By Mitchell A. Berger, Louis H. Kauffman, Boris Khesin, H. Keith Moffatt, Renzo L. Ricca, De Witt Sumners (auth.), Renzo L. Ricca (eds.)
Helmholtz's seminal paper on vortex movement (1858) marks the start of what's now known as topological fluid mechanics.After a hundred and fifty years of labor, the sector has grown significantly. within the final a number of a long time unforeseen advancements have given topological fluid mechanics new impetus, making the most of the striking development in knot idea and geometric topology at the one hand, and in mathematical and computational fluid dynamics at the different.
This quantity includes a wide-ranging number of up to date, beneficial examine papers written by way of probably the most eminent specialists within the box. themes variety from basic features of mathematical fluid mechanics, together with topological vortex dynamics and magnetohydrodynamics, integrability concerns, Hamiltonian constructions and singularity formation, to DNA tangles and knotted DNAs in sedimentation. a considerable introductory bankruptcy on knots and hyperlinks, masking parts of contemporary braid thought and knot polynomials, in addition to extra complicated themes in knot category, offers a useful addition to this material.