LEADER 05441nam 22007095 450 001 9910254298903321 005 20200630093646.0 010 $a3-319-61244-1 024 7 $a10.1007/978-3-319-61244-7 035 $a(CKB)3710000001631063 035 $a(MiAaPQ)EBC4981388 035 $a(DE-He213)978-3-319-61244-7 035 $a(PPN)203852443 035 $a(EXLCZ)993710000001631063 100 $a20170819d2017 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 14$aThe Many Faces of Elastica$b[electronic resource] /$fby Ivaïlo M. Mladenov, Mariana Hadzhilazova 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (223 pages) $cillustrations 225 1 $aForum for Interdisciplinary Mathematics,$x2364-6748 311 $a3-319-61242-5 320 $aIncludes bibliographical references and index. 327 $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. 330 $aThis book provides an introduction to the mathematical aspects of Euler's elastic theory and its application. The approach is rigorous, as well as visually depicted, and can be easily digested. The first few chapters introduce the needed mathematical concepts from geometry and variational calculus. The formal definitions and proofs are always illustrated through complete derivations and concrete examples. In this way, the reader becomes acquainted with Cassinian ovals, Sturmian spirals, co-Lemniscates, the nodary and the undulary, Delaunay surfaces, and their generalizations. The remaining chapters discuss the modeling of membranes, mylar balloons, rotating liquid drops, Hele-Shaw cells, nerve fibers, Cole's experiments, and membrane fusion. The book is geared towards applied mathematicians, physicists and engineers interested in Elastica Theory and its applications. 410 0$aForum for Interdisciplinary Mathematics,$x2364-6748 606 $aBiomathematics 606 $aBiophysics 606 $aBiological physics 606 $aMechanics 606 $aMechanics, Applied 606 $aMathematical physics 606 $aPhysiological, Cellular and Medical Topics$3https://scigraph.springernature.com/ontologies/product-market-codes/M31020 606 $aBiological and Medical Physics, Biophysics$3https://scigraph.springernature.com/ontologies/product-market-codes/P27008 606 $aTheoretical and Applied Mechanics$3https://scigraph.springernature.com/ontologies/product-market-codes/T15001 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 615 0$aBiomathematics. 615 0$aBiophysics. 615 0$aBiological physics. 615 0$aMechanics. 615 0$aMechanics, Applied. 615 0$aMathematical physics. 615 14$aPhysiological, Cellular and Medical Topics. 615 24$aBiological and Medical Physics, Biophysics. 615 24$aTheoretical and Applied Mechanics. 615 24$aMathematical Applications in the Physical Sciences. 615 24$aMathematical Physics. 676 $a516.36 700 $aMladenov$b Ivaïlo M$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767158 702 $aHadzhilazova$b Mariana$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254298903321 996 $aThe Many Faces of Elastica$92235922 997 $aUNINA