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.
Recommended Citation
Jiménez, Silvia, "Homogenization of nonlinear partial differential equations" (2010). LSU Doctoral Dissertations. 3729.
https://repository.lsu.edu/gradschool_dissertations/3729
Committee Chair
Lipton, Robert
DOI
10.31390/gradschool_dissertations.3729