We establish the criterion for chaos in three-planet systems, for systems similar to those discovered by the Kepler spacecraft. Our main results are as follows: (i) The simplest criterion, which is based on overlapping mean motion resonances (MMRs), only agrees with numerical simulations at a very crude level. (ii) Much...
We establish the criterion for chaos in three-planet systems, for systems similar to those discovered by the Kepler spacecraft. Our main results are as follows: (i) The simplest criterion, which is based on overlapping mean motion resonances (MMRs), only agrees with numerical simulations at a very crude level. (ii) Much...
Over 10 billion tons of concrete are produced for the construction industry every year, making concrete the second most used substance on Earth, only surpassed by water. With such high importance as a building material, there is significant need for the ability to accurately model concrete behavior. As a quasi-brittle...
Soft matter is the field of science concerning soft and deformable materials: such as liquids, gels, and foams. Active matter is a sub-field of soft matter that considers systems that contain active agents or particles that consume energy for self-propulsion or to exert mechanical stress on the surrounding system. In...
We study the symmetry groups with respect to various equivalence relations defined on subshifts, and more generally, on Cantor systems. Two basic notions of equivalence for dynamical systems are conjugacy and flow equivalence. In this dissertation, we focus on the well-studied automorphism group, which is the group of self-conjugacies, and...
The promise of a clean, renewable, and abundant energy supply make the efficient conversion of solar energy to electricity a compelling scientific and societal goal. In the following chapters, I will describe my efforts to advance one class of photovoltaic technology, dye-sensitized solar cells, by demonstration and characterization of unexplored...
X-ray reflectivity (XRR) versatile technique that characterize the surface structures. However, due to the lack of phase information of X-ray data, the reconstruction of electron density profile (EDP) from XRR data is an ill-posed inverse problem that requires extra attention. In Chapter 1, several key concepts in XRR data analysis...