Physical Sciences and Mathematics Commons^™

A Measurement Of The Differential Drell-Yan Cross Section As A Function Of Invariant Mass In Proton–Proton Collisions At √ S = 13 Tev, William Robert Tabb

Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–

The Drell-Yan process, a crucial mechanism for producing lepton pairs in highenergy hadron collisions, serves as an essential probe for testing the Standard Model of particle physics. This dissertation presents a comprehensive measurement of the differential cross section with respect to the invariant mass of the lepton pairs, utilizing data collected by the CMS experiment at CERN from 2016 to 2018. Cross sections are essential for refining our understanding of parton distribution functions and the underlying quantum chromodynamics processes, thereby providing constraints on theoretical predictions. In this analysis, the cross sections are compared to theoretical models and simulations, offering new …

A Study On The Vanishing Of Ext, Andrew J. Soto Levins

Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–

This thesis has two goals. The first is to study an Ext analog of the rigidity of Tor, and the second is to study Auslander bounds.

In Chapter 2 we show that if R is an unramified hypersurface, if M and N are finitely generated R-modules, and if the nth Ext modules of M against N is zero for some n less than or equal to the grade of M, then the ith Ext module of M against N is zero for all i less than or equal to n. A corollary of this says that if …

Spreads And Transversals And Their Connection To Geproci Sets, Allison Joan Ganger

Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–

Spreads of [set of prime numbers]³ over finite fields can yield geproci sets. We study the existence of transversals to such spreads, proving that spreads with two transversals exist for all finite fields, before further considering the groupoids coming from spreads when transversals do or do not exist. This is further considered for spreads of higher dimensional projective spaces. We also consider how certain spreads might generalize to characteristic zero and the connection to the previously known geproci sets coming from the root systems D₄ and F₄.

Advisor: Brian Harbourne

On Regularity Of Graph C*-Algebras, Gregory Joseph Faurot

Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–

We prove that for any countable directed graph E with Condition (K), the corresponding graph C*-algebra C*(E) has nuclear dimension at most two. We also prove that the nuclear dimension of certain extensions is at most one, which can be applied to certain graphs to achieve the optimal upper bound of one. Finally, we generalize some previous results for O_∞ -stability of graph algebras, and prove some partial results for Z-stability.

Advisor: Christopher Schafhauser

Gevrey Class Estimates Towards Null Controllability Of A Fluid Structure Interaction System, Dylan Mcknight

Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–

Fluid-Structure Interaction concerns the interaction of parabolic fluids and hyperbolic elastic structures via numerous mechanisms such as boundary coupling and pressure. These models find application in blood flow, fluid flow in the eye, and air flow over plane wings. Parabolic equations are well known for “infinite speed of propagation,” which manifests itself via a uniform bound on the resolvent of the infinitesimal generator of the associated strongly continuous semigroup. Qualitatively, a solution of a parabolic pde with rough initial data is immediately smooth for any positive time. A priori, it is not clear whether a fluid structure interaction inherits any …

On Neumann Boundary Conditions For Nonlocal Models With Finite Horizon, Scott Alex Hootman-Ng

Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–

Nonlocal models are have recently seen an explosive interest and development in the context of fracture mechanics, diffusion, image processing, population dynamics due to their ability to approximate differential-like operators with integral operators for inherently discontinuous solutions. Much of the work in the field focuses on how concepts from partial differential equations (PDEs) can be extended to the nonlocal domain. Boundary conditions for PDEs are crucial components for applications to physical problems, prescribing data on the domain boundary to capture the behavior of physical phenomena accurately with the underlying model. In this thesis we specifically examine a Neumann-type boundary condition …

Semigroup Well-Posedness And Finite Element Analysis Of A Biot-Stokes Interactive System, Sara Mcknight

Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–

The coupling of a porous medium modeled by the Biot equations and a fluid has many biological applications. There are numerous ways by which to model the fluid and to couple the porous medium with the fluid. This particular model couples the Biot equations to Stokes flow along the boundary, through the Beavers-Joseph-Saffman conditions. We address semigroup well-posedness of the system via an inf-sup approach, which along the way requires consideration of a related but uncoupled static Biot system. We also present the results of finite element analysis on both the uncoupled Biot system and the coupled system.

