I had the opportunity to visit the nonlinear physics group at the University of Chile in Santiago this past December. During my stay, I met with researchers working on a broad range of theory and experiments that really highlight the universality of nonlinear phenomena across many fields.
I am broadly interested in the emergence of patterns throughout the natural world. Similar patterns can be found in very different systems: think about all the places you find stripes similar to ripples that appear on sand dunes in the desert. Another example, labyrinth patterns, have been observed in magnetic nano-particle suspensions called ferro-fluids and on pufferfish.
More striking in my mind is the fact that spatially localized structures that consist of a patch of pattern embedded in a homogeneous background can emerge even though there is no preferred location in the system. This is, however, a universal phenomenon that has been observed in a wide variety of nonlinear systems throughout biology, chemistry and physics.
A motivation for my thesis work comes from understanding the formation and dynamics of vegetation patterns in semi-arid regions. The patterns arise in these ecosystems to optimize the use of water or other limited resources. I am particularly interested in how spatially localized patches of vegetation respond to periodic fluctuations in growth conditions, say variations in precipitation.
The original purpose for my visit to Chile was to take my theoretical predictions that were motivated by plant ecology and apply them to a nonlinear optics experiment. This experiment uses a liquid crystal cell similar to what is in your TV screen to generate localized structures whose dynamics can be studied in great detail. Moreover, the researchers can introduce fluctuations in time that play the same role as variations in precipitation for vegetation patches. Unfortunately, an earthquake misaligned the optical components of the experiment a few weeks before I arrived and they weren’t able to get it running again before I left. Maybe this will give me an excuse to go back?
I was, however, able to make a connection between vegetation models and another experiment being done there to study Faraday waves on the surface of a vertically vibrated container of fluid. Michael Faraday first studies the basic setup in the 1800’s when he noticed that a wealth of different patterns could appear depending on the frequency and amplitude of the vibrations. Amazingly, this simple experiment is still producing new and surprising results today. For example, the researchers at U. Chile found that they could generate spatially localized patterns by using a container that is very thin in one direction. Moreover, the localized patterns didn’t appear for the amplitudes of vibration that they expected. It turns out that the reason may have an analogy to the large-scale redistribution of water in plant ecology of semi-arid regions. This is work in progress.
While in Chile, I was also fortunate enough to attend an international workshop on instabilities and nonequilibrium structures in Valparaiso. Having spent the previous week in Santiago getting to know some of the researchers in attendance at the workshop made the experience much more enriching for me. I was able to have more in-depth academic discussions because I already knew many people and had background knowledge of their current research focus. I found some time for sightseeing with a few other students during on an off day at the conference. One of the highlights was a visit to the Nobel Prize-winning poet Pablo Neruda’s house in Valparaiso. We happened to run into my advisor there.
My time in Chile has exposed me to a diverse range of applications of nonlinear physics. I learned about dynamics in systems ranging from fluid systems, nonlinear optical media, and magnetic materials to ecology, traffic, and the Chilean school system. Thanks to my gracious hosts in Santiago and an engaging workshop in Valparaiso, I have returned to Berkeley with new ideas and connections to researchers in Chile and across the world.
Punit Gandhi is a Ph.D. candidate in the physics department at UC Berkeley. He studies pattern formation and was funded by a CONYCIT grant to develop models of experimentally observed localized structures in collaboration with the nonlinear physics group at Universidad de Chile.