Nonlinear stability of source defects in oscillatory media

In this paper, we prove the nonlinear stability under localized perturbations of spectrally stable time-periodic source defects of reaction-diffusion systems. Consisting of a core that emits periodic wave trains to each side, source defects are important as organizing centers of more complicated flows. Our analysis uses spatial dynamics combined with an instantaneous phase-tracking technique to obtain detailed pointwise estimates describing perturbations to lowest order as a phase-shift radiating outward at a linear rate plus a pair of localized approximately Gaussian excitations along the phase-shift boundaries; we show that in the wake of these outgoing waves the perturbed solution converges time-exponentially to a space-time translate of the original source pattern.https://arxiv.org/abs/1802.07676First author draf

Reducing Oxidative Stress in Retinitis Pigmentosa Mouse Model P23H

Retinitis Pigmentosa is a genetic disorder that can disrupt our vision through the deterioration of rods cells and, eventually, cone cells. A study found that patients with RP have higher oxidative stress levels than a control group. Patients who exhibit higher levels of reactive oxygen species would not be able to adequately compensate with normal levels of antioxidant enzymes. Furthermore, previous studies have shown that SOD3 was essential for reducing the oxidative damage done to the injured tissue. Through this study, we hope to provide a method to minimize the damage done by RP and to establish the importance of the extracellular matrix in photoreceptors’ health. Transgenic heterozygous SOD3OE were crossed with a knock-in gain of function heterozygous RhoP23H/+ to produce our target genotype for this experiment, SOD3OE/RhoP23H/+. At post-natal day 30 and 60, the mice’s retinal functional ability was tested using ERG. One retina from each mouse was collected for Western blot for protein analysis, while the other was embedded in paraffin for structural analysis. The results show that the SOD3OE/RhoP23H/+ has higher ERG at P30, but not statistically significant. At P60, the ERG’s were reduced, indicating that SOD3OE cannot mitigate the effects of RhoP23H/+. The mutation overwhelms the effectivity of SOD3, and, as a result, is not a viable treatment plan for this mutation. Although the overexpression of the anti-oxidant has not entirely counteracted RhoP23H/+, this study advances the understanding of the importance of extracellular enzymes and the possibility of delaying the onset of RP in patients.Honors CollegeBiomedical Engineering, Department o

Reparametrization modes in 2d CFT and the effective theory of stress tensor exchanges

We study the origin of the recently proposed effective theory of stress tensor exchanges based on reparametrization modes, that has been used to efficiently compute Virasoro identity blocks at large central charge. We first provide a derivation of the nonlinear Alekseev--Shatashvili action governing these reparametrization modes, and argue that it should be interpreted as the generating functional of stress tensor correlations on manifolds related to the plane by conformal transformations. In addition, we demonstrate that the rules previously prescribed with the reparametrization formalism for computing Virasoro identity blocks naturally emerge when evaluating Feynman diagrams associated with stress tensor exchanges between pairs of external primary operators. We make a few comments on the connection of these results to gravitational theories and holography.Comment: 18 pages, 2 figures. v3: matches published versio

Nonlinear stability of source defects in the complex Ginzburg-Landau equation

In an appropriate moving coordinate frame, source defects are time-periodic solutions to reaction-diffusion equations that are spatially asymptotic to spatially periodic wave trains whose group velocities point away from the core of the defect. In this paper, we rigorously establish nonlinear stability of spectrally stable source defects in the complex Ginzburg-Landau equation. Due to the outward transport at the far field, localized perturbations may lead to a highly non-localized response even on the linear level. To overcome this, we first investigate in detail the dynamics of the solution to the linearized equation. This allows us to determine an approximate solution that satisfies the full equation up to and including quadratic terms in the nonlinearity. This approximation utilizes the fact that the non-localized phase response, resulting from the embedded zero eigenvalues, can be captured, to leading order, by the nonlinear Burgers equation. The analysis is completed by obtaining detailed estimates for the resolvent kernel and pointwise estimates for the Green's function, which allow one to close a nonlinear iteration scheme.Comment: 53 pages, 5 figure

What are the Implications of One-to-one Technology Implementation?

