|Office Location:||029B Physics Bldg|
|Office Phone:||(919) 660-2872|
My research interest is the study of nonlinear dynamics, with a special emphasis on systems in which spatial patterns may form. Spontaneous pattern formation is a widespread natural phenomenon which has been observed in fluid convection, nonlinear optics, chemical reaction-diffusion experiments, colonies of swimming micro-organisms, visual hallucinations and a host of other physical, chemical and biological systems. Many pattern forming systems can be described by nonlinear partial differential equations. Theoretical studies of these equations are valuable because they help us understand pattern formation in real systems, and because they may yield insight into other dynamical behaviors. I use tools from elementary group theory, dynamical systems theory, asymptotic analysis, and scientific computing to study dynamics these systems. I am currently focusing my efforts on two problems, namely vertically vibrated fluid layers (Faraday waves) and swarming biological populations. A detailed research statement is available at http:// www.math.duke.edu/~chad/research.html, or by request.
Please go to http://www.math.duke.edu/~chad to view my main web site.