Separability and Hidden Symmetries of Kerr-Taub-NUT Spacetime in Kaluza-Klein Theory

The Kerr-Taub-NUT spacetime in the Kaluza-Klein theory represents a localized stationary and axisymmetric object in four dimensions from the Kaluza-Klein viewpoint. That is, it harbors companion electromagnetic and dilaton fields, thereby showing up the signature of the extra fifth dimension. We explore the separability structure of this spacetime and show that the Hamilton-Jacobi equation for geodesics admits the complete separation of variables only for massless geodesics. This implies the existence of the hidden symmetries in the spacetime, which are generated by the conformal Killing tensor. Using a simple trick built up on a conformally related metric (an "effective" metric) with the Killing tensor, we construct the explicit expression for the conformal Killing tensor.Comment: 10 pages; REVTe

Silicon Quantum Dots Conjunctive with Stable Radicals: Potential Application in Non-invasive Cancer Diagnostics

Quantum Dots, and nanomaterials in general, are one of the most promising areas of current physical study, especially their potential medical uses. In this study we introduced Nitroxide free radicals into a Silicon Quantum Dot (SiQD) solution and conducted experiments on the modified SiQDs in order to characterize their physical properties. We gathered emission, excitation, absorption and electron spin resonance (ESR) spectra of both modified and unmodified SiQDs. Previous studies have shown the possibility of using proteins as markers for cancer detection. Our measurements show the potential of using the interaction between these protein markers and SiQDs as a form of non-invasive cancer diagnostics

Examining the Disruptive Innovation Theory by Analysing Tesla, Inc.

The shift to electrification with electric vehicles (EV) is regarded as a phenomenon that is expected to permanently revolutionize the whole automotive industry and social habits of customers along with global economies and supply chains. Coinciding with the trend in early 2000s, at a time when the electric vehicle market was not formed yet, a startup called “Tesla Inc.” entered the market with all-electric strategy. As both developer and pioneer of the EVs, the company had gained a serious position in the industry, while being a part of the market's formation and development in remarkably two decades. Similar to the company's progress, ‘Disruptive Innovation Theory’ is well-known concept in academia that focuses on how companies create market disruption through their innovations. Although having some overlapping aspects with the theory, Tesla’s contrasting strategies, such as market entry, necessitates examination in the focus of theory. The main goal of the study was to analyze how Tesla's approach redefines the theory of disruptive innovation by comparing and contrasting the case’s strategy with theory’s framework through three different dimensions: Tesla's disruption in the automotive industry, its high-end market entry against theory’s low-end approach, and incumbent companies respond to such innovative progress. By placing Tesla as a case, the study was designed to unfold progress of both the company and its industry from framework of the theory. Thus, regarding the qualitative research design, the development of the EV phenomenon and the company was unfolded with the process study approach for observing how the status quo in the market was formed overtime. Due to inclusiveness of the focused fields, secondary data was chosen as the source and obtained from several academic and business outputs (i.e., newspapers, company/industry, and governmental outputs) that were specifically focusing on automotive industry and the case company. Outcomes revealed that Tesla's contradictory approach did not essentially redefine the disruptive innovation theory. Although the company’s both financial and industrial growth along with its achieved position contributed to the electrification phenomenon in the industry, it instead served as an alternative business-case through following a pattern that does not comply with the theory, not only in terms of its market entry, but also in many different layers (e.g., innovation, product, marketing, organizational strategies). Additionally, the approach of the incumbents also did not fully conform to the theory: despite the governmental regulations pushing them for lowering carbon emissions, evolutionary progress (instead of revolutionary) of battery technology (in terms of performance and cost), mainstream customers preference and lack of sufficient charging infrastructure in cities were considered as the main reasons for their delay. Despite being a popular case in academia with similar case-theory comparisons, this study was constructed on the company's past to present (and even future) strategies and presented its growth pattern using up-to-date data. Contrary to previous studies, the case was analyzed not only from a market entry perspective, but also from other aspects highlighted by the theory. In addition, considering the managerial implications, the study highlighted Tesla’s case as an alternative approach in terms of positioning and developing innovations in market and the pattern to follow for other companies in the industry

Design and Construction of a Race Team Equipment Box

This senior project discusses the design and construction of a race team equipment box. This equipment box was located on the rear of a modified golf cart. The rear half of the golf cart was modified by creating framework around the rear so that the equipment box would rest on top and be able to detach from it. The equipment box was able to hold all necessary equipment that is needed in the pits. Each items location was placed ergonomically so they can be reached with ease in an efficient manner. Located on both sides of the equipment box were tires holders. These tire holders swivel 360 degrees so the tires can be sanded. The equipment box has one shelf in it so that there are two areas to store parts. Once the project was completed, a “fit check” was done to make sure the equipment box could hold all that it needed. It was found that the equipment box met all specifications put into place and exceeded expectations. The equipment box was able to hold over 500 lbs. of equipment and still function properly. It also had an area for a third tire to be held. The tire holders worked well and were able to hold the tire while also being able to swivel to the four different positions

Searching for dark matter substructure: a deeper wide-area community survey for Roman

We recommend a deeper extension to the High-Latitute Wide Area Survey planned to be conducted by the Nancy Grace Roman Space Telescope (\emph{Roman}). While this deeper-tier survey extension can support a range of astrophysical investigations, it is particularly well suited to characterize the dark matter substructure in galactic halos and reveal the microphysics of dark matter through gravitational lensing. We quantify the expected yield of \emph{Roman} for finding galaxy-galaxy-type gravitational lenses and motivate observational choices to optimize the \emph{Roman} core community surveys for studying dark matter substructure. In the proposed survey, we expect to find, on average, one strong lens with a characterizable substructure per \emph{Roman} tile (0.28 squared degrees), yielding approximately 500 such high-quality lenses. With such a deeper legacy survey, \emph{Roman} will outperform any current and planned telescope within the next decade in its potential to characterize the concentration and abundance of dark matter subhalos in the mass range 10$^7$-10$^{11}$\,M$_{\odot}$.Comment: 5 pages, 3 figures, Roman Core Community Survey (CCS) White Pape