Falaco Solitons

Falaco Solitons

The black spots on the bottom of the swimming pool are signatures of topological defects dynamically induced in the surface (of fluid density discontinuity) that separates the water and the air. The topological defects are called Falaco Solitions and, in the words of I. Prigogine, they are states of matter far from (thermodynamic) equilibrium Yet, in a still pool of water these topological defects have a surprisingly long lifetime -- they will last for many minutes.

A remarkable feature of Falaco solitons is that they are easy to create and are so ubiquitous. Similar topological phenomena are to be expected in discontinuities at all scales -- from the micro physics of nucleii to the galactic defects in cosmology.

Take a closer look or download from LANL archive


Just after WW II, one of my first contacts at MIT was a Brazilian young man named Jose Haraldo Hiberu FALCAO.
He was in metallurgy and I was in physics.
WE became close friends and roommates during the period 1946-1950. He spent much of his time chasing the girls and playing soccer for MIT.

Now MIT is not known for its athletic achievements, and when one weekend Haraldo scored two goals - giving MIT one of its few wins (ever) - the sports section of one of the Boston papers, misspelled his name with the headline ~


Frankly I do not remember the exact headline from > 55 years ago, but one thing is sure: Haraldo was known as FALACO ever since.

Haraldo moved back to Brazil and our ways parted.

I became interested in many things, the most pertinent to this story included topological defects and topological evolution in physical systems.

In 1986 I thought it would be great fun to go to Rio to see my old college friend, and then go to Machu Pichu to watch Haley's comet go by. My son was an AA pilot, so as parents we got a free Airline Ticket ticket to Brazil

Haraldo had married into a very wealthy family and had constructed a superb house, that his wife had designed, hanging onto a cliff-side above Sao Coronado beach south of Rio. He had a white marble swimming pool next to the house fed by a pristine stream of clear water.

The morning after my wife and I arrived in Rio (Haraldo's chauffeur met us at the airport in a big limo) I got up, after sleeping a bit late, and went to the pool for a morning dip. Haraldo and his family had gone to work, and no one was about. I sat in the pool. wondering about the fortunes of life, and how Haraldo - who I had help tutor to get through MIT - was now so very wealthy, and here I was - just a poor university professor.

I climbed out of the pool, and was met by two servants who had been waiting in the wings. One handed me a towel and a terry cloth robe, and the other poured coffee and set out some breakfast fruit, croissants, etc.

I put a lot of sugar into the strong Brazilian coffee, as Haraldo had taught me to do long ago, and was stirring the coffee when I turned toward the pool (about 5-10 minutes after climbing out of the pool). In the otherwise brilliant sunshine, two black disks (about 15 cm in diameter ) with bright halo rings were slowing translating along the pool floor.
The optics caught my attention. Is there something about the southern hemisphere that is different?

I went over to the pool, jumped in to investigate what was going on, and Voila!!!, the black discs disappeared. I thought: Here was my first encounter of the third kind and I blew it.

I climbed out of the pool, again, and then noticed that a pair of Rankine vortices was formed as my hips left the water, and that these rotational surfaces of positive Gauss curvature, within a few seconds, decayed into a pair of rotational surfaces of negative Gauss curvature. Each of the ultimate rotational surfaces were as if someone had depressed slightly a rubber sheet with a pencil point forming a dimple. As the negative Gauss curvature surfaces stabilized, the optical black disks were formed on the bottom of the pool. The extraordinary thing was that the surface deformations, and the black spots, lasted for some 15 minutes !!!. They were obviously rotational solitons.

The rest is history, and is described on my website and articles in some detail. Snell's law projects the solar rays in the manner observed, but what was not at first apparent was that there is a circular "string" -- a 1D topological defect -- that connects the two 2D topological defects of negative Gauss curvature. The string extends from one dimple to the other, and is evident if you add a few drops of dye to the water. Moreover, experimentation indicated that the long term soliton stability was due to the Global effect of the "string" connecting the two dimpled rotational surfaces. Dye injection later on demonstrated the 1D arc connecting the dimples. If the arc is sharply severed, the dimples do not "ooze" away, as you would expect from a diffusive process; instead they disappear quite abruptly.
The Falaco Solitons have the confinement properties of two quarks on the end of a string.

Upon returning to the US, I gave a talk at the 1986-87 Dynamics Days meeting in Austin, Texas, describing the observations.
I called the objects FALACO SOLITONS, for they came to my attention in Haraldo's pool in Rio.
Haraldo will get his place in history.

I knew that finally I had found a visual, easily reproduced, experiment that could be used to show people the importance and utility of Topological defects in the physical sciences.
The observations were highly motivating.
The topological ideas have led u;timately to
1. A non-statistical method of describing processes that are thermodynamically irreversible.
2. Applications of Topological Spin and Topological Torsion in classical and quantum field theories.
3. Another way of forming Fermion pairs
4. A suggestion that spiral galaxies may be stabilized by a connecting "thread".
5. and a number of patentable ideas in fluids, electromagnetism, and chemistry.

Most of these ideas are available on Cartan's Corner.


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Last update 01/23/2009
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