172 citations · 216 across the 9 of their papers we have counts for
11 papers
Spatially Extended Dislocations Produced by the Dispersive Swift-Hohenberg Equation
Brenden Balch, Patrick D. Shipman, R. Mark Bradley
Motivated by previous results showing that the addition of a linear dispersive term to the two-dimensional Kuramoto-Sivashinsky equation has a dramatic effect on the pattern format…
Phase-Diffusion Equations for the Anisotropic Complex Ginzburg-Landau Equation
Derek Handwerk, Gerhard Dangelmayr, Iuliana Oprea +1
The anisotropic complex Ginzburg-Landau equation (ACGLE) describes slow modulations of patterns in anisotropic spatially extended systems near oscillatory (Hopf) instabilities with…
Julia and Mandelbrot sets for dynamics over the hyperbolic numbers
Vance Blankers, Tristan Rendfrey, Aaron Shukert +1
Julia and Mandelbrot sets, which characterize bounded orbits in dynamical systems over the complex numbers, are classic examples of fractal sets. We investigate the analogs of thes…
A fractal dimension for measures via persistent homology
Henry Adams, Manuchehr Aminian, Elin Farnell +6
We use persistent homology in order to define a family of fractal dimensions, denoted for each homological dimension , assigned to a proba…
Informing the structure of complex Hadamard matrix spaces using a flow
Francis C. Motta, Patrick D. Shipman
The defect of a complex Hadamard matrix is an upper bound for the dimension of a continuous Hadamard orbit stemming from . We provide a new interpretation of the defect as t…
An Unoriented Variation on de Bruijn Sequences
Christie S. Burris, Francis C. Motta, Patrick D. Shipman
For positive integers , a de Bruijn sequence is a finite sequence of elements drawn from characters whose subwords of length are exactly the words of le…