Dissertation Defense Announcements

Rock weathering, or the mechanical and chemical breakdown of rock over time, creates the landscape on which all terrestrial life is built. Here, I quantify the rates and controls over mechanical weathering [rock cracking/fracturing] f surficial boulder deposits in Eastern California using by collecting rock and crack field measurements, clast size distribution data from the field, and rock elastic properties using laboratory testing. I used a chronosequence or space-for-time approach, whereby data are collected from rocks or sediments that have been exposed to natural weathering conditions for a range of times, using the properties of the stable deposits to represent the amount of weathering that occurs over the time span of exposure. I studied rocks at three sites, with rocks being exposed to Earth surface conditions from 0 to 148,00 years [148 ka].

I manually measured 8763 crack lengths, widths, and orientations from 2221 in situ boulders on Earth’s surface and found that that rock cracking is initially fastest when rocks are exposed to Earth’s surface conditions, with rocks accumulating cracks at a rate of 9-1502 mm of cracks per m^2 rock surface over a thousand years, or 0.1-36 individual cracks per m^2 rock surface over a thousand years. After this point, rocks continue to crack, but the rate of crack growth slows down. After about 30 ka, the growth rate is <36 mm of cracks/m^2 of rock surface per ka, or <1 individual cracks/m^2 of rock surface per ka. Using all rock and crack data I determined that age itself has the most consistent, positive, statistically significant correlation with the number of fractures per rock surface area [fracture number density] and the total length of fractures measured per rock surface area [fracture intensity].

From two sites, I collected a granitic boulder from each dated deposit for rock mechanics testing. These data show that rock compliance increases over time while mechanical weathering leads to an increase in microscale cracks, which alter the rock’s strength and elastic strain response under stress. Using the laboratory analyses and local weather station data, I implemented a simple daily stress model applying Paris’ law of subcritical crack growth to predict single crack growth after each day of weather conditions, for a period of 5000 years. Cracking occurred over only a limited number of unusually intense weather days when the daily range of air temperatures was the largest. In the two semi-arid sites, these cracking days were hot, dry summer days; in the arid site, the day when the most crack growth was predicted coincided with summer monsoonal rains. The model is highly sensitive to rock elastic properties, which supports the theory that a gradual increase in bulk compliance allows rocks to withstand stress without cracking over thousands of years.

Finally, I present clast size data to show that for volcanic and carbonate rocks, there is a correlation between the geometry of cracking observed on the rocks and the shape of sediments on older deposits: when many cracks are parallel to the rock surface, older deposits tend to have more flattened rocks on them. This shows that cracking rates and crack geometries can play a strong role in clast size and shape evolution over geologic time, and mechanical weathering should be considered when interpreting sediments in the geologic record.

These findings are directly applicable to geoscientists attempting to understand weathering, landscape evolution, and geological hazards. More broadly, the decreasing rock cracking rates that accompany slow mechanical property changes represent a real-world example of material fatigue vs. material failure.

In recent years, there has been an increase in attacks, including advanced persistent threats (APTs), and the techniques used by the attacker in these attacks have reached unprecedented sophistication. Threat hunters use various monitoring tools to monitor and collect all these attack actions (which blend in with benign user activities) for cyber threat hunting—the end devices store monitored activities as generated logs/events. Moreover, Organizations like NIST and CIS provide guidelines (CSC) to enforce cyber security and defend against those attacks.

Although the end hosts and networking devices can record all benign user and adversary actions, it is infeasible to monitor everything. In existing approaches, high memory usage and communication overhead to transfer events to the central server create scalability issues on the monitored network. Single event matching on the end-host devices approach to detect attacks generates false alerts, causing the alert fatigue problem. This dissertation presents a distributed hierarchical monitoring agent architecture to overcome those limitations of existing tools and research works.

Additionally, there are no well-defined automated measures and metrics to validate the enforcement of CSC. Manually analyzing and developing measures and metrics to monitor and implementing those monitoring mechanisms are resource-intensive tasks and massively dependent on the security analyst's expertise and knowledge. To tackle those problems, we use LLM as a knowledge base and reasoner to extract measures, metrics, and monitoring mechanism implementation steps from CSC descriptions to reduce the dependency on security analysts with the help of few-shot learning with chain-of-thought prompting. This dissertation presents CSC enforcement assessment with the help of our distributed hierarchical monitoring agent architecture and prompt engineering.

The orbital angular momentum of light is a promising candidate as an information carrier in optical communication systems to enhance the capacity of data channels. However, the effects of atmospheric turbulence significantly degrade the quality of light beams, thereby imposing limitations on the range of reliable data transmission. To address this issue, researchers have been actively seeking methods to enhance the resilience of light against fluctuations of refractive index due to the atmospheric turbulence. It has long been recognized that partially coherent beams exhibit greater robustness in propagation through turbulence. Consequently, transitioning from full coherence to partial coherence has been suggested as a solution. Conversely, in OAM-based communications, reducing coherence results in broadening of the OAM spectrum, thus increasing cross-talk between adjacent channels. Therefore, utilizing partially coherent beams in free space communications entails both Benefits and drawbacks.
The main objective of this dissertation is to explore various classes of partially coherent beams through analytical approaches in order to identify a robust OAM spectrum in the presence of atmospheric turbulence. The results are presented in three different articles. The first article introduces a simplified version of the extended Huygens-Fresnel principle which is a widely used method of turbulence propagation. The discoveries outlined in the first article substantially alleviate the mathematical complexity associated with propagation in random media, thereby enabling analytical exploration of the propagation of partially coherent beams in random media.
The second article presents an optimization criterion associated with a specific class of partially coherent beams, substantially enhancing their resistance against turbulence. Finally, the third article thoroughly investigates the behavior of three categories of partially coherent beams in interaction with atmosphere, providing a detailed comparison of their respective resistance. The compilation of these three articles presents a comprehensive study of the impact of atmospheric fluctuations on the orbital angular momentum spectrum of partially coherent beams.

Large cohort studies under simple random sampling could be prohibitive to conduct with a limited budget for epidemiological studies seeking to relate a failure time to some exposure variables that are expensive to obtain. In this case, two-phase studies are desirable. Failure-time-dependent sampling (FDS) is a commonly used cost-effective sampling strategy in such studies. To enhance study efficiency upon FDS, counting the auxiliary information of the expensive variables into both sampling design and statistical analysis is necessary.

In survival analysis, it's commonly assumed that all subjects in a study will eventually experience the event of interest. However, this assumption may not hold in various scenarios. For example, when studying the time until a patient progresses or relapses from a disease, those who are cured will never experience the event. These subjects are often labeled as ``long-term survivors'' or ``cured'', and their survival time is treated as infinite. When survival data include a fraction of long-term survivors, censored observations encompass both uncured individuals, for whom the event wasn't observed, and cured individuals who won't experience the event. Consequently, the cure status is unknown, and survival data comprise a mixture of cured and uncured individuals that can't be distinguished beforehand. Cure models are survival models designed to address this characteristic.

Chapter~2 discusses the semiparametric inference for a two-phase failure-time-auxiliary-dependent sampling (FADS) design that allows the probability of obtaining the expensive exposures to depend on both the failure time and cheaply available auxiliary variables. Chapter~3 considers the generalized case-cohort design for studies with a cure fraction. A few directions for future research are discussed in Chapter~4.