Type of Document Dissertation Author Jiménez , Silvia Author's Email Address email@example.com URN etd-06182010-104212 Title Homogenization of Nonlinear Partial Differential Equations Degree Doctor of Philosophy (Ph.D.) Department Mathematics Advisory Committee
Advisor Name Title Lipton, Robert Committee Chair Adkins, William Committee Member Litherland, Richard Committee Member Sengupta, Ambar Committee Member Shipman, Stephen Committee Member Vaidyanathan, Ramachandran Dean's Representative Keywords
- power law
- layered media
- dispersed media
- periodic domain
Date of Defense 2010-05-04 Availability unrestricted AbstractThis 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.
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