Coverart for item
The Resource The Many Faces of Elastica, by Ivaïlo M. Mladenov, Mariana Hadzhilazova, (electronic resource)

The Many Faces of Elastica, by Ivaïlo M. Mladenov, Mariana Hadzhilazova, (electronic resource)

Label
The Many Faces of Elastica
Title
The Many Faces of Elastica
Statement of responsibility
by Ivaïlo M. Mladenov, Mariana Hadzhilazova
Creator
Contributor
Author
Subject
Language
eng
Summary
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.--
Member of
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Mladenov, Ivaïlo M
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Hadzhilazova, Mariana.
Series statement
  • Springer eBooks
  • Forum for Interdisciplinary Mathematics,
http://library.link/vocab/subjectName
  • Mathematics
  • Mathematical physics
  • Biomathematics
  • Mechanics
  • Mechanics, Applied
Label
The Many Faces of Elastica, by Ivaïlo M. Mladenov, Mariana Hadzhilazova, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-61244-7
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
978-3-319-61244-7
Dimensions
unknown
Extent
1 online resource (XV, 212 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319612447
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-61244-7
Other physical details
85 illustrations, 6 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1001768217
Label
The Many Faces of Elastica, by Ivaïlo M. Mladenov, Mariana Hadzhilazova, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-61244-7
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
978-3-319-61244-7
Dimensions
unknown
Extent
1 online resource (XV, 212 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319612447
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-61244-7
Other physical details
85 illustrations, 6 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1001768217

Library Locations

    • Badia FiesolanaBorrow it
      Via dei Roccettini 9, San Domenico di Fiesole, 50014, IT
      43.803074 11.283055
Processing Feedback ...