Another Cool Visual Illusion

Just a reminder that reality happens in the mind. pic.twitter.com/svqAl4xjze

— Science (@scienmag) August 27, 2017

(Tip of the cap to Justin Lanier.)

Another Optical Illusion: How Many Circles Can You Find?

Here's another optical illusion. It's not as visually striking as the other one I posted recently, but it's interesting (and, unlike the other one, the basic qualitative feature of the illusion is not one that I have not encountered before).

In this image there are 16 circles. Don't you find them? Look again carefully & discover the 'coffer illusion' https://t.co/zPpephKSos pic.twitter.com/fnzOFI83GP

— Massimo (@Rainmaker1973) August 9, 2017

Awesome Optical Illusion: Bathroom Tile Edition

Versions of this optical illusion (much less elaborate variants of it) appear to be ubiquitous in restaurant bathroom tiles. :)

Terrific optical illusion by Victoria Skye. @RichardWiseman @chriscfrench pic.twitter.com/IeSFupAcfU

— Martin S Taylor (@martinstaylor) August 7, 2017

Ambiguous Cylinder Illusion

The ambiguous cylinder illusion is funky.

Awesome Visual Illusion

This visual illusion is really cool!

Note: I originally referred to this illusion as an "optical illusion", but my friend Steve Van Hooser, a visual neuroscientist, has pointed out my use of the incorrect term: "I know you are a stickler for details, and as a visual neuroscientist I feel you'd want to know: say "visual illusion" rather than "optical illusion". Because the visual system produces this illusion. There are true "optical" illusions, like the illusion of water on a hot road ahead. That is an optical illusion because it is the diffraction of light that causes the illusion." (I have made this same error on several prior blog posts, which I may eventually look up and correct.)

Möbius Strips: Now Apparently Three-Dimensional

Today I found out about a new paper that reports the generation of Möbius strips of optical polarization, which is very exciting. Unfortunately, the paper's abstract starts out in a very depressing manner that makes me cringe: "Möbius strips are three-dimensional geometrical structures, fascinating for their peculiar property..." Nooooooo!

Although does need three dimensions embed a Möbius strip in an ambient (extrinsic) space, a Möbius strip is a two-dimensional manifold.

(Tip of the cap to Physics Today for their Facebook post of a popular article about the new discovery. Notice the comment about the number of dimensions in the correction. In this case, the popular piece has done better than the paper's abstract.)

Motion Sickness from an Optical Illusion in a Seminar

The talk that is just finishing in the neural rhythms and oscillations workshop concerns optical illusions. The speaker walked us through and demonstrated the "flickering pinwheel illusion" in his slide. It's a very interesting phenomenon, but unfortunately that slide has also very seriously kicked in my motion sickness. Sigh... I feel sick.

And then later on in the talk, the speaker was connecting this stuff to illusions in things like stroboscopic lights, drugs, and migraines. As some of you know, the latter of these is extremely familiar to me from my own experiences --- and stroboscopic lights have triggered them on occasion (and I specifically try to avoid stroboscopic lights). Sigh. Well, at least I have provided another data point.

I guess some neuroscience talks ought to include motion-sickness alerts along with them? I really hope this doesn't mess me up for the rest of the day.

This also reminds me of Kramer's epilectic reaction to Mary Hart on Seinfeld. Just imagine that seen from Seinfeld, except with people at a conference watching a talk on optical illusions and me in the background playing the part of Kramer.

Update: It turns out that another audience member (who also has a history of migraines) who knew better purposely covered her eyes during that slide. I didn't know that such illusions could cause such things, so if I had possessed the scientific knowledge beforehand, I could have done something about it. Burned by my lack of knowledge!

Experimental Results Related to DNLS Equations

The final version of this paper is actually over a year old, but it was just published as a book chapter in a monograph written by one of my collaborators (Panos Kevrekidis). Panos wrote the first sections of the book, and then he invited a number of people to contribute individual chapters on more specific topics. He asked me to write a paper based on experiments relevant to discrete nonlinear Schrodinger (DNLS) equations because of the fact that I work closely with experimentalists on a number of topics. Hence, this paper is a review article that covers a theorist's view on experimental results. (Note that I purposely ran the paper by several experimental colleagues in relevant fields to ensure that I didn't say anything stupid.)

The title of the published version of the chapter (which you probably won't be able to download for free, which is why I included the link to the version on my website) has "DNLS" because the acronym has already been well-established by that point in the context of the book.

Keep your eyes on this spot for a number of additional papers. I have a bunch of stuff that's about to come out. Also, I have a comment to make related to the first-mover scientific advantage, but I'll leave that for a different blog entry because it relates to my networks research rather than nonlinear waves research.

