • local theory of curves • Mathematical Applications in the Physical Sciences • Mathematical Modelling • Mathematical Physics • Mathematics • mathematics and statistics • mechanics of solids • medical physics • mylar balloon • .NET • .NET Collections • .NET Compact Framework • .NET Enterprise Servers • .NET Framework • .NET Mobile Information Server • .NET My Services • .NET Remoting • .NET Windows Forms • nodoid • 'N Sync (Pop-Gruppe) • Physiological, Cellular and Medical Topics • rotating liquid drop • Stalk model • Sturmian spirals • Theoretical and Applied Mechanics • unduloid • 'Unter den Linden' (Friedhof) Reutlingen • Whewell parameterization • Yoneda method |
ISBN-10 | 3-319-61242-5 / 3319612425 |
ISBN-13 | 978-3-319-61242-3 / 9783319612423 |
Zustand | Neuware |
Haben Sie eine Frage zum Produkt? |
aus dem Bereich