ISR News Story
Antman receives NSF grant to study nonlinear problems of solid mechanics
The researchers hope to develop powerful new mathematical methods for analyzing the large and rapid deformations of solid bodies. This work has applications both to new technological materials including "smart" materials and to old biological materials, such as living tissue. (Although it has been known for 50 years how to derive the equations governing such deformations cleanly from first principles without ad hoc approximations, the mathematical tools for treating these equations are only now being developed and refined.) The specific problems under study include (1) the deformation of thin shell-like bodies in a fluid flow, (2) the loss of stability of such a shell subjected to pulsating pressures, (3) the swimming of eels, (4) the rigorous justification of useful approximations for the motions of the body when the loads it bears are applied slowly or when the loads are very large or when the body is of light weight, (5) the buckling of shells, (6) strange effects for spinning bodies, (7) the development and the preclusion of shocks (which are large and sudden discontinuities in velocity and deformation), and (8) the construction of effective methods of computation. Antman is continuing to make carefully formulated physical theories accessible to mathematicians, and to make modern techniques of applicable mathematics accessible to scientists and engineers, with special attention to graduate students.
June 19, 2007