Scientific computing, math & more

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Results for: 2019

Stability of Kuramoto Oscillators

I am working with Indika Rajapakse and Steve Smale to investigate the stability of the dynamic system describing Kuramoto oscillators. Indika and Steve are interested in Kuramoto oscillators for two reasons; the self synchronization provides a model of the cells in a beating heart and the dynamic system is an example for Morse-Smale theory. I am personally interested in the Kuramoto model as it relates to deep brain stimulation (DBS) for open-loop control of human movement disorders. Mykuramotoprogram demonstrates both stable and unstable critical points. Roundoff error may destabilize an unstable critical point....read more >>

Experiments With Kuramoto Oscillators

I have learned a lot more about Kuramoto oscillators since I wrote my blog postthree weeks ago. I am working with Indika Rajapakse at the University of Michigan and Stephen Smale at the University of California, Berkeley. They are interested in the Kuramoto model because they are studying the beating of human heart cells. At this point we have some interesting results and some unanswered questions....read more >>

Kuramoto Model of Synchronized Oscillators

Fireflies on a summer evening, pacemaker cells, neurons in the brain, a flock of starlings in flight, pendulum clocks mounted on a common wall, bizarre chemical reactions, alternating currents in a power grid, oscillations in SQUIDs (superconducting quantum interference devices). These are all examples of synchronized oscillators....read more >>

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Hadamard Matrices

I have just returned from theICIAM2019 conferencein Valencia, Spain. It was a huge conference -- 4,000+ attendees, dozens of prize and invited talks, hundreds of parallel minisympsia. I gave a talk in a two-part minisymposium organized by Nick Higham and Rob Corless. I outlined the first part of the talk inthis bloga month ago. This post outlines the second part, which was about Hadamard matrices. Some of it is taken from a post inthis blogfive years ago....read more >>

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Posts 1 - 10 of 22