7 papers
Calculus on Wave Fronts
Oliver Knill
We define a deformation of the exterior derivative that is a bounded operator and preserves the symmetries of the geometry. It satisfies a modified wave equation that honors the st…
Remarks about Connection and Dirac matrices
Oliver Knill
The connection Laplacian L and the Dirac matrix D are both n x n matrices defined from a given finite simplicial complex G with n sets. In both cases, there is interlacing of the e…
Block Jacobi matrices, Barycentric limits and Manifolds
Oliver Knill
We deform block triangular Jacobi matrices appearing in geometry, look at multi-scale Barycentric limits of geometries and droplet boundary manifolds in Potts networks.
Density of wave fronts
Emily Kang, Oliver Knill
We prove that wave fronts on a flat torus become dense. As a corollary, wave fronts become dense for a square billiard or for the geodesic flow on the flat Klein bottle or the cube…
Interacting Geodesics on Discrete Manifolds
Oliver Knill
We define an evolution of multiple particles on a discrete manifold . Each particle alone moves on geodesics and particles can interact if they are on the same facet. They move…
Geodesics for Discrete manifolds
Oliver Knill
The geodesic flow on a finite discrete q-manifold with or without boundary is defined as as a permutation of its ordered q-simplices. This allows to define geodesic sheets and a no…