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Theses and Dissertations
DRUM includes all UMD theses and dissertations from 2003 forward.
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Recent Submissions
Dataset for "Resistance of Boron Nitride Nanotubes to Radiation-Induced Oxidation" as published in The Journal of Physical Chemistry C
(2024) Chao, Hsin-Yun (Joy); Nolan, Adelaide M.; Hall, Alex T.; Golberg, Dmitri; Park, Cheol; Yang, Wei-Chang David; Mo, Yifei; Sharma, Renu; Cumings, John
Special Lagrangians in Milnor Fibers and Almost Lagrangian Mean Curvature Flow
(2024) Pinsky, Mirna; Rubinstein, Yanir A.; Mathematics
The focus of this thesis is twofold:
(1) We solve the Shapere–Vafa Problem: We construct embedded special Lagrangian spheres
in Milnor fibers. We give a necessary and sufficient condition for the existence of embedded special Lagrangian spheres in Milnor fibers.
(2) We solve the Thomas–Yau Problem for Milnor fibers: We prove the Thomas–Yau conjecture for the almost Lagrangian mean curvature flow (ALMCF) for Milnor fibers, under the
assumption that the initial Lagrangian is an embedded positive Lagrangian sphere satisfying a
natural stability condition proposed by Thomas–Yau but adapted to Milnor fibers by us.
In addition, we formulate a new approach to resolving the Thomas–Yau conjecture in arbitrary almost Calabi–Yau manifolds.
The Thomas–Yau conjecture proposes certain stability conditions on the initial Lagrangian
under which the Lagrangian mean curvature flow (LMCF) exists for all time and converges to the
unique special Lagrangian in the Hamiltonian isotopy class, and therefore also homology class
of the initial Lagranigan.
One of the reasons for studying LMCF in Calabi–Yau manifolds (or ALMCF in almost
Calabi–Yau manifolds) is that the Lagrangian condition, as well as homotopy and homology
classes, are preserved. Therefore, if the flow converges, it converges to a special Lagrangian.
We develop a method for finding special Lagrangian spheres in Milnor fibers. We provide
examples which illustrate different situations which occur (the total number of special Lagrangian
spheres is at least deg f − 1 and at most 1/2 deg f(deg f − 1), where f is the polynomial defining
the Milnor fiber).
We show that the almost Lagrangian mean curvature flow of Lagrangian spheres in Milnor
fibers can be reduced to a generalized mean curvature flow of paths in C. This reduction is
different from the one found by Thomas–Yau. We show that the limit of the flow is either a
straight line segment or a polygonal line, corresponding to a special Lagrangian sphere or a chain
of such spheres. We prove that under certain conditions (more general than the ones achieved by
Thomas–Yau) the flow results in a special Lagrangian sphere.
Finally, we develop a method for associating a curve in C with a compact Lagrangian in
a more general setting of an almost Calabi–Yau manifold. We show that when the Lagrangian
flows by ALMCF that the corresponding curve remains convex and shortens its length. The
limit is either a straight line segment corresponding to a special Lagrangian or a polygonal line
resulting in a decomposition of the original Lagrangian.
Examining pre-training interpersonal skills as a predictor of post-training competence in mental health care among lay health workers in South Africa
(2023) Rose, Alexandra Leah; Magidson, Jessica F.; Psychology; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
A worldwide shortage of mental health specialists contributes to a substantial global mental health treatment gap. Despite evidence that lay health workers (LHWs), or health workers with little formal training, can effectively deliver mental health care, LHWs vary widely in their abilities to competently deliver mental health care, which undermines the quality of care and patient safety. Prior research from both high-income and low- and middle-income countries suggests this variability may be predicted by LHW interpersonal skills, yet this relationship is little explored to date. The first aim of the current study, which uses an exploratory sequential mixed methods design, was to explore qualitative perspectives through semi-structured individual interviews (n=20, researchers, policymakers, NGO staff, LHWs) in Cape Town, South Africa on interpersonal skills relevant to delivery of mental health interventions by LHWs. The second aim was to quantitatively examine the preliminary effectiveness of pre-training interpersonal skills in predicting post-training competence following a mental health training among LHWs in Cape Town (n=26). Using a standardized LHW assessment measure adapted to the setting, two raters rated ten-minute standardized role plays conducted before and after the training for pre-training interpersonal skills and post-training competence. Qualitative findings highlight the perceived importance of and challenges with assessing interpersonal skills among LHWs being trained in psychological intervention. Quantitative analyses did not identify any interpersonal skills as significant predictors of post-training competence. However, interpersonal skills improved during the training itself, specifically verbal communication, suggesting the potential promise of further research in this area. Recruitment of larger samples with more variable training outcomes would be important in future studies examining predictors of LHW competence. Further research may ultimately help identify areas of intervention to support more LHWs in attaining competence and can help play an important role in increasing access to psychological services globally.
Integrated Geochemical Studies of the Shuram Excursion in Siberia and South China
(2024) Pedersen, Matthew; Kaufman, Alan J; Geology; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
The Ediacaran Period Shuram Excursion (SE) is a globally-distributed and highly controversial phenomenon where over millions of years, sedimentary carbonates record δ13C values of -10‰ and lower. This carbon cycle anomaly may reflect disequilibrium in the world’s oceans, driven by the oxidation of a large pool of dissolved organic carbon (DOC), with the oxidants sourced from the intense weathering of the continents, forcing major changes to ocean chemistry through the ventilation of the deep ocean, evidenced by a positive shift in carbonate uranium isotope values, and invoking the onset of early animal biomineralization. This study utilizes high-resolution carbonate Li isotopes from two SE-successions, U isotopes, REE abundances and Ce anomalies which reveal the dynamic interplay between intensified continental weathering associated with tectonic reconfiguration and the subsequent environmental and ecological response that may have been amplified by the ecosystem-engineering abilities of a newly discovered sponge-grade animal.
Eventually Stable Quadratic Polynomials over Q(i)
(2024) McDermott, Jermain; Washington, Lawrence C; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
Let $f$ be a polynomial or a rational function over a field $K$. Arithmetic dynamics studies the algebraic and number-theoretic properties of its iterates $f^n:=f \circ f \circ ... \circ f$.\\
A basic question is, if $f$ is a polynomial, are these iterates irreducible or not? We wish to know what can happen when considering iterates of a quadratic $f= x^2+r\in K[x]$. The most interesting case is when $r=\frac{1}{c}$, which we will focus on, and discuss criteria for irreducibility, i.e. \emph{stability} of all iterates. We also wish to prove that if 0 is not periodic under $f$, then the number of factors of $f^n$ is bounded by a constant independent of $n$, i.e. $f$ is \emph{eventually stable}. This thesis is an extension to $\Qi$ of the paper \cite{evstb}, which considered $f$ over $\mathbb{Q}$.
This thesis involves a mixture of ideas from number theory and arithmetic geometry. We also show how eventual stability of iterates ties into the density of prime divisors of sequences.