My last major thread before I relinquish my hold over this account will be on another topic I am really interested in math and science called "Chimeras" (kinda like this cat that I definitely included in my PhD defense slides because...cats of course) #physics #Dynamics

Luckily, I have a background in Greek & Roman Mythology (yay studying Latin for 9 years)

A chimera in Greek Mythology is beast whose earliest written evidence is credited to Homer's Iliad: a fire-breathing hybrid between lion's head, a goat's body, and a serpent's tail

"Just like this beast was created to be a plague for men, so too was this problem a plague for me, but unlike the men of mythology, my goal is not to defeat the chimera, but to subdue the beast and understand its behavior." -- a quote from my Ph.D. thesis.

Anyway, a chimera when talking about coupled oscillators is a phenomenon where, given identical oscillators, a spatio-temporal (space & time) pattern will emerge that have regions of different patterns. A major paper that looked at this was by @stevenstrogatz et al using

the Kuramoto model (which I discussed yesterday when talking about synchronization). What was found is in this plot from their paper: a section of oscillators phase synchronize while a section of oscillators remain decoherent. But all the oscillators are identical! The equations

that describe them are the same! One interesting feature of this Kuramoto model is that they use coupling that is called "non-local." Yesterday I talked a bit about globally coupled oscillators (the metronomes) and locally coupled oscillators (the fireflies). Nonlocal is

something in between. Not only are the oscillators affected by the ones near by, but by some farther out.

Chimera states show up in other models too and can be seen with spiral waves which I also talked about earlier! The chimeras below are found in work by @KenShowalter et al

where we see the core of the spirals on the left have oscillators that are decoherent while outside of the core we see some nicely ordered phases in propagating waves. These is seen EXPERIMENTALLY!! They look at the nonlocally coupling the arrays of Belousov–Zhabotinsky reactions

(Remember earlier the video in this link) https://twitter.com/realscientists/status/1283466536884346886?s=20)

So this isn't just a feature in mathematical models! But we are all still trying to understand what is possible and where these show up.

There are some suggestions that this may explain phenomenon like uni-hemispherical sleep in dolphins where half the brain is synch and half

is decoherent, but I am not 100% sure if that is shown yet? (Correct me if I am wrong please).

Anyway, there are chimeras found in mechanical networks, and chemical networks and biological networks. And we are still looking to understand them more: what models yield chimeras?

What sort of coupling is needs? How many variables?

I just want to say to look forward from a paper of mine in the future for some more chimera fun ;)

Also, please comment with a photo if you have any chimera cats. I love them.