In this project, we created a code that was able to simulate the dynamics of a three site Hubbard model ring connected to an infinite dissipative bath and driven by an electric field. We utilized the master equation approach, which will one day be able to be implemented efficiently on a quantum computer. For now we used classical computing to model one of the simplest nontrivial driven dissipative systems. This will serve as a verification of the master equation method and a baseline to test against when we are able to implement it on a quantum computer. For this report, we will mainly focus on classifying the DC component of the current around our ring. We notice several expected characteristics of this DC current including an inverse square tail at large values of the electric field and a linear response region at small values of the electric field.

This research evaluates the capabilities of typical radiological measures and dual-energy systems to differentiate common kidney stones materials: uric acid, oxalates, phosphates, struvite, and cystine. Two different X-ray spectra (80 kV and 120 kV) were applied and the dual-energy ratio of individual kidney stones was used to figure out the discriminability of different materials. A CT cross-section with a prospective kidney stone was analyzed to see the capabilities of such a technique. Typical radiological measures suggested that phosphates and oxalate stones can be distinguished from uric acid stones while dual-energy seemed to prove similar effectiveness.

Although extracellular throughout their lifecycle, trypanosomes are able to persist despite strong host immune responses through a process known as antigenic variation involving a large, highly diverse family of surface glycopro- tein (VSG) genes, only one of which is expressed at a time. Previous studies have used mathematical models to investigate the relationship between VSG switching and the dynamics of trypanosome infections, but none have explored the role of multiple VSG expression sites or the contribution of mosaic gene conversion events involving VSG pseudogenes.

Women are twice as likely as men to develop Major Depressive Disorder (MDD), and current MDD therapies are only effective for about a third of patients. Hormonal transitions, specifically those involving estradiol (E2), have been found to contribute to this increased vulnerability in women. This study aimed to investigate potential mechanisms underlying the sex differences seen in MDD vulnerability, specifically the role of E2. The brain region-specific changes induced by chronic stress differ for female rats than for male rats. Therefore, we aimed to determine the effects of sex and chronic stress on E2 expression in four brain regions: the hippocampus, medial prefrontal cortex, amygdala, and cerebellum. Sprague-Dawley rats (n = 48, 24 males, 24 females; n=12/Tx group) were subjected to daily wire mesh restraint stress (6 h/21 days), and were euthanized and dissected the day following the end of chronic restraint stress (day 22). Ultra high-pressure liquid chromatography-mass spectroscopy was used to directly measure E2 in the brain regions. Quantitative real-time PCR was used to indirectly assess E2 expression via mRNA for aromatase (ARO-L) and estrogen receptors (ERβ, ERɑ, and GPR30), as well as expression of inflammatory cytokines (IL-1β and TNF-ɑ). Our findings suggest that chronic stress may lead to changes in local estradiol expression in the brain that are both sex-dependent and brain region-specific, while the data are preliminary given the small sample size. We found that expression of ARO-L mRNA, a measure of local E2 production, tended to increase in the HIPP, but decrease in the mPFC following chronic stress, and in the mPFC this pattern was only observed in males. Local estradiol production in the brain seems to act as a potential compensatory mechanism in the hippocampus, but as a protective mechanism in the mPFC, which is highly sensitive to chronic stress.

I examine the effects of metallicity on solar mass stellar evolution, trying to replicate a previous result in Windhorst et.al., 2018, in which a zer metallicity solar mass star did not reach the AGB, and thus may turn into a helium white dwarf. In trying to replicate this result, I used the M.E.S.A. stellar evolution code and was unable to reproduce this result. While M.E.S.A has undergone several updates since the previous result was obtained, more current evidence suggests that this may have been a one-time occurrence, as no helium white dwarfs were produced for low-metallicity models. Nonetheless, interesting results were obtained, including a lowest metallicity value for which CNO burning does not significantly contribute during the main sequence, 1 −10 Z , which produces noticeable effects on post main sequence evolution. All models are run with no rotation, one solar mass, and a series of MESA parameters kept constant, with the only exception being metallicity. Any metallicity value listed as Nd −10 is an absolute mass fraction, and Z is relative to solar metallicity, 2d*10 −2 .

