3 citations · 3 across the 6 of their papers we have counts for
6 papers
Graphon Limits of Graph Reaction--Diffusion Equations
Edith J. Zhang, James Scott, Qiang Du
A graph reaction--diffusion (RD) equation is a system of differential equations that is defined on the nodes of a graph. Consider a sequence of growing graphs that converges in cut…
On parameterized nonlocal-fractional transmission problems and associated function spaces
Qiang Du, Zhaolong Han, Tadele Mengesha +2
In this paper, we consider a family of seamlessly coupled nonlocal models associated with transmission conditions across an interface. The models are derived from the variation of…
Weighted nonlocal operators and their applications in semi-supervised learning
Qiang Du, James M. Scott
Motivated by problems in machine learning, we study a class of variational problems characterized by nonlocal operators. These operators are characterized by power-type weights, wh…
Ginzburg--Landau Functionals in the Large-Graph Limit
Edith Zhang, James Scott, Qiang Du +1
Ginzburg--Landau (GL) functionals on graphs, which are relaxations of graph-cut functionals on graphs, have yielded a variety of insights in image segmentation and graph clustering…
Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems
Qiang Du, James M. Scott, Xiaochuan Tian
We present a study on asymptotically compatible Galerkin discretizations for a class of parametrized nonlinear variational problems. The abstract analytical framework is based on v…
Ohta-Kawasaki energy for amphiphiles: asymptotics and phase-field simulations
Qiang Du, James M. Scott, Zirui Xu
We study the minimizers of a degenerate case of the Ohta-Kawasaki energy, defined as the sum of the perimeter and a Coulombic nonlocal term. We start by investigating radially symm…