A working knowledge of mathematics is a vital requirement for introductory university physics courses. However, there is mounting evidence which shows that many incoming introductory physics students do not have the necessary mathematical ability to succeed in physics. The investigation reported in this thesis used preinstruction diagnostics and interviews to examine this problem in depth. It was found that in some cases, over 75% of students could not solve the most basic mathematics problems. We asked questions involving right triangles, vector addition, vector direction, systems of equations, and arithmetic, to give a few examples. The correct response rates were typically between 25% and 75%, which is worrying, because these problems are far simpler than the typical problem encountered in an introductory quantitative physics course. This thesis uncovered a few common problem solving strategies that were not particularly effective. When solving trigonometry problems, 13% of students wrote down the mnemonic "SOH CAH TOA," but a chi-squared test revealed that this was not a statistically significant factor in getting the correct answer, and was actually detrimental in certain situations. Also, about 50% of students used a tip-to-tail method to add vectors. But there is evidence to suggest that this method is not as effective as using components. There are also a number of problem solving strategies that successful students use to solve mathematics problems. Using the components of a vector increases student success when adding vectors and examining their direction. Preliminary evidence also suggests that repetitive trigonometry practice may be the best way to improve student performance on trigonometry problems. In addition, teaching students to use a wide variety of algebraic techniques like the distributive property may help them from getting stuck when working through problems. Finally, evidence suggests that checking work could eliminate up to a third of student errors.

Because of its massive nature and simple two-body structure, the heavy meson bottomonium (the flavorless bound state of the bottom quark and anti-quark) is among the simplest systems available for the study of the strong force and quantum chromodynamics (QCD)—a feature which has made it of special interest to particle physicists.

Despite being bound by the strong force, bottomonium exhibits a rich spectrum of resonances corresponding to excited states extremely analogous to that of positronium or even familiar atomic systems. Transitions between these levels are possible via the absorption or emission of either a photon, gluon, or gluons manifesting as light hadrons. The goal of this thesis was to establish a theoretical value for the currently unmeasured partial decay width for one such transition—the electromagnetic decay channel hb -> etab gamma. To this end, two methods were utilized.

The first approach relied on the presumption of a nonrelativistic constituent quark model interacting via a simple static potential, allowing for radial wave functions and energy eigenvalues to be obtained for the states of interest via the Schrödinger equation. Upon an application of the standard electromagnetic multipole expansion followed by a utilization of the electric dipole E1 decay width formula, a value of 57.7 ± 0.4 keV was obtained.

The second approach stemmed from the effective Lagrangian describing the bottomonium P to S electromagnetic transitions and relied on the presumption that a single coupling constant could be approximated as describing all nP to mS transitions regardless of spin. A value for this coupling constant could then be extracted from the 1P to 1S spin triplet data and used to predict the width for the singlet 1P to 1S transition. The partial decay width value found in this manner was 47.8 ± 2.0 keV.

Various other methods and models have established a predicted range of 35 to 60 keV for this partial decay width. As the values determined in this thesis fall within the expected range, they agree well with our current understanding of this electromagnetic transition and place further confidence on the expected range.

The FoF1 ATP synthase is a molecular motor critical to the metabolism of virtually all life forms, and it acts in the manner of a hydroelectric generator. The F1 complex contains an (αβ)3 (hexamer) ring in which catalysis occurs, as well as a rotor comprised by subunit-ε in addition to the coiled-coil and globular foot domains of subunit-γ. The F1 complex can hydrolyze ATP in vitro in a manner that drives counterclockwise (CCW) rotation, in 120° power strokes, as viewed from the positive side of the membrane. The power strokes that occur in ≈ 300 μsec are separated by catalytic dwells that occur on a msec time scale. A single-molecule rotation assay that uses the intensity of polarized light, scattered from a 75 × 35 nm gold nanorod, determined the average rotational velocity of the power stroke (ω, in degrees/ms) as a function of the rotational position of the rotor (θ, in degrees, measured in reference to the catalytic dwell). The velocity is not constant but rather accelerates and decelerates in two Phases. Phase-1 (0° - 60°) is believed to derive power from elastic energy in the protein. At concentrations of ATP that limit the rate of ATP hydrolysis, the rotor can stop for an ATP-binding dwell during Phase-1. Although the most probable position that the ATP-binding dwell occurs is 40° after the catalytic dwell, the ATP-binding dwell can occur at any rotational position during Phase-1 of the power stroke. Phase-2 of the power stroke (60° - 120°) is believed to be powered by the ATP-binding induced closure of the lever domain of a β-subunit (as it acts as a cam shaft against the γ-subunit). Algorithms were written, to sort and analyze F1-ATPase power strokes, to determine the average rotational velocity profile of power strokes as a function of the rotational position at which the ATP-binding dwell occurs (θATP-bd), and when the ATP-binding dwell is absent. Sorting individual ω(θ) curves, as a function of θATP-bd, revealed that a dependence of ω on
θATP-bd exists. The ATP-binding dwell can occur even at saturating ATP concentrations. We report that ω follows a distinct pattern in the vicinity of the ATP-binding dwell, and that the ω(θ) curve contains the same oscillations within it regardless of θATP-bd. We observed that an acceleration/deceleration dependence before and after the ATP-binding dwell, respectively, remained for increasing time intervals as the dwell occurred later in Phase-1, to a maximum of ≈ 40°. The results were interpreted in terms of a model in which the ATP-binding dwell results from internal drag at a variable position on the γε rotor.

