Showing 1 - 3 of 3 Items

Date: 2023-01-01

Creator: Sean E. Li

Access: Open access

We consider an earlier analysis by Baumgarte and de Oliveira (2022) of static Bona-Massó slices of stationary, nonrotating, uncharged black holes, represented by Schwarzschild spacetimes, and generalize that approach to Reissner-Nordström (RN) spacetimes, representing stationary, nonrotating black holes that carry a nonzero charge. This charge is parametrized by the charge-to-mass ratio λ ≡ Q/M, where M is the black-hole mass and the charge Q may represent electrical charge or act as a placeholder for extensions of general relativity. We use a height-function approach to construct time-independent, spherically symmetric slices that satisfy a so-called Bona-Massó slicing condition. We compute quantities such as critical points and profiles of geometric quantities for several different versions of the Bona-Massó slicing condition. In some cases we do this analytically, while in others we use numerical root-finding to solve quartic equations. We conclude that in the extremal limit as λ → 1, all slices that we consider approach a unique slice that is independent of the chosen Bona-Massó condition. We then study dynamical, i.e. time-dependent, Bona-Massó slices by analytically predicting the qualitative behavior of the central lapse, i.e. the lapse at the black-hole puncture, for a particular slice that Alcubierre (1997) proposed to mitigate gauge shocks. These shock-avoiding slices are a viable alternative to the very common so-called 1 + log slices but exhibit different behavior in dynamical simulations. We use a perturbation of the radial coordinate at the location of the puncture to recover approximately harmonic late-time oscillations of the central lapse that Baumgarte and Hilditch (2022) observed in numerical simulations.

Date: 2024-01-01

Creator: Brady R Nichols

Access: Open access

The Froude number is the ratio of kinetic energy to gravitational potential energy used during locomotion and is often used to analyze gait transitions. Here, I compare and contrast the human walk-run gait transition, which occurs at a consistent Froude number of 1 because there exists a mechanical speed limit to walking, and the sea star crawl-bounce gait transition, which occurs around Froude numbers of 1*10^-3. In this thesis I investigate why sea stars exhibit two gaits despite lacking brains and moving at Froude numbers far below other known gait transitions, hypothesizing (1) that the crawl-bounce transition may be mechanical and thus still depends on the Froude number, and (2) that the crawl-bounce transition is best modeled gradually compared to the instantaneous human walk-run transition. Thirty sea stars were filmed and the resulting kinematic data is used here to inform thinking about the crawl-bounce transition. I first discuss damped driven harmonic motion of a single oscillator, but eventually turn to using coupled oscillators and deriving that a coupling constant between metronomes on a moving base is the Froude number, which is therefore relevant for the crawl-bounce transition. I lastly discuss a purely mathematical analogue of the crawl-bounce transition as a Hopf bifurcation in horizontal speed and vertical velocity phase space, which leads to a rough model with results qualitatively similar to observed kinematic data from films, and indicates that a gradual transition is in fact a good fit for the crawl-bounce transition.

Date: 2023-01-01

Creator: Lorenzo Hess

Access: Open access

Reuse of N95 FFRs helps mitigate the effects of shortages. UV-C exposure is an ideal method for the decontamination necessary for FFR reuse. Recent research quantifies the transmittance of UV-C through the 3M1870+ and 3M9210+ FFRs [1]. Other research measures the reduction in viral load in relation to UV-C exposure time [11]. We design and program a ray tracing simulator in MATLAB to characterize the distribution of scattered photons in N95 FFRs. We implement an object-oriented FFR with configurable physical characteristics. We use the simulator to record the number of photons available for decontamination in each sub-layer of the filtering layers of the 3M1870+ and 3M9210+ for a given number of photons incident to the layers. We make assumptions about the photon absorption and viral deactivation in each sub-layer to derive a relation between the number of incident photons and the number of viruses remaining. The transmittance computed by our simulator matches the experimentally measured transmittance. The diameter of the simulated scattered beam also matches the experimentally measured scattered beam diameters. Our data, combined with our assumptions about absorption and deactivation, however, fail to account for the dropoff in viral load observed at about 25 seconds of exposure time in the 3M1870+.