5 papers
Discontinuity Analysis and Semi-Analytic Spectral Approximation for the Nonlocal Poisson Equation
Thinh Dang, Bacim Alali, Nathan Albin
We study a nonlocal Poisson problem with discontinuous source term and analyze how the regularity of the integral kernel determines the discontinuity structure of the corresponding…
A Fast Algorithm for Finding Minimum Weight Cycles in Mining Cyclic Graph Topologies
Heman Shakeri, Torben Amtoft, Behnaz Moradi-Jamei +2
Cyclic structures are fundamental topological features in graphs, playing critical roles in network robustness, information flow, community structure, and various dynamic processes…
Fourier Spectral Method for Nonlocal Equations on Bounded Domains
Ilyas Mustapha, Bacim Alali, Nathan Albin
This work introduces efficient and accurate spectral solvers for nonlocal equations on bounded domains. These spectral solvers exploit the fact that integration in the nonlocal for…
The scaling limit of fair Peano paths
Nathan Albin, Joan Lind, Pietro Poggi-Corradini
We study random Peano paths on planar square grids that arise from fair random spanning trees. These are trees that are sampled in such a way as to have the same (if possible) edge…
Regularity of Solutions for Peridynamics Equilibrium and Evolution Equations on Periodic Distributions
Thinh Dang, Bacim Alali, Nathan Albin
Results on the peridynamics equilibrium and evolution equations over the space of periodic vector-distributions in multi-spatial dimensions are presented. The associated operator c…