Results for: Graphics

Stability of Kuramoto Oscillators

Posted by Cleve Moler,

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. My kuramoto program demonstrates both stable and unstable critical points. Roundoff error may destabilize an unstable critical point.... read more >>

Experiments With Kuramoto Oscillators

Posted by Cleve Moler,

I have learned a lot more about Kuramoto oscillators since I wrote my blog post three 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 >>

The Reuleaux Triangle and Curves of Constant Width

Posted by Cleve Moler,

Why are manhole covers round? It is so they won't fall through the hole they are intended to cover. They have the same diameter regardless of where it is measured. If the hole has a slightly smaller diameter, it is not possible to orient the cover so that it will fall through. A square or rectangular cover can be turned slightly and it will easily fit through the hole.... read more >>