1 citations · 2 across the 4 of their papers we have counts for
13 papers
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…
State complexes for metamorphic robots
A. Abrams, R. Ghrist
A metamorphic robotic system is an aggregate of homogeneous robot units which can individually and selectively locomote in such a way as to change the global shape of the system. W…
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…
Flowlines transverse to fibred knots and links
R. Ghrist, E. Kin
We consider vector fields on knot/link complements in which are transverse to the fibres of a fibration of the complement over a circle. We prove that a large class of fibred…
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…
Finding topology in a factory: configuration spaces
A. Abrams, R. Ghrist
This expository article describes applications of topological configuration spaces to the control of robotic systems. In particular, we review recent work by the authors on configu…