http://worldcat.org/entity/work/id/137543742

Partial Differential Equations from the Materials Sciences: Analysis and Computation

This report describes accomplishments in the areas of electromagnetic scattering and smart materials achieved under Grant No. F49620-95-1-0113. With regards to problems of wave propagation, advances in the development of high-order perturbation methods are reported. These include the derivation and coding of algorithms for the numerical solution of the scalar and vector forward scattering problems for two- and three-dimensional configurations and the formulation of corresponding approaches to inverse scattering calculations and to the estimation of normal and quasi-normal cavity modes. Concurrent achievements in the study of smart materials are also recounted here. They include the development of nonlinear homogenization theories intended to capture overall elastic behaviors (e.g., of shape-memory alloys, SMA), or magnetic and rheological responses (such as those of magnetorheological fluids, MRF). The latter project was undertaken in collaboration with scientists at the Lord Corporation, the worldwide leader in MRF technology, and was geared towards the incorporation of advanced mathematical modeling and simulations into the design of MRF.

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