10 citations · 27 across the 12 of their papers we have counts for
12 papers
Analysis and Simulations of a Nonlocal Gray-Scott Model
Loic Cappanera, Gabriela Jaramillo, Cory Ward
The Gray-Scott model is a set of reaction-diffusion equations that describes chemical systems far from equilibrium. Interest in this model stems from its ability to generate spatio…
Dynamics of a linearly-perturbed May-Leonard competition model
Gabriela Jaramillo, Lidia Mrad, Tracy L. Stepien
The May--Leonard model was introduced to examine the behavior of three competing populations where rich dynamics, such as limit cycles and nonperiodic cyclic solutions, arise. In t…
Can large inhomogeneities generate target patterns?
Gabriela Jaramillo
We study the existence of target patterns in oscillatory media with weak local coupling and in the presence of an impurity, or defect. We model these systems using a viscous eikona…
Rotating spirals in oscillatory media with nonlocal interactions and their normal form
Gabriela Jaramillo
Biological and physical systems that can be classified as oscillatory media give rise to interesting phenomena like target patterns and spiral waves. The existence of these structu…
Numerical Methods for a Diffusive Class Nonlocal Operators
Loic Cappanera, Gabriela Jaramillo, Cory Ward
In this paper we develop a numerical scheme based on quadratures to approximate solutions of integro-differential equations involving convolution kernels, , of diffusive type. I…
A Modified Split Bregman Algorithm for Computing Microstructures Through Young Measures
Gabriela Jaramillo, Shankar Venkataramani
The goal of this paper is to describe the oscillatory microstructure that can emerge from minimizing sequences for nonconvex energies. We consider integral functionals that are def…
Target Patterns in a 2-D Array of Oscillators with Nonlocal Coupling
Gabriela Jaramillo, Shankar Venkataramani
We analyze the effect of adding a weak, localized, inhomogeneity to a two dimensional array of oscillators with nonlocal coupling. We propose and also justify a model for the phase…
The Effect of Impurities on Striped Phases
Gabriela Jaramillo, Arnd Scheel, Qiliang Wu
We study the effect of algebraically localized impurities on striped phases in one space-dimension. We therefore develop a functional-analytic framework which allows us to cast the…
Pacemakers in large arrays of oscillators with nonlocal coupling
Arnd Scheel, Gabriela Jaramillo
We model pacemaker effects of an algebraically localized heterogeneity in a 1 dimensional array of oscillators with nonlocal coupling. We assume the oscillators obey simple phase d…
Inhomogeneities in 3 dimensional oscillatory media
Gabriela Jaramillo
We consider localized perturbations to spatially homogeneous oscillations in dimension 3 using the complex Ginzburg-Landau equation as a prototype. In particular, we will focus on…
Deformation of Striped Patterns by Inhomogeneities
Gabriela Jaramillo, Arnd Scheel
We study the effects of adding a local perturbation in a pattern forming system, taking as an example the Ginzburg-Landau equation with a small localized inhomogeneity in two dimen…
Study of multi black hole and ring singularity apparent horizons
Gabriela Jaramillo, Carlos O. Lousto
We study critical black hole separations for the formation of a common apparent horizon in systems of - black holes in a time symmetric configuration. We study in detail the al…