This thesis examines the interpretations derived from the Kac Ring Model, and the adding of a modification to the original model via “kick backs,” which can be interpreted to represent time reversals in the individual Kac rings. The results of this modification are analyzed, and their implications explored. There are three main parts to this thesis. Part 1 is a literature review which explains the working principles of the original Kac ring and explores its numerous applications. Part 2 describes the software and the theoretical & computational methodology used to implement the model and gather data. Part 3 analyzes the data gathered and makes a conclusion about its implications. There is an appendix included which contains some figures from Part 3 in a larger size, as it wasn’t possible to make the figures bigger within the text due to formatting.

Various biologically inspired flow field designs of the gas distributor (interconnector) have been designed and simulated. Their performance using Nafion-212 with humidified H₂ and Air at 80 °C with the ANSYS Fluent Fuel Cell module software was evaluated. Novel interdigitated designs were optimized by obeying biologically inspired branching rules. These rules allow for more mathematically formal descriptions of flow field designs, enabling relatively simple optimization. The channel to land ratio was kept equivalent between designs with typical values between 0.8 and 1.0. The pressure drop and the current density distribution were monitored for each design on both anode and cathode sides. The most promising designs are expected to exhibit lower pressure drop however, low pressure drop can also be an indication of potential water flooding at higher operating current density. A biologically inspired interdigitated design with 9 inlet channels exhibited reduced pressure drop and improved current density distribution compared to all other interdigitated designs evaluated in this study. The simulated fuel cell performance data at ambient pressure with humidified H₂ and air compares well with the experimental data using a single serpentine flow field design.

Recently fabricated two-dimensional phosphorene crystal structures have demonstrated great potential in applications of electronics. In this paper, strain effect on the electronic band structure of phosphorene was studied using first-principles methods including density functional theory (DFT) and hybrid functionals. It was found that phosphorene can withstand a tensile stress and strain up to 10 N/m and 30%, respectively. The band gap of phosphorene experiences a direct-indirect-direct transition when axial strain is applied. A moderate −2% compression in the zigzag direction can trigger this gap transition. With sufficient expansion (+11.3%) or compression (−10.2% strains), the gap can be tuned from indirect to direct again. Five strain zones with distinct electronic band structure were identified, and the critical strains for the zone boundaries were determined. Although the DFT method is known to underestimate band gap of semiconductors, it was proven to correctly predict the strain effect on the electronic properties with validation from a hybrid functional method in this work. The origin of the gap transition was revealed, and a general mechanism was developed to explain energy shifts with strain according to the bond nature of near-band-edge electronic orbitals. Effective masses of carriers in the armchair direction are an order of magnitude smaller than that of the zigzag axis, indicating that the armchair direction is favored for carrier transport. In addition, the effective masses can be dramatically tuned by strain, in which its sharp jump/drop occurs at the zone boundaries of the direct-indirect gap transition.