This is a grant under the Scientific Computing Research Equipment for the Mathematical Sciences program of the Division of Mathematical Sciences of the National Sciences Foundation. This program supports the purchase of special purpose computing equipment dedicated to the conduct of research in the mathematical sciences. This equipment is required for several research projects and would be difficult to justify for one project alone. Support from the National Science Foundation is coupled with discounts and contributions from manufacturers and with substantial cost-sharing from the institutions submitting the proposal. This program is an example of academic, corporate, and government cooperation in the support of the basic research in the mathematical sciences. This equipment will be used to support five research projects in the Department of Mathematics of Georgetown University: extremal problems for trigonometric polynomials, directed by George Benke; phase boundaries in nonlinear viscoelasticity, directed by Hans Engler; modelling, analysis and numerical simulation in nonlinear structural dynamics, directed by John E. Lagnese; numerical simulation of nonlinear mechanical control systems involving flexible elements, Guenter Leugering; computation of exact scattering strength from a random ocean surface at high wind speeds, directed by A. Paul Stokes.