My research aims to tackle the limitations of automatic differentiation (AD) within Physics Informed Neural Networks (PINNs), specifically focusing on the difficulties with non differentiable functions in petroleum engineering applications, such as fluid f low in porous media. By addressing these critical constraints, the applicability and accuracy of AD can be significantly improved, leading to enhanced problem solving capabilities and a deeper understanding of complex phenomena. Overcoming the challenges o f AD in managing non differentiable functions not only opens up new opportunities for its application in petroleum engineering but also extends its potential in other fields facing similar issues.

This work presents an overview of the development of efficient aerial highways for Unmanned Aerial Vehicles (UAVs). Our study attempts to preemptively solve the problem of increasing air traffic by designing a highway system similar to highways for ground transportation. Aerial vehicles could run into safety issues such as mid-air collisions, engine failure, and losing communication between drones and their operators. Our proposed highway design will mitigate the damages caused by these issues or avoid them altogether. We formulated the highway design into an optimization problem that optimizes the placement of the highways to maximize proximity to the delivery routes while minimizing the total distance traveled. Our results show that highways organize traffic, which reduces the probability of mid-air collisions and helps strategically place fewer communication and control centers along the corridors.

Detonation is the supersonic mode of propagation of combustion waves. It can be described as a supersonic front sustained by an exothermic reaction zone. However, the structure of the front is not planar and exhibits both three-dimensional and transient features. This translates into the so-called cellular structure of detonation and is visualized by inserting a sooted plated on the side walls of the tube. In this case, a fish-scale pattern is observed and can be studied to further understand the properties of the detonation. In particular, a correlation between cell mean width and the chemical properties of the detonation (induction length) was demonstrated. However, most of the soot-foil studies report very limited information on the soot foil giving only an estimated value of the cell mean width. In this work, we aim at characterizing the statistical distribution of cells in the soot foil by providing the mean cell width, the standard deviation, and the size of the distribution. Several parameters while be varied to highlight the advantages of this approach.

Boundary layer analysis is crucial to evaluate drag forces and transferred heat in supersonic applications. This project aims to simulate laminar flow around a 1D flat plate using the Entropy Stable Discontinuous Collocated (SSDC) solver designated for Computational Fluid Dynamics (CFD) problems. Utilizing several programs such as Gmsh, Jupyter Notebook and ParaView, the problem setup is designed based on the Reynolds and Mach numbers. The results are compared to Blasius Theorem for flat plate boundary layers.

This project aimed to study the changes in crystallinity in P3HT: PCBM through morphology investigation, using polarized light microscopy for screening and evaluating the quality of the thin films. Thermal annealing at different temperatures was applied to control the crystallinity of P3HT: PCBM. A variety of characterization techniques was utilized, including UV-Vis spectrophotometer, spectrofluorometer, and Atomic Force Microscopy to measure thin films' properties such as absorbance, photoluminescence, and surface roughness, respectively. The results showed improvement in the morphology of the thin films upon thermal annealing, resulting in an increase in surface roughness, enhanced material absorption, and the production of PCBM crystals. In addition, a strong correlation was observed between the information on morphology in the PLM images and the measurement of other techniques. This study provides valuable insights into the properties and behavior of P3HT: PCBM thin film, and proves that PLM is capable of capturing high-quality images of birefringent materials with high contrast.