The Examination of the Arithmetic Surface (3, 5) Over Q

This thesis is centered around the construction and analysis of the principal arithmetic surface (3, 5) over Q. By adjoining the two symbols i,j, where i2 = 3, j2 = 5, such that ij = -ji, I can produce a quaternion algebra over Q. I use this quaternion algebra to find a discrete subgroup of SL2(R), which I identify with isometries of the hyperbolic plane. From this quaternion algebra, I produce a large list of matrices and apply them via Mobius transformations to the point (0, 2), which is the center of my Dirichlet domain. This list of transformed points is my orbit sampling. The possible walls of the Dirichlet domain are perpendicular bisectors of the hyperbolic geodesic segments between (0, 2) and points from my orbit sampling. Once I produced the list of all perpendicular bisectors, I plot them. From this plot, I refine the collection to only the walls for my Dirichlet domain. I then analyze this surface by finding its hyperbolic area, and the matrices that correspond to gluing one side to the other. The production of this hyperbolic surface by adjoining (3,5) over Q is an “example problem”. This example problem produces a hyperbolic polygon that could be used to show others the process of finding a Dirichlet domain or producing a hyperbolic polygon. One reason why one may want to find a hyperbolic surface is for the list of generators that correlates to the edge gluings. This list of generators can be used in other areas of mathematics and science. This project brought together many areas of math, including topology, hyperbolic geometry, linear algebra, group theory, and noncommutative algebra. Additionally, this project involved a significant programming component, in which I wrote and implemented code in Sage, a Python based computer algebra system

Test of Lorentz Violation with Astrophysical Neutrino Flavor

Presented at the Seventh Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 20-24, 201

An effective many-body theory for strongly interacting polar molecules

We derive a general effective many-body theory for bosonic polar molecules in strong interaction regime, which cannot be correctly described by previous theories within the first Born approximation. The effective Hamiltonian has additional interaction terms, which surprisingly reduces the anisotropic features of dipolar interaction near the shape resonance regime. In the 2D system with dipole moment perpendicular to the plane, we find that the phonon dispersion scales as \sqrt{|\bfp|} in the low momentum (\bfp) limit, showing the same low energy properties as a 2D charged Bose gas with Coulomb ($1/r$) interactions.Comment: Same as published version (11 pages, 2 figure

Baryon-induced collapse of dark matter cores into supermassive black holes

Non-linear structure formation for fermionic dark matter particles leads to dark matter density profiles with a degenerate compact core surrounded by a diluted halo. For a given fermion mass, the core has a critical mass that collapses into a supermassive black hole (SMBH). Galactic dynamics constraints suggest a $\sim 100$ keV/$c^2$ fermion, which leads to $\sim 10^7 M_\odot$ critical core mass. Here, we show that baryonic (ordinary) matter accretion drives an initially stable dark matter core to SMBH formation and determine the accreted mass threshold that induces it. Baryonic gas density $\rho_b$ and velocity $v_b$ inferred from cosmological hydro-simulations and observations produce sub-Eddington accretion rates triggering the baryon-induced collapse in less than a Gyr. This process produces active galactic nuclei in galaxy mergers and the high-redshift Universe. For TXS 2116-077, merging with a nearby galaxy, the observed $3\times 10^7 M_\odot$ SMBH, for $Q_b = \rho_b/v_b^3 = 0.125 M_\odot/(100 \text{km/s pc})^3$, forms in $\approx 0.6$ Gyr, consistent with the $0.5$-$2$ Gyr merger timescale and younger jet. For the farthest central SMBH detected by the \textit{Chandra} X-ray satellite in the $z=10.3$ UHZ1 galaxy observed by the James Webb Space Telescope (\textit{JWST}), the mechanism leads to a $4\times 10^7 M_\odot$ SMBH in $87$-$187$ Myr, starting the accretion at $z=12$-$15$. The baryon-induced collapse can also explain the $\approx 10^7$-$10^8 M_\odot$ SMBHs revealed by the JWST at $z\approx 4$-$6$. After its formation, the SMBH can grow to a few $10^9 M_\odot$ in timescales shorter than a Gyr via sub-Eddington baryonic mass accretion.Comment: Accepted for publication in The Astrophysical Journal Letter

Re: Alemtuzumab-Induced Resolution of Pulmonary Noninfectious Complications in a Patient with Chronic Graft-versus-Host Disease

This study investigated the validation of the psychological resilience scale adaptation from youth development module (RYDM) for secondary school. The psychological RYDM is measured by six factors psychological assets was strongly associated with students academic success. A sample of study is 158 seventh grade students from five secondary schools in Singaraja, Bali Province (75 or 47.4% male and 83 or 52.6%  female, with age range 12-13 years). The constructs validation was conduct by exploratory factor analysis (EFA) method, with SPSS 22.0. Five iterations of the EFA reducing 18 original items to 14 items and 6 original factors to 5 factors. Five factors and 14 items produced are consistent with the conceptual basis used in the original RYDM. The stability of new five factors is formed by a split sample analysis method showed the all of the items of factors identified in the earlier testing stable adequacy of forming a common factor in this analysis in the first and second iteration. The results of analysis the item-total correlation on 14 item (n = 158) showed Cronbach's Alpha value of 0.777. Implications the study for guidance and counseling practice in schools is discussed

Association of acculturation with cardiac structure and function among Hispanics/Latinos: a cross-sectional analysis of the echocardiographic study of Latinos.

