Mathematical ideas from topology, algebra, and other abstract fields are extremely useful. Experimental work involves the characterization of chaotic vibrations in elastic structures, acoustic devices robotic control systems, and electromechanical devices. An experimental research effort involving nonlinear vibrations and chaotic dynamics seeks to characterize chaotic vibrations in elastic structures, fluid-elastic systems, robotic control systems, and electromechanical devices. Experimental tools developed witht he aid of new mathematical ideas, such as fractals, are used to investigate nonlinear dynamics, especially large dynamic deformtions of elastic and inelastic structures. Fluid mechanics .
Several projects involve applications of fluid mechanics.
In one, methods from the kinetic theory of gases are being used to determine balance laws and constitutive relations for rapid flows of granular materials. Standard kinetic theory is modified to account for the inelasticity of the particles and the presence of boundaries. An algorithm had been developed that expresses the shearing stress at the base of a granular heap moving down an incline. This is being used to study the runout flows in chutes and hoppers as well as naturally occurring avalanches and mud slides. Other areas of study are the properties of strongly swirling flows and the loss of stability during the transition to turbulence in vortex breakdown.