Identifier

etd-06182010-104212

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

This dissertation is concerned with properties of local fields inside composites made from two materials with different power law behavior. This simple constitutive model is frequently used to describe several phenomena ranging from plasticity to optical nonlinearities in dielectric media. We provide the corrector theory for the strong approximation of fields inside composites made from two power law materials with different exponents. The correctors are used to develop bounds on the local singularity strength for gradient fields inside microstructured media. The bounds are multiscale in nature and can be used to measure the amplification of applied macroscopic fields by the microstructure. These results are shown to hold for finely mixed periodic dispersions of inclusions and for layers.

Date

2010

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Lipton, Robert

Share

COinS