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001 978-3-319-61244-7
003 DE-He213
005 20210118154722.0
007 cr nn 008mamaa
008 170819s2017 gw | s |||| 0|eng d
020 _a9783319612447
_9978-3-319-61244-7
024 7 _a10.1007/978-3-319-61244-7
_2doi
050 4 _aQH323.5
072 7 _aPBW
_2bicssc
072 7 _aMAT003000
_2bisacsh
072 7 _aPBW
_2thema
082 0 4 _a570.285
_223
100 1 _aMladenov, Ivaïlo M.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 4 _aThe Many Faces of Elastica
_h[electronic resource] /
_cby Ivaïlo M. Mladenov, Mariana Hadzhilazova.
250 _a1st ed. 2017.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aXV, 212 p. 85 illus., 6 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aForum for Interdisciplinary Mathematics,
_x2364-6748
505 0 _aPreface -- 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.
520 _aThis 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.
650 0 _aBiomathematics.
650 0 _aBiophysics.
650 0 _aBiological physics.
650 0 _aMechanics.
650 0 _aMechanics, Applied.
650 0 _aMathematical physics.
650 1 4 _aPhysiological, Cellular and Medical Topics.
_0http://scigraph.springernature.com/things/product-market-codes/M31020
650 2 4 _aBiological and Medical Physics, Biophysics.
_0http://scigraph.springernature.com/things/product-market-codes/P27008
650 2 4 _aTheoretical and Applied Mechanics.
_0http://scigraph.springernature.com/things/product-market-codes/T15001
650 2 4 _aMathematical Applications in the Physical Sciences.
_0http://scigraph.springernature.com/things/product-market-codes/M13120
650 2 4 _aMathematical Physics.
_0http://scigraph.springernature.com/things/product-market-codes/M35000
700 1 _aHadzhilazova, Mariana.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319612423
776 0 8 _iPrinted edition:
_z9783319612430
776 0 8 _iPrinted edition:
_z9783319870328
830 0 _aForum for Interdisciplinary Mathematics,
_x2364-6748
856 4 0 _uhttps://doi.org/10.1007/978-3-319-61244-7
912 _aZDB-2-SMA
999 _c453968
_d453968
942 _cEB
506 _aAvailable to subscribing member institutions only. Доступно лише організаціям членам підписки.
506 _fOnline access from local network of NaUOA.
506 _fOnline access with authorization at https://link.springer.com/
506 _fОнлайн-доступ з локальної мережі НаУОА.
506 _fОнлайн доступ з авторизацією на https://link.springer.com/