This research study was used to examine my research question, “What are the implications of one-t- -one technology implementation?” This study specifically focused on the implications of one-to-one technology, one-to-one technology efficiency, and how teachers/students interact and feel about oneto- one technology. The study also describes these implications and future suggestions regarding one-to-one technology implementation and research. The study was conducted at a suburban high school located in Miami Dade County Public Schools and the tenth grade students would be surveyed through their English classes with the teacher’s consent. A census of tenth grade English teachers was taken and their classes were surveyed as well. The survey was constructed with questions/statements to provide quantitative and qualitative responses regarding one-to-one technology implementation. The electronic device being distributed and used in class were specifically electronic tablets. From the data, tables, graphs, and histograms were created to present the data. Teachers seem to use their electronic tablets regularly and find that the investment in electronic tablets is worth it. The electronic tablets also acts as an extra computer at home and they see the electronic tablet as a way for students to search up information directly in classrooms when discussing interesting topics. Students seem to use their electronic tablets minimally and were neutral on the finding the investment in electronic tablets worth it. Students agreed that the electronic tablets mitigated tasks and provided apps to enrich learning. Both teachers and students found the electronic tablets to have too many technological issues to outweigh the educational advantages

Building San Francisco, CA

The objective of this report is to conduct a thorough analysis and evaluation of the existing fire life safety and fire protection systems in place at the Building located in San Francisco, California. The building is classified as a Type II-A building and serves predominantly as office space. The building is six stories tall with a total gross area of approximately 97,170 SF. The initial portion of this report concentrates on a thorough prescriptive-based analysis, which provides an evaluation of the egress design, fire alarm system, communication systems, fire suppression system, structural and construction design, smoke control, and flammability requirements. The results of this comprehensive analysis demonstrate that the building complies with the requirements of the applicable building and fire codes. The subsequent portion of this report provides a performance-based analysis, which evaluates two distinct fire and life safety assessments. The first assessment involved the evaluation of the I.T. room located in the basement, with a focus on identifying potential flashover occurrences, the activation times of smoke and sprinkler detection, and the possibility of secondary ignition. The outcomes of this analysis revealed that flashover is unlikely to occur, with smoke detection activation taking approximately 674 seconds, and sprinkler activation occurring approximately 744 seconds after the onset of the fire. Note that the activation times appear relatively long for a room of this size, which is understood to be primarily due to the inclusion of the fire\u27s incipient slow growth phase. The results also indicated that secondary ignition does occur. These results suggest that the room is vulnerable to a fire scenario that could significantly impact the operations of the business and safety of occupants. To mitigate this risk, it is recommended that a fire protection system, such as a clean agent halon system or CO2 system, be installed to suppress fires and minimize equipment damage. Additionally, regular equipment maintenance performed by qualified professionals should be conducted to minimize the risk of ignition. The room should also be regularly inspected to ensure that the space does not contain large amounts of combustible materials to reduce potential fuel sources. The second fire scenario involves the atrium, which connects the basement level to the second floor. The design fire occurs at the base of the atrium in the basement. The scenario was assessed using Fire Dynamic Simulator (FDS) and Pathfinder to determine the Available Safe Egress Time (ASET) and Required Safe Egress Time (RSET). The primary objective was to determine whether the ASET exceeds the RSET, thus ensuring that the building and its associated life safety systems can maintain a safe and tenable environment for all occupants to evacuate safely. The ASET analysis will specifically focus on the deployment of the fire-rated shutters to assess whether the conditions on the levels above the fire, as well as the areas remote from the fire, will remain safe and suitable for the evacuation of building occupants. Pathfinder was utilized to determine the RSET, and the results indicated a time of 1034 seconds (~18 minutes) which takes into account a 1.5x safety factor. ASET was calculated by FDS, which simulated and assessed various tenability criteria, including smoke layer descent, heat exposure, visibility, and carbon monoxide dosing. The results indicated that the ASET could be maintained for 18 minutes for floors and areas remote from the fire. This is primarily due to the activation of fire-rated shutters, which compartmentalized the basement from the floors above. It should be noted that the atrium complies with all applicable prescriptive code requirements. The analysis emphasizes the crucial role of fire safety equipment functioning properly to ensure the safety of occupants within the building. The primary recommendation is to minimize potential ignition sources and fuel sources near the atrium. Additionally, regular equipment inspection and maintenance from qualified professionals should be conducted to ensure that the fire alarm system, automatic sprinkler system, and fire-rated shutters operate properly

Schwarzian transformations at null infinity

I describe the Schwarzian behavior of the gravitational field at null infinity under superrotations, to be understood as an \textit{unobservable} gauge artifact. To this end I review the induced geometry of null infinity and the construction of the gauge-invariant News tensor that characterizes gravitational radiation. I discuss potentially important implications for the celestial holography program, suggesting in particular that the uplift of the AdS$_3$/CFT$_2$ correspondence directly relates to the unobservable gauge sector.Comment: 17 pages + appendi