This experiment looks at the role of friction in granular silos when the bottom floor is raised quasi-statically (very slowly).  When disks made of a special plastic are placed between appriopriately designed polarizers and backlit, the ones experiencing higher stresses light up.  The disks are approximately 5mm in diameter.  The photo shows the stress in the system at the start and after slowly pushing the bottom with a piston through approximately 1.5 cm.  Analysis of the pattern of stress chains will clarify the mechanisms by which dry granular materials such as sand, coal, rice, or pills respond to external loads.

This experiment is being carried out in collaboration with researchers Evelyne Kolb and Guillaume Overlez from the University Pierre & Marie Curie in Paris. 

To understand the population dynamics of biological systems it is sometimes necessary to take into account the spatial structure of the population.  That is, different types of organisms subject to the same external environmental pressures may thrive or not, depending on how the individuals tend to be arranged in space.  For example, a species that tends to form dense clusters may be more susceptible to extinction due to a disease that has only a minor effect on a species that tends to be more sparsely distributed.

The figure at right shows a snapshot of a simulation of simple "organisms" that remain stationary and are characterized by a single trait: their natural mortality rate.  Individuals with the average mortality are gray, those with smaller (or larger) are green (or red).  Individuals are born next to their parent, inheriting their parent's mortality rate plus a small random mutation.  They die either from natural causes or from diseases, which are very rare.  The disease kills all organisms that belong to the connected cluster where it originates.  The total spread in mortality rates represented in this picture is about 10% of the average. 

he emergent spatial structure in the model we have investigated is of interest both for bioligists and physicists.  First, it is a crucial ingredient in the evolutionary stability of this simple system.  The mechanism that selects for a stable natural mortality rate is based entirely on the different spatial properties of colonies with different mortality rates, not on the traits of individual organisms.  Second, it is an example of a nonequilibrium physical structure that arises as a solution to a complex optimization problem, and may be characterized as a "self-organized critical" structure leading to a power-law distribution of epidemic sizes.

This  central theme covers a variety of specific projects that are supported by the Air Force Office of Scientific Research, DARPA, the Office of Naval Research, and NASA. The physical phenomena are concerned with the linear and nonlinear dynamic instabilities and limit cycle oscillations that may arise from the interaction between a flexible structure and a surrounding convecting fluid flow. Aircraft, naval craft and rotorcraft and their propulsion systems are important examples where such issues arise in practice, although comparable phenomena arise in bioengineering (blood flow through arteries), biological marine propulsion, civil engineering (osillations of long span bridges and tall buildings in high winds) and other fields of science and technology. The major research issues are how to deal with the complexity of very high dimensional systems on the order of a million degrees of freedom that describe the fluid/ structure system and how to identify and model the wide range of nonlinear effects that may be important. The latter include structural freeplay, geometrically large motions and non-classical damping as well as fluid shock waves and turbulence. Of course, several of our studies focus solely on a fluid or structural system.

The theoretical and experimental methods run the full gamut of modern techiques developed by the nonlinear dynamics research community including basin boundary construction, dimensional determination, and characterization of chaos. New developments receiving special emphasis are control of nonlinear oscillations, determination of stability of limit cycle oscillations based upon experimental data, system identification and determination of isola through continuation methods and the development of Proper Orthogonal Decomposition techniques to extract the dominant eigenmodal features of very high dimensional systems.

One  intriguing application of the chaos control methods we have developed is in the biological area. We have initiated a program to characterize in vitro the dynamics of small pieces of rapidly paced cardiac muscle and to use feedback methods to suppress or control the observed bifurcations by applying small perturbations to the tissue. We find that there are only a small number of classes of bifurcations in the tissue, but that there is significant variation in the prevalence of these behaviors from animal to animal.

In addition, we are using similar methods to control in vivo a fibrillating sheep atrium. The eventual long term goal of this project is to develop an implantable defibrillator that will maintain a healthy rhythm in humans prone to the onset of atrial fibrillation using only small electrical shocks. In our current experiments with sheep, we use a high-density mapping system to record the spatial-temporal complexity occurring on the surface of the heart during atrial fibrillation. Small control shocks are applied to a single electrode attached to the surface of the heart based on real-time measurements of the cardiac dynamics at a nearby spatial location.

This research is collaboration with Mr. Robert Oliver and Ms. Soma Sau (graduate students in Biomedical Engineering), and Profs. Wanda Krassowska (Biomedical Engineering), David Schaeffer (Mathematics), Joshua Socolar (Physics), and Patrick Wolf (Biomedical Engineering).

Coating flows and moving contact lines arise in a diverse range of applications including the design of paints, the liquid lining of the lungs, and microchip coatings. Driven films often undergo `fingering' instabilities seeded by surface imperfections. Recent studies show that by driving the film with a surface stress while maintaining an opposing body force, new dynamics, involving stable undercompressive fronts, are possible. At right, the output of a numerical simulation of the dynamics shows the beginning of the interaction of the front with some imperfections in the surface.

This work is being done in collaboration with Dr. Michael Shearer of NCSU.