Professor Alarcon’s lab is producing proton beam detectors, and this project is focused on informing the decision as to which layout of detector is more effective at producing an accurate backprojection for an equal number of data channels. The comparison is between “square pad” detectors and “wire pad” detectors. The square pad detector consists of a grid of square pads all of identical size, that each collect their own data. The wire pad detector consists of large rectangular pads that span the entire detector in one direction, with 2 additional layers of identical pads each rotated by 60° from the previous. In order to test each design Python was used to simulate Gaussian beams of varying amplitudes, position and size and integrate them in each of the two methods. They were then backprojected and fit to a Gaussian function and the error between the backprojected parameters and the original parameters of the beam were measured.

In this experiment an Electrodynamic Ion Ring Trap was constructed and tested. Due to the nature of Electrostatic fields, the setup required an oscillating voltage source to stably trap the particles. It was built in a safe manner, The power supply was kept in a project box to avoid incidental contact, and was connected to a small copper wire in the shape of a ring. The maximum voltage that could be experienced via incidental contact was well within safe ranges a 0.3mA. Within minutes of its completion the trap was able to trap small Lycopodium powder spores mass of approximately 1.7*10^{-11}kg in clusters of 15-30 for long timescales. The oscillations of these spores were observed to be roughly 1.01mm at their maximum, and in an attempt to understand the dynamics of the Ion Trap, a concept called the pseudo-potential of the trap was used. This method proved fairly inaccurate, involving much estimation and using a static field estimation of 9.39*10^8 N\C and a charge estimate on the particles of ~1e, a maximum oscillation distance of 1.37m was calculated. Though the derived static field strength was not far off from the field strength required to achieve the correct oscillation distance (Percent error of 9.92%, the small discrepancy caused major calculation errors. The trap's intended purpose however was to eventually trap protein molecules for mapping via XFEL laser, and after its successful construction that goal is fairly achievable. The trap was also housed in a vacuum chamber so that it could be more effectively implemented with the XFEL.

The purpose of this senior thesis is to explore the abstract ideas that give rise to the well-known Fourier series and transforms. More specifically, finite group representations are used to study the structure of Hilbert spaces to determine under what conditions an element of the space can be expanded as a sum. The Peter-Weyl theorem is the result that shows why integrable functions can be expressed in terms of trigonometric functions. Although some theorems will not be proved, the results that can be derived from them will be briefly discussed. For instance, the Pontryagin Duality theorem states that there is a canonical isomorphism between a group and the second dual of the group, and it can be used to prove $Plancherel$ theorem which essentially says that the Fourier transform is itself a unitary isomorphism.

Carbon allotropes are the basis for many exciting advancements in technology. While sp² and sp³ hybridizations are well understood, the sp¹ hybridized carbon has been elusive. However, with recent advances made using a pulsed laser ablation in liquid technique, sp¹ hybridized carbon allotropes have been created. The fabricated carbon chain is composed of sp¹ and sp³ hybridized bonds, but it also incorporates nanoparticles such as gold or possibly silver to stabilize the chain. The polyyne generated in this process is called pseudocarbyne due to its striking resemblance to the theoretical carbyne. The formation of these carbon chains is yet to be fully understood, but significant progress has been made in determining the temperature of the plasma in which the pseudocarbyne is formed. When a 532 nm pulsed laser with a pulsed energy of 250 mJ and pulse length of 10ns is used to ablate a gold target, a peak temperature of 13400 K is measured. When measured using Laser-Induced Breakdown spectroscopy (LIBS) the average temperature of the neutral carbon plasma over one second was 4590±172 K. This temperature strongly suggests that the current theoretical model used to describe the temperature at which pseudocarbyne generates is accurate.

The first numerical predictions of the dynamical diquark model of multiquark exotic hadrons are presented. Using Born-Oppenheimer potentials calculated from lattice QCD and phenomenological diquark(triquark) masses, mass eigenvalues that are degenerate in spin and isospin are computed from numerical solutions to both coupled and uncoupled Schroedinger equations. Assuming reasonable estimates of the fine-structure splittings, we find that the band structure of our mass spectra agrees well with the experimentally observed spectrum of charmonium-like states. Using our best fits, we predict a number of unobserved states, such as pentaquark states that lie below the charmonium-plus-nucleon threshold.