Pandemonium is at work even in the most tranquil places. For instance, a young girl playing in the sand on a beach may not realize it, but the sand pile she has created is a study in complexity. As she sprinkles more sand on the top of the pile, a set of mathematical equations govern how each grain behaves, but the way the pile functions as a whole is seemingly random. Gregory Schwedock ’10 is interested in how order emerges from such simplicity. This summer, he is working with Litchfield Professor of Physics Peter Millet on a project that deals with concepts like self-organized criticality, chaos and synchronization. They derived the basis of his research from several books on the subject, such as Sync: The Emerging Science of Spontaneous Order, by Steven H. Strogatz.
“We are trying to gain a better understanding of complex systems to hopefully make better predictions about outcomes in the real world,” Schwedock said. “The breadth of unanswered questions and fields they apply to is huge.”
At the root of his studies is a mathematical curiosity known as self-organized criticality. An ordinary example of a criticality is seen in thermodynamics. Take the transition from the liquid to gas phase. As a substance gets hotter and hotter, it will reach a certain temperature at which there is no distinction between the liquid phase and the gas phase. At this “critical point,” the strange fluid becomes a combination of the two states. Thus in thermodynamics, the critical state is achieved through adjustment of a parameter, temperature. But in self-organized criticality, this is not true.
To see what self-organized criticality really means, observe the little girl’s sand pile. Every action she directs toward it is attracted to a critical point – that is, the accumulation of sand will eventually reach a point that could cause other parts of the structure to collapse. But unlike the example in thermodynamics, the sand pile does not rely on human manipulation of variables in order to approach a critical point. In other words, it is not possible to foresee what repercussions the impact of a falling grain of sand could have. The girl could pepper her sand pile with additional grains, and the effect would be spontaneous - it might cause nothing to happen, or it might cause large sections of the pile to “avalanche.” In chaotic systems, seemingly ordinary interactions like the delicate touch of two particles render unpredictable events. Schwedock’s goal this summer is to learn more about the rules that govern the sand pile and other examples displaying self-organized criticality, like earthquakes and forest fires.
Another related area of research Schwedock is investigating is the ability to “sync” – that is, some phenomena are able to coordinate their cells’ behavior in time. Some living beings that exhibit this behavior are fireflies, ants, humans (the brain and heart), and pendulums. Even man-made entities demonstrate the tendency to “sync” unstructured behavior: social networks, fads, traffic, and mathematical creations like fractals.
Schwedock says that he is interested in this kind of research because it implements bottom-up systems like democracy, birds flying in a pattern, or a ant colony working as an amalgamation of the smaller, simpler roles that the members of the colony play. In a broader sense, the individual actions at the bottom of the pyramid give rise to a grander system at the top. Every part of the system is plain when it stands alone, but when working together, they foster complexity.
Although he originally came to Hamilton considering designing an interdisciplinary major, Schwedock is now a physics major in the process of declaring a computer science minor. Last semester he was abroad in India, but when on campus he participates in a club ice hockey team, Rhyme Lab, and the Frisbee team. After he graduates he plans to start a business involving the organization of personal media files. Depending on how this goes, he will consider attending graduate school in these topics.
“We are trying to gain a better understanding of complex systems to hopefully make better predictions about outcomes in the real world,” Schwedock said. “The breadth of unanswered questions and fields they apply to is huge.”
At the root of his studies is a mathematical curiosity known as self-organized criticality. An ordinary example of a criticality is seen in thermodynamics. Take the transition from the liquid to gas phase. As a substance gets hotter and hotter, it will reach a certain temperature at which there is no distinction between the liquid phase and the gas phase. At this “critical point,” the strange fluid becomes a combination of the two states. Thus in thermodynamics, the critical state is achieved through adjustment of a parameter, temperature. But in self-organized criticality, this is not true.
To see what self-organized criticality really means, observe the little girl’s sand pile. Every action she directs toward it is attracted to a critical point – that is, the accumulation of sand will eventually reach a point that could cause other parts of the structure to collapse. But unlike the example in thermodynamics, the sand pile does not rely on human manipulation of variables in order to approach a critical point. In other words, it is not possible to foresee what repercussions the impact of a falling grain of sand could have. The girl could pepper her sand pile with additional grains, and the effect would be spontaneous - it might cause nothing to happen, or it might cause large sections of the pile to “avalanche.” In chaotic systems, seemingly ordinary interactions like the delicate touch of two particles render unpredictable events. Schwedock’s goal this summer is to learn more about the rules that govern the sand pile and other examples displaying self-organized criticality, like earthquakes and forest fires.
Another related area of research Schwedock is investigating is the ability to “sync” – that is, some phenomena are able to coordinate their cells’ behavior in time. Some living beings that exhibit this behavior are fireflies, ants, humans (the brain and heart), and pendulums. Even man-made entities demonstrate the tendency to “sync” unstructured behavior: social networks, fads, traffic, and mathematical creations like fractals.
Schwedock says that he is interested in this kind of research because it implements bottom-up systems like democracy, birds flying in a pattern, or a ant colony working as an amalgamation of the smaller, simpler roles that the members of the colony play. In a broader sense, the individual actions at the bottom of the pyramid give rise to a grander system at the top. Every part of the system is plain when it stands alone, but when working together, they foster complexity.
Although he originally came to Hamilton considering designing an interdisciplinary major, Schwedock is now a physics major in the process of declaring a computer science minor. Last semester he was abroad in India, but when on campus he participates in a club ice hockey team, Rhyme Lab, and the Frisbee team. After he graduates he plans to start a business involving the organization of personal media files. Depending on how this goes, he will consider attending graduate school in these topics.
