1 citations · 2 across the 4 of their papers we have counts for
5 papers · 1 filter
Scalar parabolic PDE's and braids
R. Ghrist, R. C. Vandervorst
The comparison principle for scalar second order parabolic PDEs on functions admits a topological interpretation: pairs of solutions, and , ev…
Generic hydrodynamic instability of curl eigenfields
John B. Etnyre, Robert Ghrist
We prove that for generic geometry, the curl-eigenfield solutions to the steady Euler equations on the three torus are all hydrodynamically unstable (linear, L^2 norm). The proof i…
Morse theory on spaces of braids and Lagrangian dynamics
R. W. Ghrist, J. B. Van den Berg, R. C. Vandervorst
In the first half of the paper we construct a Morse-type theory on certain spaces of braid diagrams. We define a topological invariant of closed positive braids which is correlated…
Stratified integrals and unknots in invisid flows
John B. Etnyre, Robert W. Ghrist
We prove that any steady solution to the real analytic Euler equations on a Riemannian 3-sphere must possess a periodic orbit bounding an embedded disc. One key ingredient is an ex…
Gradient flows within plane fields
John Etnyre, Robert Ghrist
We consider the dynamics of vector fields on three-manifolds which are constrained to lie within a plane field, such as occurs in nonholonomic dynamics. On compact manifolds, such…