Mathematical Sciences and Systems Engineering

Project Summary

Large–scale lunar construction requires transporting vast quantities of material from Earth to the Moon. Two competing infrastructure concepts are high–cadence reusable rocket launches and a space elevator system (“Galactic Harbour”). While rockets have proven operational feasibility, they suffer from high marginal cost per ton and discrete failure risks. In contrast, a space elevator provides continuous throughput but introduces time dependent mechanical risks such as sway stabilization, fatigue, and transfer slip at the apex hub. The purpose of this work is to develop a unified mathematical framework that compares both systems under consistent assumptions and evaluates which system achieves a target delivery of 100 million metric tons most efficiently.

Project Objective

To rigorously stress-test the economic and temporal viability of Earth's two primary heavy-lift paradigms—Super Heavy Rockets and Space Elevators—against the 100 Million Metric Ton requirement for permanent lunar colonization. To build an unbiased, unified mathematical model using a Stochastic Jump-Diffusion Framework. This ensures both infrastructures are evaluated under symmetrical technological learning curves and subject to real-world probabilistic hazards (MMOD strikes and launch failures). To map out the true financial burn rate of a civilizational-scale logistics chain by applying a continuous Net Present Value (NPV) decay a long period of time.

Analysis

The Space Elevator is economically unviable in Low Earth Orbit (LEO). The simulation proves that continuous MMOD hazards not only throttle logistical throughput by forcing the tether offline but also create an unrecoverable financial trap. Delivering 100 million tons to the lunar surface is a multi-millennial endeavor. Even when operating a maximum-capacity super-heavy rocket fleet governed by Wright's Law, achieving the infrastructure required for an independent 100,000-person colony takes around 1500 years.

Acknowledgement

We would like to thank Dr. Tenali and Dr. Mosincat for their help in presenting this model, as well as for being excellent teachers.

Project Summary

This project studies how stochastic networks respond to random failures by analyzing the probability that different forms of cumulative damage reach critical levels in different orders. Rather than looking only at whether a network eventually becomes unstable, the project focuses on how that instability develops and which damage pattern is most likely to appear first. To do this, the work models repeated random failure events, tracks how losses build over time across several network measures, and applies analytical probability methods to derive closed-form expressions for selected threshold-crossing outcomes. The works aims to use transform-based analysis to describe system behavior in a mathematically rigorous, but still understandable, way. By connecting these results to questions of vulnerability, the project helps show how local random failures can accumulate into broader system-level risk and how those patterns can be used to better understand network resilience.

Project Objective

The objective of this project is to derive useful probability expressions for threshold-crossing behavior in a stochastic network model and to use those results to assess resilience under random failures. By determining how likely different critical-loss sequences are, the project aims to provide a clearer basis for evaluating network weakness, interpreting overall risk, and guiding strategies that improve reliability and reduce vulnerability.

Acknowledgement

I would like to thank Dr. White and the NETS Lab for their continued support throughout my undergraduate career.

Project Summary

The stomach contains highly acidic gastric fluid with a very low pH and a thin mucus lining protects the stomach from self digestion while keeping nearby epithelial cells at a neutral pH. This project builds off of Schreiber and Scheid's hypothesis, which suggests that the mucus layer acts as a barrier and transport medium for hydrogen ions releasing them in the lumen through degradation of mucin by pepsinogen. A mathematical model was developed to describe mucin secretion, degradation and hydrogen ion transport, then a steady state analysis was completed to determine an expected range for the thickness of the mucus layer. The results achieved show that the tested model is plausible for maintaining a healthy thickness, and the particular relationship between advection and diffusion in regulating the thickness of the mucus layer.

Project Objective

The objective of this project was to develop and analyze a mathematical model which can determine how the protective mucus barrier can be maintained and be of stable thickness while in the presence of such harsh conditions.

Analysis

The one dimensional model is based on two differential equations describing mucin variation and hydrogen ion movement. Based on the hypothesis a balance should be struck between degradation and secretion of mucin, so a steady state analysis was performed to focus on the thickness of the mucus layer over time. Assumptions were made that the pepsinogen activates instantaneously at the interface between the lumen and mucus layer leading to the degradation of the mucin. Solving this differential equation can show the hydrogen ion profile and the thickness as a function of the activation threshold of pepsinogen.

Future Works

Further work for this model involves refining the activation function at which pepsinogen activates and to move away from an instantaneous model to a continuous rate model.