48 citations · 81 across the 9 of their papers we have counts for
11 papers
Nonlocal Approximation of Slow and Fast Diffusion
Katy Craig, Matt Jacobs, Olga Turanova
Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlin…
Speed-up of traveling waves by negative chemotaxis
Quentin Griette, Christopher Henderson, Olga Turanova
We consider the traveling wave speed for Fisher-KPP (FKPP) fronts under the influence of repulsive chemotaxis and provide an almost complete picture of its asymptotic dependence on…
A blob method for inhomogeneous diffusion with applications to multi-agent control and sampling
Katy Craig, Karthik Elamvazhuthi, Matt Haberland +1
As a counterpoint to classical stochastic particle methods for linear diffusion equations, we develop a deterministic particle method for the weighted porous medium equation (WPME)…
Quantifying Robotic Swarm Coverage
Brendon G. Anderson, Eva Loeser, Marissa Gee +5
In the field of swarm robotics, the design and implementation of spatial density control laws has received much attention, with less emphasis being placed on performance evaluation…
Non-local competition slows down front acceleration during dispersal evolution
Vincent Calvez, Christopher Henderson, Sepideh Mirrahimi +2
We investigate the super-linear spreading in a reaction-diffusion model analogous to the Fisher-KPP equation, but in which the population is heterogeneous with respect to the dispe…
Quantitative Assessment of Robotic Swarm Coverage
Brendon G. Anderson, Eva Loeser, Marissa Gee +5
This paper studies a generally applicable, sensitive, and intuitive error metric for the assessment of robotic swarm density controller performance. Inspired by vortex blob numeric…
Uniform convergence for the incompressible limit of a tumor growth model
Inwon Kim, Olga Turanova
We study a model introduced by Perthame and Vauchelet that describes the growth of a tumor governed by Brinkman's Law, which takes into account friction between the tumor cells. We…
On a model of a population with variable motility
Olga Turanova
We study a reaction-diffusion equation with a nonlocal reaction term that models a population with variable motility. We establish a global supremum bound for solutions of the equa…
Error estimates for approximations of nonlinear uniformly parabolic equations
Olga Turanova
We introduce the notion of δ-viscosity solutions for fully nonlinear uniformly parabolic PDE on bounded domains. We prove that δ-viscosity solutions are uniformly close to the actu…
Error estimates for approximations of nonhomogeneous nonlinear uniformly elliptic equations
Olga Turanova
We obtain an error estimate between viscosity solutions and δ-viscosity solutions of nonhomogeneous fully nonlinear uniformly elliptic equations. The main assumption, besides unifo…
The spiral index of knots
Colin Adams, William George, Rachel Hudson +4
Two new invariants that are closely related to Milnor's curvature-torsion invariant are introduced. The first, the spiral index of a knot, captures the minimum number of maxima amo…