Upcoming Doctoral Dissertations

"Long-term sea-level change, driven by interacting processes occurring at global, regional, and coastal scales, poses significant challenges for the coastal regions of the United States over the coming decades and centuries. At the coastal scale, wind-generated waves have received little attention in sea-level change assessments. Wave setup, the wave-driven increase in mean coastal water level due to wave breaking, remains constrained in long-term analyses because it is not explicitly represented in tide-gauge records or satellite altimetry." Read more

"This research investigates computational complexity aspects of word problems in HNN extensions. The study builds upon Miller’s classical result demonstrating the existence of HNN extensions with decidable word problems but undecidable conjugacy problems." Read more

"Every NASA mission that has landed on Mars has used a supersonic parachute to decelerate the spacecraft during descent. The broadcloth material used to construct parachute canopies is a thin, woven, permeable textile. The small length scales of the pores in the fabric cannot be resolved in full-scale parachute simulations, so reduced-order permeability models are used instead. In this work, incompressible Computational Fluid Dynamics (CFD) simulations through a simplified pore geometry are compared to experimental permeability test data to verify the geometric parameters used in these models." Read more

"We study one-variable equations over the lamplighter group $\MZ_2 \wr \MZ$. While the decidability of arbitrary equations over $L_2$ remains open, we prove that the Diophantine problem for single equations in one variable is decidable. Our approach reduces the problem to a divisibility question for families of parametric Laurent polynomials over $\MZ_2$, whose coefficients depend linearly on an integer parameter." Read more

"Gait analysis plays a pivotal role in assessing functional mobility in healthy and clinical populations. Wearable gait analysis technologies have opened a realm of new possibilities for investigators, sparking renewed interest and providing tools to answer open research problems. This work aims to leverage new gait analysis technologies to address two open challenges." Read more