Letter from Chile, December 2003
Dear Chicago Students --
Leo Kadanoff and I spent some time getting aquainted with the nonlinear physics research in Chile this month. The occasion was a one-week international meeting at which Leo and I spoke. I also spent the previous week meeting researchers in Chile. I'm writing this letter to tell you about the cool research going on. I saw some neat experiments and even more theory. Still, I'll emphasize the experiments, because I think these would have most interest to you.
Sergio's site Has a lot of information, but you may find it hard to navigate. Many of his content files aren't linked. To see a raw list go here.
Background
As you probably read elsewhere in this site, there are two departments in two universities where most stuff seemed to be going on. The first is the University of Chile, in the Faculty of applied science. Most of their strength is in theory, but these theorists are not afraid to do experiments and supervise experiments. Our main contact there is Prof. Sergio Rica. He is also the co-ordinator of our exchange program from the Chile side---my counterpart in Chile. The other main group is at the University of Santiago. Our main contact there is Prof. Francisco Melo, an experimentallist.
I spent a morning looking over Prof. Melo's lab. Francisco was away so Eugenio Hamm showed me around
wrinkling
One big interest in the University of Santiago is the wrinkling of thin elastic sheets. Aside from Melo, Prof. Enrique Cerda is doing both theory and experiments on wrinkling. The basic question is the three-dimensional buckling pattern that comes when an elastic sheet is stretched. If you pull with your hands on the two ends of a sheet of paper, you see ripples appear along the lines of stress; its wavelength is a centimeter or so. But where did that length scale come from? It is much smaller than the size of the paper, but much bigger than the thickness. It doesn't depend a lot on the amount of stress: you can pull harder but the wavelength doesn't change. Cerda and collaborators showed in a recent Nature article that the wavelength is a fractional power of the length and the thickness. Now they are investigating other geometries and other kinds of stress. There is a lot of variation depending on these things. The main current interest is in a circular membrane. A rubber sheet is draped over a circular hoop and pulled taut by many weights hanging from the sheet beyond the ring. This sheet is nice and smooth with no wrinkles. But now a small funnel is placed under the middle of the sheet and air is drawn out of it so that it sucks the membrane in. Now dozens of radial wrinkles appear around the funnel, and they extend out partway to the outer hoop. But how many wrinkles occur and how far they extend depends on the stress at the boundary. The basic features are understood, but only the simplest kinds of stress have so far been considered.
I saw another aspect of wrinkling in Eugenio Hamm's lab. He studies crumpling singularities---the points of lines that form when an elastic sheet is crushed. These singularities multiply as one crushes harder and harder. But how does this multiplication occur? How is a new singularity born and how does it grow, move and develop? One simple geometry to watch the singularities develop is to place a piece of office paper on a table between two books. First move the books together a bit so that the paper is obliged to bow up off the table. then poke down on the top of the paper with a pencil point. As you push harder, you will see shallow vertices move away from the point and then begin to revolve around it. Eugenio's setup shows richer behavior. He has a thin cylindrical sheet. He compresses it and twists it until a latticework pattern of ridges appears. By controlling the overall stress he can make the singular points move around and dance around each other.
sand
Melo's lab has several projects on granular flow; their effort is comparable to Chicago's. A student named Leonardo Caballero showed me a striking, nonintuitive behavior of vibrated sand that remains unexplained. The experiment takes place on a shallow black plastic dome 5 cm in radius. The dome is placed in a shallow cylindrical tray. Around the perimeter of the dome some fine white sand is scattered---enough to fill the annular ditch around the edge of the dome to a depth of a few particles. The whole thing is on a vibrator that can vibrate rigidly up and down at 10-20 Hz. Leonardo turns the vibrator on and we watch the white grains dance in their trough. Soon the dance becomes organized. Fingers of sand begin to climb up the sides of the dome like so many tears of wine. Half a dozen of them climb up from around the perimeter, stretch into the center and then haul up their trailing parts until all the sand is all at the top of the dome! It works with a variety of surfaces and geometries. Does this work with only one grain? No. Does it work if you evacuate the air from the region where the sand is? No.
surfactant controlled crystal growth
Our teeth are made of a calcium mineral that does not grow naturally under physiological conditions. The body induces this particular crystal structure by shaping the molecular environment somehow during growth. Jorge Pavez in Melo's group studies the role of surfactants in controlling this growth. They have found surfactants that seem to have the desired effect. The surfactants also influence the overall form of the crystallites.
flipping vortices in a wind tunnel
Rodrigo Hernandez in the University of Chile has a wind tunnel for studying air flows at the intermediate Reynolds characteristic of an airplane wing. It is a long, square plexiglas tube about a foot on a side. Big fans on either end force the air through the tube and circulate it around via another larger duct. Here's a photo. In the middle of the tunnel sits a little wing with control surfaces that can be adjusted remotely. The flow around fixed surfaces of this kind has long been studied by engineers. Hernando's interest is in the response of the flow to a rapid, local motion of the surfaces. One possibility is that the motion makes a qualitative change in the vortices that stream off the surfaces. Here's some more air turbulence stuff.
Granular vortex in phase space
Patricio Cordero is a theorist who studies structure formation in inelastic granular gases. He showed us a remarkable, simple example. It is a one-dimensional line of point particles heated at one end and cooled at the other. When the contrast between the two ends grows beyond a certain level, a remarkable singularity appears in the interior. Cordero pictures it by representing all the particles in the two-dimensional space of co-ordinate and momentum. The thousands of particles in his simulation flow around in this phase space. The singular region looks like a vortex in this phase space. Since the particles have no volume, they spiral to a point at the center of the vortex. Here's a movie. The density there grows without bound. No one knows how it works, nor have its scaling properties yet been characterized well.
unsintering
A young theorist named Felipe Barra studies instabilities of a metal surface placed under mechanical stress. The metal can seek to lower its stress energy by allowing atoms to diffuse over its surface. This results in remarkable instabilities and shapes.
Rodrigo Soto is another theorist at University of Chile who does granular simulations. He discovered some new varieties of phase separation in inelastic granular gases. There's a movie elsewhere on this site.
evaporation patterns
Sergio Rica is fascinated with many kinds of patterns, as you probably have seen elsewhere on this site. He studies theoretical examples in numerical quantum fields. He also studies experimental examples in drying paint. His paint was diluted, so that it lacked the viscous properties that produce a thick, even coat of paint. But it still have plenty of suspended pigment particles. He let the paint dry between two panes of glass with a millimeter spacing between them. If you've ever let buttermilk dry on the sides of a glass, you've seen the kind of graceful branched structures that result. These patterns seem to be variants of the lace patterns that U of C student Robert Deegan saw in his own evaporation experiments. Between the branches, are draped festoons fine lines. It seems that as the water retracted in discrete jumps as it evaporated.
A little MRSEC
Like Chicago, the University of Chile has a block-funded materials research lab, headed by Fernando Lund. The U of C's Prof. Jaeger is on its external review board. Anyone interested in traditional materials research should be aware of Prof. Lund's operation.
---Tom Witten, December 2003