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Date of Award
Physics and Astronomy
Nonlinear phenomena are ubiquitous in nature and in almost every discipline of science. Various nonlinear dynamic theories are being developed to investigate a wide range of complex nonlinear systems. In this work, we study two types of nonlinear phenomena. The first type involves understanding and controlling the properties and dynamics of two-dimensional (2D) material systems. We develop a binary phase field crystal (PFC) model which simultaneously addresses diffusive dynamics of large-scale systems and resolves material microstructures, and apply the model to the study of two material systems. (1) We use this PFC model to investigate the self assembly of 2D binary colloidal structures with sublattice ordering. A variety of ordered phases and their coexistence have been identified, including some structures observed in experiments and our theoretical predictions of some new phases, as well as the corresponding stability and phase diagrams. Elastic properties, phase transformation, and grain nucleation and growth of these modulated/ordered phases have also been examined. (2) The PFC model is parameterized for the study of hexagonal boron nitride monolayers, to identify the structures, energies, and dynamics of both symmetrically and asymmetrically tilt grain boundaries. Our results reproduce all types of dislocation cores found in previous experiments and first-principles calculations, and predict some new defect structures for various boundary misorientations, including the 60o inversion domain boundaries. In addition, we identify a defect-mediated growth dynamics for inversion domains governed by the collective atomic migration and defect core transformation at grain boundaries and junctions, a process that is related to inversion symmetry breaking in binary lattice.
The other type of nonlinear phenomena covered in this research is related to acute injuries in biomedical systems. We develop a nonlinear dynamical theory of acute cell injury describing a competition between total injury-induced damage (D) and total injury-induced stress responses (S). Our theory includes a non-autonomous model that identifies the dynamic time courses given a single injury, and determines the conditions and bistability diagrams governing the survival vs death outcomes of the cell under different initial conditions and model parameters. The model is also extended to construct a multi-injury model that is used to examine the effects of pre- and post-conditioning and post-injury drug treatment. We test the theory of single injury by using a rodent model of global cerebral ischemia, and hypothesize that changes in polysome-bound mRNAs and denatured protein aggregates in injured neurons would estimate S and D, respectively. The experimental data is fit to the theory using the Nelder-Mead method. This validation of the model is the first step towards applying it to develop effective therapies against clinically-important forms of acute cell injury.
Taha, Doaa, "Nonlinear Dynamic Studies Of Pattern-Forming And Biomedical Systems" (2017). Wayne State University Dissertations. 1882.