Advisor: Sara …

Perturbations Of Representations Of Cartan Inclusions, Catherine Zimmitti

Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–

A free semigroup algebra is the unital, weak operator topology closed algebra generated by a collection of Cuntz-Toeplitz isometries in B(H). Ken Davidson and David Pitts asked in [9] if a self-adjoint free semigroup algebra exists; Charles Read answered this question in [28] by constructing such an example, which Ken Davidson later simplified in [8]. The construction takes a standard representation of O₂ and multiplies it by a unitary operator in the diagonal MASA of the representation. This results in a new "perturbed" representation of O₂ generating a self-adjoint free semigroup algebra.

In this thesis, …

Virtual Unknotting Numbers For Families Of Virtual Torus Knots, Kaitlin R. Tademy

Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–

A virtual torus knot T(p,q,VC) sits in the intersection of the well-understood torus knot and the not-so-well-understood virtual knot, making it an intriguing object to study.

The unknotting number of a classical knot K is defined unambiguously. However, "the" unknotting number when K is a virtual knot is not as clear to define, since virtual knots have both classical and virtual crossings. We will define virtual unknotting number vu(K) as the minimum number of (classical) crossing changes required to unknot K. Under this definition of virtual unknotting, not all …

Torus Surgery, Fibrations, Multisections, And Spun 4-Manifolds, Nicholas Paul Meyer

Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–

A compact n-manifold X is fibered if it is a fiber bundle where the fiber F and base space B are manifolds. Fibered manifolds are particularly nice, as they are essentially classified by their monodromy maps. Two common examples of 4-dimensional fibered manifolds are surface bundles over surfaces and 3-manifold bundles over the circle.

The main focus of this dissertation is to investigate fibered 4-manifolds whose boundaries are the 3-torus and how these manifolds glue together to give new closed, fibered 4-manifolds. In particular, suppose W is diffeomorphic to S¹ × E_Y (K) where Y …

Nonlocal Frameworks For Nonlinear Conservation Laws And Advection-Diffusion Processes, Anh Thuong Vo

Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–

Conservation laws are fundamental principles that play an important role in modeling various phenomena in physics, chemistry, and biology. However, their limitations, such as the development of shocks despite smooth initial conditions, are well known. The nonlocal model framework can be used to overcome these challenges. Nonlocal frameworks utilize integral operators that mimic differential operators but also incorporate long-range interactions within a finite horizon. This approach not only allows for non-smooth solutions, but also provides flexibility in modeling different phenomena. This study investigates the convergence of nonlocal divergence operators, defined with a general flux density function, to their classical counterparts. …

Asteroidal Sets And Dominating Targets In Graphs, Oleksiy Al-Saadi

Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–

The focus of this Ph.D. thesis is on various distance and domination properties in graphs. In particular, we prove strong results about the interactions between asteroidal sets and dominating targets. Our results add to or extend a plethora of results on these properties within the literature. We define the class of strict dominating pair graphs and show structural and algorithmic properties of this class. Notably, we prove that such graphs have diameter 3, 4, or contain an asteroidal quadruple. Then, we design an algorithm to to efficiently recognize chordal hereditary dominating pair graphs. We provide new results that describe the …

Game-Theoretic Approaches To Optimal Resource Allocation And Defense Strategies In Herbaceous Plants, Molly R. Creagar

Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–

Empirical evidence suggests that the attractiveness of a plant to herbivores can be affected by the investment in defense by neighboring plants, as well as investment in defense by the focal plant. Thus, allocation to defense may not only be influenced by the frequency and intensity of herbivory but also by defense strategies employed by other plants in the environment. We incorporate a neighborhood defense effect by applying spatial evolutionary game theory to optimal resource allocation in plants where cooperators are plants investing in defense and defectors are plants that do not. We use a stochastic dynamic programming model, along …