Actuators based on the interaction of electric and magnetic fields with materials (often referred to as smart actuators or smart structures), are of current interest at a variety of length scales. Arrays of electrostatic micro-actuators have found their way into applications in displays. For future applications involving interactions of such arrays with fluids it is likely that one needs to solve problems of communication and control in such arrays. One possible approach that is appealing in this context is the use of pattern-forming dynamical systems to realize control over large arrays. In this talk, based on joint work of Eric Justh and the speaker, we discuss the properties of a class of partial differential equations that have interesting pattern-formation characteristics. We analyze qualitative properties via suitable energy functionals. We also discuss some of the modeling aspects of individual actuators that lead us to this approach. This work is supported by Army Research Office under the ODDR&E MURI97 Program Grant No. DAAG55-97-1-0114 to the Center for Dynamics and Control of Smart Structures (through Harvard University), and an ARCS Fellowship awarded to Eric Justh.

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