The Moser, Crawford and Red Sock winners of 2013.

By Lennaert van Veen
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SIAG chair Hans Kaper presents the Moser Prize to Nacy Kopell.

 

The Moser Prize was presented to Nancy Kopell, Boston University, who presented Moser Lecture on the Dynamics of Cognition. The selecting committee cited her fundamental contributions to dynamical systems theory, and for her formative influence on the foundations of mathematical neuroscience. The committee pointed out that Nancy has been at the forefront of the applied dynamical systems community spanning four decades. In the area of dynamical systems she is well known for pivotal work on traveling waves and pattern formation, coupled oscillators, geometric singular perturbation theory, and systems with multiple time scales. In addition, she has had a formative influence on modern mathematical biology, through incisive research contributions on biological rhythms and synchronization of neural circuits. The evolution of mathematical neuroscience and mathematical biology in general has been shaped by dynamical systems concepts, many due to Nancy and collaborators. Her involvement with biologists stands as an illuminating example of how nonlinear dynamics can engage with application areas.


SIAG chair Hans Kaper presents the Crawford Prize to Panayotis G. Kevrekidis.

 

The Crawford Prize Winner was Panayotis G. Kevrekidis, University of Massachusetts. He was cited for his recent contributions to our understanding of localized solutions of nonlinear wave equations, and for developing these for a variety of applications in nonlinear optics and condensed matter physics, including Bose Einstein condensates and granular crystals.


The Red Sock awards: left to right: James Yorke, Leah Shaw, Tere Seara, Tingli Xing, Jeremy Wojcik, Morgan Frank, Eric Siero and Sarah Iams.

 

Eric Siero, Leiden University, Netherlands.
Dynamics of Vegetation Patterns under Slowly Varying Conditions
Eric Siero is a PhD student in Leiden where he also did his undergraduate studies. He is fond of cycling and loves playing ultimate frisbee. About his prize winning poster he writes: "We study an extension of the Klausmeier model for vegetation patterns, that incorporates nonlinear diffusion. With continuation software an overview of coexistent stable steady states can be constructed: the Busse balloon. It is found that patterns exhibited by the model repeatedly suffer from abrupt decreases in wavenumber ultimately leading to desert, as a parameter decreases. On the poster it is shown that these abrupt changes correspond directly to interactions with the boundary of the Busse balloon. The project is supervised by Arjen Doelman and Jens Rademacher."
Morgan Frank, University of Vermont, USA.
Happiness and movement on Twitter
Morgan Frank is beginning his second year pursuing a masters in Applied Mathematics with a certificate in Complex Systems from the University of Vermont. He has been working under Prof. Danforth and Prof. Dodds in the Computational Storylab where he has been investigating patterns in human mobility through geo-tagged tweets, predicting links in dynamic networks using evolutionary strategies, and investigating chaos in dynamical systems. More about his work can be found on his website. When he is not doing work, he enjoy running, cycling, swimming, and skiing. He hopes to pursue a PhD along with continuing his research in the next few years.
About his poster he writes: "The patterns of life exhibited by large populations have been described and modeled both as a basic science exercise and for a range of applied goals such as reducing automotive congestion, improving disaster response, and even predicting the location of individuals. However, these studies have previously had limited access to conversation content, rendering changes in expression, such as happiness, as a function of movement invisible. In addition, they typically use the communication between a mobile phone and its nearest antenna tower to infer position. In this study, we use a collection of 37 million geolocated tweets to characterize the movement patterns of 180,000 individuals, taking advantage of orders of magnitude of increased spatial accuracy relative to previous work. We characterize changes in word usage as a function of movement by employing the hedonometer, and find that expressed happiness increases logarithmically with distance from an individual's average location.".
Sarah Iams, Cornell University.
Computing Stability of mosquito motion
Sarah Iams is currently finishing her dissertation at the Center for Applied Mathematics at Cornell University, where she has been studying mosquito motion via observation, measurement, and modeling. Her adviser is John Guckenheimer. She has spent the past year as a visiting instructor in Mathematics at Bowdoin College, and will be at Northwestern University in the Fall as the Golovin Assistant Professor in the department of Engineering Sciences and Applied Mathematics.
About the poster she writes: "Male Aedes aegypti mosquitoes are highly maneuverable flyers. Their sensory feedback system enables them to remain aloft for flights that are on a long timescale relative to their wingbeat frequency of 800 Hz. By thinking of the insect’s body motion over the course of a single wingbeat as a periodic orbit of a dynamical system, we use numerical simulation to probe the instability characteristics of its motion. Given a specified periodic wing motion, we identify initial conditions of the body state that correspond to periodic orbits of the insect’s velocity and orientation variables. We perturb the initial conditions and rerun the simulation to compute the Jacobian matrix of the periodic map. We find that the periodic motion is asymptotically stable at higher forward velocities, but that this matrix is non-normal. Non-normality leads to algebraic growth of perturbations on timescales of up to 80 wingbeats.
The direction of the fastest growing perturbations is shown in the graph below.
"
Jeremy Wojcik and Tingli Xing (Georgia State University).
Chaos: Stirred Not Shaken
Jeremy Wojcik worked as an aircraft maintenance technician for 12 years, while pursuing a physics undergraduate degree, first in Michigan then in Georgia. He finished his PhD in Mathematics, specializing in nonlinear ODEs, dynamical systems, and bifurcation theory. His PhD research was in individual and small networks of biological oscillators. Having a soft spot in his heart for Lorenz and Lorenz-like systems, he continued research on Lorenz-like systems, as well as space based and ground based optical systems. His goal is to find parsimonious solutions to realistic physical systems, the more complicated or difficult the better. He is married with a 7 year old son, and enjoys backpacking, photography, hockey, soccer and aikido.
Tingli Xing hails from China. She came to the USA with a MSc degree in mathematics, having worked on compact attractors for a reaction-diffusion system in $\\mathbb{R}^n$. She taught in a high-school in China from 1998 to 2002 and then worked as a lecturer in Chongqing university from 2005 to 2008. She came to GSU in 2009 to pursue a PhD degree, first with Dr. Imre Patyi and then with Dr. Andrey Shilnikov. Her thesis work is on a symbolic dynamics tool-kit for Lorenz-like systems. "From pure mathematics to applied mathematics, I am exploring a brand new world and it is exciting to me!".
About the poster they write: "Painting the kneading invariants reveals the hidden structure of codimension-two bifurcations such as those found in the Lorenz system and Shimizu-Morioka models. We introduce a novel method based on the kneading invariants to elucidate the detailed bifurcation structure. The method will allow for the practical extension for kneading invariants with more than 2 symbols as well as bifurcation of higher codimension."

Lennaert van Veen
With the help of Committee Chairs
Tim Sauer and Mary Silber
and all Red Sock awardees.

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