Exponential Growth in Two-Dimensional Topological Fluid Dynamics

Two{dimensional Topological Dynamics

Topological Fluid Dynamics

T opological fluid dynamics is a young mathematical discipline that studies topological features of flows with complicated trajectories and their applications to fluid motions, and develops group-theoretic and geometric points of view on various problems of hydrodynamical origin. It is situated at a crossroads of several disciplines, including Lie groups, knot theory, partial differential equat...

Dynamics of topological solitons in two-dimensional ferromagnets

Dynamical topological solitons are studied in classical two–dimensional Heisenberg easy–axis ferromagnets. The properties of such solitons are treated both analytically in the continuum limit and numerically by spin dynamics simulations of the discrete system. Excitation of internal mode causes orbital motion. This is confirmed by simulations. Submitted to: J. Phys.: Condens. Matter PACS number...

Topological fluid dynamics for fluid dynamicists

These notes are preliminary and informal. My aim is to provide an introduction to some of the basic ideas that have emerged in recent decades in the fluids literature that have a fundamentally topological character. That is, rather than focusing on details such as velocity profile or pressure field, this material deals with persistent invariant properties of a flow field, features which often h...

One{dimensional Topological Dynamics