Hybrid Systems Research: Derive digital control programs for distributed autonomous systems (such as network routing, highway and air control, distributed simulation) from mathematical models and methods of relaxed variational calculus on differentiable manifolds constructed to describe the problems.

Stability of Symmetric Tensegrity Structures: Study structures to determine geometric conditions that imply stability. We plan to calculate and make widely available a catalog of stable tensegrity structures that would be of use to architects and sculptors, as well as engineers. Preliminary calculations in Maple and on an IRIS workstation indicate that there are over a hundred essentially different families of such structures that have the rotational symmetry of the regular dodecahedron alone.

A Universal Finite Element Mesh Strategy for Optimal Numerical Resolution of a Class of Physical Problems with Power Type Singularities: There are extremely important classes of physical problems whose resolution requires the solution of partial differential equations. As a few examples we mention problems in structural mechanics, thermodynamics, semiconductor simulation, fluid dynamics and electricity and magnetism. We will investigate a new theory which we believe will yield optimal approximations, in fact even superconvergent approximations, and at the same time greatly simplify the solution process for certain important classes of these problems.

Robert Connelly, Chair, Mathematics Department

Catalogue of Symmetric Tensegrities