This study involves determining if different political symbols associated with ideological labels vary between the old and new terms. Specifically, the terms conservatism, liberalism, moderate, progressivism, and populism were used, where the first two are the old terms and the last two are the new terms. A survey was given to a representative sample of the United States, provided by SurveyMonkey, consisting of 205 respondents. Questions regarding favoritism/support for groups and political issues were asked to determine a trend of what each political ideology favors. Voting behavior was also evaluated to identify if there was a connection between self-identification of a political ideology or party and the frequency/type of elections that the individuals voted in. The hypothesis was that by adding progressivism to the liberalism category, the percentage of people who identify as these groups would be roughly equal to the percentage of people who identify as conservative, since the percentage of people who identify as conservative has been much greater than those who identify as liberal. The consensus was that the percentage of people who identified as liberal and progressive was greater than the percentage of those who identified as conservative. For example, the percentage of people who identified as conservative, moderate, liberal, and progressive was 25.9%, 31.7%, 27.3%, and 14.6%, respectively. Ultimately, after evaluating issue and symbolic preferences, progressivism is not just a term used in place of liberalism, but instead a whole new ideology that is different from other popular political ideologies. Considering voting behavior, there is no conclusive evidence that says that people who identify with one ideology vote more frequently or in a different election than people who identify with other ideologies.

The LOw Frequency ARray (LOFAR) is a new and innovative radio telescope designed and constructed by the Netherlands Institute for Radio Astronomy (ASTRON). LOFAR unique capable of operating in very low frequencies (10-240 MHz) and consists of an extensive interferometry array of dipole antenna stations distributed throughout the Netherlands and Europe which allows it to achieve superb angular resolution. I investigate a part of the northern sky to search for rare radio objects such as radio haloes and radio relics that may have not been able to have been resolved by other radio telescopes.

Solid-state lithium-ion batteries are a major area of research due to their increased safety characteristics over conventional liquid electrolyte batteries. Lithium lanthanum zirconate (LLZO) is a promising garnet-type ceramic for use as a solid-state electrolyte due to its high ionic conductivity. The material exists in two dierent phases, one that is cubic in structure and one that is tetragonal. One potential synthesis method that results in LLZO in the more useful, cubic phase, is electrospinning, where a mat of nanowires is spun and then calcined into LLZO. A phase containing lanthanum zirconate (LZO) and amorphous lithium occursas an intermediate during the calcination process. LZO has been shown to be a sintering aid for LLZO, allowing for lower sintering temperatures. Here it is shown the eects of internal LZO on the sintered pellets. This is done by varying the 700C calcination time to transform diering amounts of LZO and LLZO in electrospun nanowires, and then using the same sintering parameters for each sample. X-ray diraction was used to get structural and compositional analysis of both the calcined powders and sintered pellets. Pellets formed from wires calcined at 1 hour or longer contained only LLZO even if the calcined powder had only undergone the rst phase transformation. The relative density of the pellet with no initial LLZO of 61.0% was higher than that of the pellet with no LZO, which had a relative density of 57.7%. This allows for the same, or slightly higher, quality material to be synthesized with a shorter amount of processing time.

