Funded Grants

Interactions in pattern forming systems: Bridging the gap between laboratory and large scale open systems

Each of us is a machine, like an airline only much more complicated. Were we designed on a drawing board too, and were our parts assembled by a skilled engineer? The answer is no.
-Richard Dawkins from The Blind Watchmaker

The alternative answer to Dawkins' question is Darwin's and Wallace's theory of natural selection: Nature blindly produces variants, keeping only those that enhance reproductive success. The theory of natural selection presupposes the existence of differentiated organisms that can compete. Organisms are highly organized structures. Where do these structures come from? Among scientists in the field of complexity research there is the growing conviction that there is a deep logic to the emergence of structure, and that order in the physical world is not happenstance but rather the ineluctable result of the flow of energy and matter across systems.

The second law of thermodynamics tells us that an isolated system will degrade until every part of the system is the same. Conversely, an open system can exchange energy and matter with its environment, and can spontaneously develop structure from homogenous initial conditions. Based on a combination of carefully controlled experiments and theoretical analyses conducted over the latter part of the 20th century we now understand how and when structure develops in the simplest systems. These carefully controlled systems are known as pattern forming systems.

A classic demonstration of pattern formation is a pot of water on a stove. If the stove is not turned on, the water remains still. The fluid is in equilibrium, and all parts behave the same; there is no structure. But if the heat is turned on, the water begins to move in an organized manner. The water rises along the walls of the pot and falls in the middle. From initially homogeneous conditions the water has developed an organized dynamical structure. The world is filled with countless examples of this general phenomenon from the mundane--the ornate architecture of a snow flake, the crown-like splash of a drop, the dark ring around a coffee strain--to the exotic--the Earth's magnetic field, sunspots, the large scale structure of the universe.

Is life yet another example of structure emerging from uniformity? Notable scientists such as Stuart Kaufmann and Nobel Laureate Ilya Prigogine argue that it is indeed so. To paraphrase their argument, consider the analogy between the Earth and the heated pot of water. Like the pot, the Earth is in a thermal gradient between the hot Sun and cold interstellar space. Energy flows from the Sun to the Earth, and is reradiated from the Earth to empty space. Like the heated pot of water, the Earth is filled with structure: weather patterns, geological and geographical formations, and--the grandest of all, of course--living organisms. Ergo, as in the heated pot, the structure on Earth derives from the flow of energy. Implicit in this argument is an enormous extrapolation between the ordering seen in simple pattern forming systems, and the ordering seen in the world around us. The aim of my research is to bridge the disparity in complexity between the simple laboratory pattern forming systems and the large complex systems like the Earth.

My research aim is to test the hypothesis that the difference in complexity between a pattern forming system and a large open system is quantitative, not qualitative; to show that the physical principles of self-organization exhibited by patterns in laboratory experiments are the same principles that give rise to the organization in world around us. Large open systems consist of many interacting subsystems. Hence, to test the hypothesis I will systematically investigate the change in the complexity as the number of subsystems increases and their interactions strengthen. For example, to mimic the Earth one could apply a single temperature gradient to a multi-component system. This is the approach I follow in one of my proposed experiments, the stacked Rayleigh-Benard system. The traditional Rayleigh-Benard system is a refined version of the boiling water example from above. A fluid is held between a cool upper plate and a warm lower plate. The temperature gradient, as in the heated pot of water, causes convective flow, but instead of producing a single giant convection roll, the Rayleigh-Benard system organizes in to patterns (e.g. stripes, hexagons, spirals) of rising and falling fluid. My experiment would stack several of these cells but would only set the temperature on the end plates. By varying the number of cells, the gap between each pair of plates and the thickness of the plates, the number of sub-systems and the strength of their interactions can be systematically explored.

In addition to the scientific rationale, there are technological dividends to be expected from this research. Nanotechnology aspires to build materials and devices from the atom upward. Yet to build a single cubic centimeter of matter by individually placing each atom would take millions of years even at the speed of the fastest computers. Clearly, cleverer methods are needed. The current hope is that the self-organizing ability of matter can be leveraged. We know of only two instances in which matter self-organizes: at thermodynamic phase transitions, and in open driven systems (the subject of this essay). Of the two, the latter is the more flexible, and most widely employed. Hence, understanding the origin, mechanisms, and potential of self-organization in non-equilibrium systems is fundamental to advancing our engineering capabilities.