Optical Illusion of the Day

You might remember that I posted a link a while back to this awesome optical illusion of a spinning silhouette. (I can't find my blog entry on it at the moment, so I must not have tagged it very well.) Here is a more generic but still cool optical illusion that I mentioned previously.


Well, here is another really awesome optical illusion, which was posted on Bad Astronomy. Damn! It's probably not as cool as the silhouette, but I still really like it. It also makes me thing of the green/blue paradox (or whatever that's officially called). :)

Also, here is an aural illusion that I can't get to work. I get exactly the same thing whether or not my eyes are open or closed. Can somebody explain this one to me?

(Tip of the cap to Rob Neyer.)

Averaging of Nonlinearity Management with Dissipation

My paper called Averaging of nonlinearity management with dissipation just appeared in Physical Review A. My coauthors are S. Beheshti, K. J. H. Law, and P. G. Kevrekidis (all from U. Mass. Amherst).

This paper is a short but interesting bit of research whose motivation is best described with its abstract:

Motivated by recent experiments in optics and atomic physics, we derive an averaged nonlinear partial differential equation describing the dynamics of the complex field in a nonlinear Schrödinger model in the presence of a periodic nonlinearity and a periodically varying dissipation coefficient. The incorporation of dissipation in our model is motivated by experimental considerations. We test the numerical behavior of the derived averaged equation by comparing it to the original nonautonomous model in a prototypical case scenario and observe good agreement between the two.


Basically, the point is that the theoretical research involving "nonlinearity management" (which typically means using temporal and/or spatial adjustment on one or more of the nonlinear terms in a partial differential equation) uses an entirely conservative setting. However, one one applies one of these strategies experimentally, there is typically an additional dissipation mechanism that gets introduced. (We saw this in our work with experimentalists on nonlinearity management in the setting of nonlinear optics. This short paper was especially motivated by the associated series of experiments, though it's relevant for some Bose-Einstein condensate stuff as well.) Our paper take some theory for the conservative case and works it out for the periodic dissipation case that we saw in our optics experiments as an example of how one would do this more generally.

Optical illusion of the day

Take a look here for the optical illusion of the day.

I've, of course, encountered this particular type of illusion many times, but I think it's just fantastic for it to occupy the entire facade of a building.

(I found this image on the MAA website.)

Modulational instability in nonlinearity-managed optical media

I've been so productive thus far today, so I might as well continue in this direction and blog about a paper of mine that just came out in Physical Review A today. This paper, which you can find here, is the archival sequel to a paper my collaborators and I published in Physical Review Letters late last year.

Anyway, here is the info:


Title: Modulational instability in nonlinearity-managed optical media

Authors: Martin Centurion, Mason A. Porter, Ye Pu, P. G. Kevrekidis, D. J. Frantzeskakis, and Demetri Psaltis

Abstract: We investigate analytically, numerically, and experimentally the modulational instability in a layered, cubically nonlinear (Kerr) optical medium that consists of alternating layers of glass and air. We model this setting using a nonlinear Schrödinger (NLS) equation with a piecewise constant nonlinearity coefficient and conduct a theoretical analysis of its linear stability, obtaining a Kronig-Penney equation whose forbidden bands correspond to the modulationally unstable regimes. We find very good quantitative agreement between the theoretical analysis of the Kronig-Penney equation, numerical simulations of the NLS equation, and the experimental results for the modulational instability. Because of the periodicity in the evolution variable arising from the layered medium, we find multiple instability regions rather than just the one that would occur in uniform media.


We are currently trying to do a little more of a follow-up with our layered optical media setup and then I think that this series of projects will be over. (Martin, the main experimentalist has left Caltech. Demetri Psaltis, whose lab he was in, is probably leaving Caltech, which is preventing new people from joining the project on the experimental side and this sort of thing puts things in limbo anyway. Ye is spread very thin, as he is working not just on this stuff but also on biomechanics stuff and on trying to find a tenure-track job. Anyway, the hope is to submit a final short paper with experiments and some numerics (on which Ye will be the first author) and then put this down. Panos, his students, and I are working on something theoretical that is related to our series of optics projects and the long-term hope is to find another lab (maybe at Oxford or elsewhere in England?) with which we can work on future experiments.

I'll try to write about this later when I blog more about my conference, but I was apparently extremely useful in hooking up a couple of people (by seeing something and realizing exactly who Person A should talk to) for a collaboration. I really like being useful. I wish I could do that more often. (I received a thank-you e-mail about this today.)