This project details the learning of processes in nanofabrication and sensor detection fields. We sought to apply this knowledge to develop a processing procedure to fabricate sensors used to detect high energy protons.  We seek to create such a sensor to be applied to aid Mayo Clinic’s Proton Beam Therapy center for cancer treatment through providing beam detection measurements. Developed plans would allow for proton beam detectors to be able to measure beam intensity and direction which would allow for more accurate beam treatments. Current detectors require much calibration and solid state detectors can’t withstand the high-energy exposure of the proton beam for long durations. By fabricating pixelated diamond sensors we expect to produce sensitive beam readings, while extending detector length time due to diamonds durable crystalline lattice. We report processing procedures for simple 2-3 contact detectors as well as more complex multi-contact pixelated sensors used for spatial resolution of the beam. Testing of simple sensors is additionally reported with successful radioactive source detection.

We designed and constructed a cryostat setup for MKID detectors. The goal for the cryostat is to have four stages: 40K, 4K, 1K and 250mK. Prior to the start of my thesis, the cryostat was reaching 70K and 9K on the first and second stages respectively. During the first semester of my thesis I worked on getting the second stage to reach below 4K such that it would be cold enough to add a sorption fridge to reach 250mK. Various parts were machined for the cryostat and some tweaks were made to existing pieces. The largest changes were we thinned our stainless steel supports from 2mm to 10mil and we added roughly 6-10 layers of multi-layer insulation to the first and second stages. Our result was that we now reach temperatures of 36K and 2.6K on the first and second stages respectively. Next we added the sorption fridge to the 4K stage by having the 4K stage remachined to allow the sorption fridge to be mounted to the stage. Then I designed a final, two stage, setup for the 1K and 250mK stages that has maximum capabilities of housing a six inch wafer for testing. The design was sent to a machinist, but the parts were unfinished by the end of my thesis, so the parts and stage were not tested. Once the cryostat was fully tested and proven to reach the necessary temperatures, preliminary testing was done on a Microwave Kinetic Inductance Detector (MKID) provided by Stanford. Data was collected on the resonance and quality factor as they shifted with final stage temperature (5K to 285mK) and with input power (60dB to 15dB). The data was analyzed and the results agreed within expectations, as the resonant frequency and quality factor shifted down with increased temperature on the MKID. Finally, a noise characterization setup was designed to test the noise of devices, but was not fully implemented.

Radio astronomy is a subfield in astronomy that deals with objects emitting frequencies around 10 MHz to 100 GHz. The Low Frequency Array (LOFAR) is a array of radio antennas in Europe that can reach very low frequencies, roughly between 10-240 MHz. Our project was to image and clean a field from LOFAR. The data was a 10 degree square in the sky centered at a right ascension of 10:19:34.608 and a declination +49.36.52.482. It was observed for 600 seconds at 141 MHz. To clean the field, we had to flag and remove any stations that were not responding. Using a program called FACTOR, we cleaned the image and reduced the residuals. Next we checked the validity of our sources. We checked positional offsets for our sources using the TGSS survey at 150 MHz, and corrected the declination of our LOFAR sources by a factor of 0.0002 degrees. We also fixed the LOFAR fluxes by a factor of 1.15. After this systematic check, we calculated the spectral index of our sources using the FIRST survey at 1435 MHz. We plotted this spectral index against LOFAR flux as well as redshift of the sources, and compared these to literature.

X-ray Free Electron Lasers (XFELs) are used for diffractive x-ray imaging of the structure of many biological particles, such as viruses and proteins. The ultimate goal for XFEL-based microscopy is atomic resolution images of non-crystalline particles. However, data collection efficiency as well as the limited amount of measurement time given annually to researchers, such high-resolution images are presently impossible to attain. Here, we consider two potential solutions to the single-particle hit rate problem; the first looks at applying static electric fields to existing aerodynamic particle injectors, and the second looks at the viability of using time-varying electric fields associated with ion traps to create high-density regions of particles. For the static solution, we looked at applying a constant electric potential to the nozzle, as well as applying a high voltage to a ring electrode in close proximity to a grounded nozzle. We considered the breakdown field strength of the helium gas used to determine how closely the ring electrode could be placed without creating an arc that could potentially destroy expensive equipment. Then, we considered the possibility of using electrodynamic ion traps to increase particle densities. We first characterized how charged particles behave in oscillating electric fields using a simple electrode geometry. Using the general results from this, we then constructed a rudimentary ion trap to test if our experiment agreed with the theory. Finally, we conducted a literature review to determine what particle densities other scientists have been able to measure using ion traps. We then compared existing ion traps to what we expect from the nozzle injectors to determine which method may be the better solution.