70 citations · 316 across the 56 of their papers we have counts for
9 papers · 1 filter
Opinion Dynamics on Discourse Sheaves
Jakob Hansen, Robert Ghrist
We introduce a novel class of Laplacians and diffusion dynamics on discourse sheaves as a model for network dynamics, with application to opinion dynamics on social networks. These…
Braid Floer homology
J. -B. van den Berg, R. Ghrist, R. Vandervorst +1
Area-preserving diffeomorphisms of a 2-disc can be regarded as time-1 maps of (non-autonomous) Hamiltonian flows on solid tori, periodic flow-lines of which define braid (conjugacy…
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…
An index for closed orbits in Beltrami fields
John Etnyre, Robert Ghrist
We consider the class of Beltrami fields (eigenfields of the curl operator) on three-dimensional Riemannian solid tori: such vector fields arise as steady incompressible inviscid f…