Effective Behavior of Composite Materials.
Final rept. 1 Sep 83-30 Nov 84,
NEW YORK UNIV NY COURANT INST OF MATHEMATICAL SCIENCES
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The main results of our work fall into three categories which we list in order of significance to our present and future work 1 Focusing a singularity of the nonlinear Schrodinger equation. We have solved by a careful analytical-numerical method the basic question of what the local rate of blow-up is for solutions of the nonlinear Schrodinger equation with cubic nonlinearity in 2 space dimensions. This problem is a basic one that arises in many aspects of nonlinear wave propagation. 2 Selfdiffusion of interacting Brownian motions. Using methods of wave propagation in random media that we had developed earlier, we were able to study the effective behavior of a tagged Brownian particle in interaction with an infinite system of other such particles. 3 Bounds for effective properties of composites by analytic continuation. The analytic continuation method was known to work only for two component materials. In our work we extend it to multicomponent materials by using the theory of several complex variables.
- Laminates and Composite Materials