LEADER 04109nam 22008055 450 001 9910483631803321 005 20251202130511.0 010 $a9786613562234 010 $a9781280384318 010 $a128038431X 010 $a9783642008375 010 $a3642008372 024 7 $a10.1007/978-3-642-00837-5 035 $a(CKB)1000000000746032 035 $a(SSID)ssj0000318655 035 $a(PQKBManifestationID)11222359 035 $a(PQKBTitleCode)TC0000318655 035 $a(PQKBWorkID)10310555 035 $a(PQKB)11564447 035 $a(DE-He213)978-3-642-00837-5 035 $a(MiAaPQ)EBC3064237 035 $a(PPN)136300812 035 $a(EXLCZ)991000000000746032 100 $a20100301d2009 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aLectures on Topological Fluid Mechanics $eLectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 2 - 10, 2001 /$fby Mitchell A. Berger, Louis H. Kauffman, Boris Khesin, H. Keith Moffatt, Renzo L. Ricca, De Witt Sumners ; edited by Renzo L. Ricca 205 $a1st ed. 2009. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2009. 215 $a1 online resource (XII, 223 p.) 225 1 $aC.I.M.E. Foundation Subseries,$x2946-1820 ;$v1973 300 $a"Fondazione CIME." 311 08$a9783642008368 311 08$a3642008364 320 $aIncludes bibliographical references and index. 327 $aBraids and Knots -- Topological Quantities: Calculating Winding, Writhing, Linking, and Higher Order Invariants -- Tangles, Rational Knots and DNA -- The Group and Hamiltonian Descriptions of Hydrodynamical Systems -- Singularities in Fluid Dynamics and their Resolution -- Structural Complexity and Dynamical Systems -- Random Knotting: Theorems, Simulations and Applications. 330 $aHelmholtz's seminal paper on vortex motion (1858) marks the beginning of what is now called topological fluid mechanics.After 150 years of work, the field has grown considerably. In the last several decades unexpected developments have given topological fluid mechanics new impetus, benefiting from the impressive progress in knot theory and geometric topology on the one hand, and in mathematical and computational fluid dynamics on the other. This volume contains a wide-ranging collection of up-to-date, valuable research papers written by some of the most eminent experts in the field. Topics range from fundamental aspects of mathematical fluid mechanics, including topological vortex dynamics and magnetohydrodynamics, integrability issues, Hamiltonian structures and singularity formation, to DNA tangles and knotted DNAs in sedimentation. A substantial introductory chapter on knots and links, covering elements of modern braid theory and knot polynomials, as well as more advanced topics in knot classification, provides an invaluable addition to this material. 410 0$aC.I.M.E. Foundation Subseries,$x2946-1820 ;$v1973 606 $aPhysics 606 $aTopology 606 $aDynamical systems 606 $aFunctions of complex variables 606 $aClassical and Continuum Physics 606 $aTopology 606 $aDynamical Systems 606 $aSeveral Complex Variables and Analytic Spaces 615 0$aPhysics. 615 0$aTopology. 615 0$aDynamical systems. 615 0$aFunctions of complex variables. 615 14$aClassical and Continuum Physics. 615 24$aTopology. 615 24$aDynamical Systems. 615 24$aSeveral Complex Variables and Analytic Spaces. 676 $a532 686 $aSI 850$2rvk 701 $aBerger$b Mitchell Anthony$0319929 701 $aRicca$b Renzo L$0433760 712 02$aCentro internazionale matematico estivo. 712 12$aC.I.M.E. Summer School$f(2001 :$eCetraro, Italy) 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483631803321 996 $aLectures on topological fluid mechanics$94184785 997 $aUNINA