A stochastic orbital is a linear combination of occupied and unoccupied orbitals. However, calculating the stochastic electron density of a given system only requires the system’s occupied orbitals. Hence, we present two methods — analytical and Chebyshev filtering — to filter out the unoccupied orbitals. Analytical filtering directly applies the projection operator onto stochastic orbitals, while Chebyshev filtering utilizes a Chebyshev expansion to accurately represent the aforementioned projection operator. We applied these methods on the tight binding model to gauge how accurate and efficient they can approximate a given system’s analytical electron density. Using stochastic methods will allow us to discern physical properties of a given system that may be otherwise difficult to compute deterministically.

Current rapid design and fabrication techniques enable the creation of structures for a variety of applications: research, foldable robots, and art. However, these structural components are typically flat and rigid making it difficult to make curved structures. A recent area of research with the potential to address this problem are auxetics: mechanical structures made of repeating unit cells, basic building blocks composed of beams and hinges, to create unusual or counterintuitive mechanical properties. When stretched, due to their structural design, auxetics have a volume increase which enables the formation of 3D curved surfaces from a 2D sheet of material. Work in the field of auxetics primarily focuses on creating and optimizing algorithms to generate auxetic designs. This work focuses on the mechanical properties of different auxetic structures so we gathered and synthesized information regarding mechanical characteristics of auxetics in a cohesive and presentable manner for quick reference. There are a variety of unit cell types discussed in literature. Applying knowledge of auxetics, different unit cells were manufactured to gather information such as: unit cell arrangements, deployed state, design limitations to compare theoretical and real life behavior. In theory assumptions do not affect deployment, but in practice they have implications. A half dome structure was created using different kinds of materials: cardstock, PET, and polyurethane foam to investigate how the formation of a 3D curved surface is influenced by material choice. Comparing the theory and practice of auxetic structures provides insight to motivate future research in applications of auxetics.

Hydraulic Fracturing is a technique in which the fracturing of bedrock formations is caused by a pressurized liquid. Small grains of hydraulic fracturing proppants hold these fractures open. A problem with hydraulic fracturing is the friction created between the pipe wall and the fracking fluid caused by the proppant. Usually, this problem is dealt by using chemical compounds known as friction reducers. Friction reducers allow the reduction of surface treating pressure at the wellhead by reducing the drag that the pipe wall experiences while the proppant is being pumped. The main chemical additives in these friction reducers are most often polymers. We hypothesize that these friction reducers can be made by quenching hydrophobic lactide polymerization using a water soluble polymer like poly(ethylene glycol) (PEG) to make a copolymer that is more water soluble. We synthesized a series of block copolymers by ring-opening polymerization of lactide in the presence of PEG using aluminum isopropoxide compound supported by a schiff base ligand as a catalyst. The resulting triblock copolymers with relatively short polylactide blocks were characterized by various analytical techniques such as 1H NMR and DOSY. The polymers synthesized contained a hydrophilic midblock to solubilize the polymer and used hydrophobic interaction between end blocks to self-assemble. Solubilization tests showed that both the composition and molar mass are determining factors in the water solubility of the copolymers. We have synthesized numerous polymers that contain different PEG/lactide ratios which have determined which polymer structure is more effective than others.

In recent decades, chemical propulsion has played a necessary form of energy in various methods of transportation. By achieving a high yield of thrust in relatively short periods of time, it is still the standard means of exiting our Earth’s atmosphere. Though this means of transportation can be effective for near-Earth applications, chemical propulsion raises many concerns such as its reliance on limited consumption of fuel to accelerate and its total mass, motivating the acceleration of clean and sustainable forms of transportation. Electric propulsion (EP) systems aim to achieve thrust with high exhaust velocities over time by ionizing and accelerating propellants such as xenon or argon providing a high specific impulse. EP is a multidisciplinary system ranging from chemistry to electrohydrodynamics while dealing with various multiscale, multiphysics problems. To better understand these principles, we have studied these aspects in detail individually. In analyzing plasma properties with optical emission spectroscopy, we can understand plasma behavior by relating the intensities of spectral peaks to the plasma parameters such as electron temperature. Using ionic thrusters can cause sputtering where the pulsed operation may impact and damage the spacecraft. One study aims to reduce the total sputtering yield by using metallic foams such as tungsten due to their micro-architectured surface to reduce sputtering and extend the life of EP devices. Though EP produces low thrust, over time it can continue accelerating for months to years, while having the benefit of efficient propellant usage, making EP ideal for long journeys in space.