Professor Kenneth Showalter is supported by a grant from the Theoretical and Computational Chemistry Program to continue his work on nonlinear dynamics in chemical systems. The research involves studies of complex chemical dynamics in continuously stirred reactors, in homogeneous and unstirred systems, and distributed chemical systems. Three main lines of research are proposed: 1) developing techniques to control chaos using linear and nonlinear control methods; 2) studies of chemical waves in inhomogeneous and perturbed excitable media; and 3) studies of instabilities in propagating reaction-diffusion fronts. Both experimental and theoretical studies will be performed. One novel experimental project being explored by Showalter is the use of an ink jet printer to prepare patterns of immobilized catalyst for excitable chemical systems. This enables him to study chemical wave behavior in the presence of systematically designed geometric constraints which are models for excitable biological media such as the heart muscle. Nonlinear dynamics is a powerful tool for understanding complexity in nature, and it has many practical applications. Biological applications include stabilizing periodic rhythms in heart tissue and inducing periodic and chaotic behavior in hippocampal brain tissue. Major successes can also be found in applications of the principles of excitable media to cardiology, which have led to an understanding of the role spiral waves play in heart maladies such as tachycardia and fibrillation. Showalter's research provides a fundamental chemical understanding of the mechanistic underpinnings for these important biological phenomena.