OBJECTIVE:Hispanics/Latinos, the largest immigrant population in the USA, undergo the process of acculturation and have a large burden of heart failure risk. Few studies have examined the association of acculturation on cardiac structure and function. DESIGN:Cross-sectional. SETTING:The Echocardiographic Study of Latinos. PARTICIPANTS:1818 Hispanic adult participants with baseline echocardiographic assessment and acculturation measured by the Short Acculturation Scale, nativity, age at immigration, length of US residence, generational status and language. PRIMARY AND SECONDARY OUTCOME MEASURES:Echocardiographic assessment of left atrial volume index (LAVI), left ventricular mass index (LVMI), early diastolic transmitral inflow and mitral annular velocities. RESULTS:The study population was predominantly Spanish-speaking and foreign-born with mean residence in the US of 22.7 years, mean age of 56.4 years; 50% had hypertension, 28% had diabetes and 44% had a body mass index &gt;30 kg/m2. Multivariable analyses demonstrated higher LAVI with increasing years of US residence. Foreign-born and first-generation participants had higher E/e' but lower LAVI and e' velocities compared with the second generation. Higher acculturation and income &gt;20K were associated with higher LVMI, LAVI and E/e' but lower e' velocities. Preferential Spanish-speakers with an income <20K had a higher E/e'. CONCLUSIONS:Acculturation was associated with abnormal cardiac structure and function, with some effect modification by socioeconomic status

First Constraints on the Complete Neutrino Mixing Matrix with a Sterile Neutrino

Neutrino oscillation models involving one extra mass eigenstate beyond the standard three (3+1) are fit to global short baseline experimental data and the recent IceCube ν[subscript μ] + [bar over v][subscript μ] disappearance search result. We find a best fit of Δm[subscript 41][superscript 2]=1.75  eV[superscript 2] with Δx[subscript null-min][superscript 2]/d.o.f. of 50.61/4. We find that the combined IceCube and short baseline data constrain θ[subscript 34] to <80°(<6°) at 90% C.L. for Δm[subscript 41][superscript 2]≈2(6)  eV[superscript 2], which is improved over present limits. Incorporating the IceCube information provides the first constraints on all entries of the 3+1 mixing matrix.National Science Foundation (U.S.) (Grant 1505858)National Science Foundation (U.S.) (Grant 1505855

Computational diagnostics of diesel spray end-of-injection combustion recession

Diesel engines are efficient, reliable, and durable, making them a popular choice for ground transportation and heavy-duty applications. While emissions controls are challenging for diesel engines, strategies such as low-temperature combustion (LTC) strategies have been proven to reduce nitrogen oxides and particulate matter emissions that are common in diesel engines. However, these strategies can result in an increased fraction of the fuel spray being unburnt, leading to unburned hydrocarbon (UHC) emissions. Previous studies have indicated that end-of-injection (EOI) processes can support ignition near the nozzle, thereby consuming the UHCs after EOI. In particular, combustion recession is an EOI process where high-temperature ignition occurs between the nozzle and flame lift-off length, consuming UHCs in the process. Current literature suggests that combustion recession is likely attributed to auto-ignition rather than flame propagation. This is inferred through the analysis of the flame structures at different boundary conditions. However, previous studies have not presented a quantitative analysis of whether combustion recession is driven by auto-ignition or flame propagation. Chemical explosive mode analysis (CEMA) is a flame diagnostic tool based on the eigenanalysis for the chemical Jacobian to identify critical combustion events and has been used in various types of combustion setups, including LTC of diesel sprays. CEMA has been successfully used to determine flame features and is also able to identify the local propagation regimes within a flame which includes autoignition, deflagration, and extinction. Therefore, the objective of this study is to further the understanding of the combustion recession of diesel sprays through computational fluid dynamics (CFD) at LTC conditions where a customized CEMA is implemented to study the EOI combustion modes. The study involves large eddy simulations of a single-hole injection of n-dodecane in an Eulerian-Lagrangian framework performed in the CFD solver CONVERGE. The boundary conditions of the study are in the range of Engine Combustion Network’s “Spray A” conditions. At the baseline boundary conditions of “Spray A”, two chemical kinetic mechanisms are compared with experimental data. With the selected chemical mechanism, the custom implementation of CEMA is used to determine the flame features AEOI and the propagation regime of combustion recession to provide insight into the flame re-initiation mechanism. Through CEMA, it was determined that combustion recession is auto-ignition dominated: the reactive mixtures near the nozzle auto-ignite, and the ignited kernels develop through flame propagation. Lower ambient temperatures cannot support auto-ignition, which leads to the extinction of the flame near the nozzle

An Aeroacoustic Investigation of a Tiltwing eVTOL Concept Aircraft

With the advancement in electric battery design, aircraft designers and manufacturers are no longer constrained to established configurations. Developments in Vertical Take-off and Landing (VTOL) aircraft have also been seen in recent times through the design of modern tiltrotor aircraft such as the AW609 and the V-280 Valor. The combination of these developments allowed engineers to propose designs which utilise the vertical take-off and landing capabilities of a tiltrotor aircraft with electrically driven propulsion systems, deemed eVTOL (Electrically driven Vertical Take-off and Landing). This investigation aims to develop an understanding of the aeroacoustic emissions associated with an eVTOL aircraft, due to acoustics being one of the key components in future certification. The study will consist of an investigation into the baseline design, followed by an optimisation study aiming to reduce the amount of noise generated