Gabriela Jaramillo

Research Experience for Undergraduates (REU)

Summer 2021

I am looking for two motivated undergraduate students to work 7 weeks, between June 14th and July 30th 2021, for an online summer REU program. The research topics will be related to pattern formation and will be based on the theory of dynamical systems and partial differential equations. We will explore the formation, dynamics and control of spiral waves.

To participate, students must be US citizens or permanent residents, and must have not yet completed their undergraduate degree by summer 2021. Participants will receive a stipend.

The deadline for applications is March 14th, 2021. Applicants should complete the application form and submit a personal statement, transcript (unofficial OK), and one reference letter.

To complete the application process click Here.

Summer 2020

Participants: Ricardo Del Rio and Shravani Deo

Many biological systems that are composed of coupled oscillating elements, such as groups of heart cells and neural tissue, exhibit interesting behavior. When interactions between these elements is local, traveling and spiral waves form; however, when the coupling is nonlocal new patterns called chimeras states may appear. These novel states consists of regions of synchronous behavior mixed with regions where oscillators act independently of each other.

In this project, we used a system of FitzHugh-Nagumo (FHN) equations to study how nonlocal coupling affects pattern formation and the emergence of chimera states. A network of 50 FHN oscillators arranged in a square grid was considered. We found that oscillating spot chimeras and striped chimeras appear depending on the type of coupling used (See poster here).

A second aspect of the project explored the formation of spiral waves in a cellular automaton model. In this model the dynamics of each cell, or oscillator, is governed by a set of rules that take into account the state of the cell itself and its nearest neighbors. Again a square grid of 50 cells was considered. We found that when the number of nearest neighbors that are considered increases the spiral's wavenumber decreases. That is, the spacing between the spiral arms widens (See figures a) b) and c) below).