Applied Mathematics Commons^™

Mass Effects On Energy Transfer Paths In Nonlinear Vibrating Systems, Manal Mustafa

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

This dissertation examines the role of mass in nonlinear systems, uncovering its role in enabling passive energy redistribution and robust vibration control in both idealized and real-world structures. Focusing on a strongly nonlinear two-degree-of-freedom system, it investigates how changes in mass ratio influence the dynamics of energy transfer, nonlinear normal modes (NNMs), and dissipation behavior.

A number of significant contributions are introduced in this work beginning with the introduction of the frequency-energy-peaks (FE-pks) plot, a novel tool that visualizes how energy flows through the system, revealing transient resonance orbits, internal resonance effects, and effectively capturing the different nonlinear phenomena with …

Evaluating Risk And Return Of Corn And Soybean Marketing Strategies Using Monte Carlo Simulation Methods, Johanna Ilves

Department of Agricultural Economics: Dissertations, Theses, and Student Research

This study evaluates the performance of pre-harvest marketing strategies for corn and soybeans, using Monte Carlo simulation techniques. Given the increasing volatility in commodity prices and the evolving landscape of agricultural markets, producers face growing challenges in developing effective marketing plans that manage risk and enhance profitability. This thesis examines thirteen marketing strategies from 2008 to 2024, including benchmark harvest-only sales and various pre-harvest futures contract approaches. Historical futures price data for December corn and November soybean contracts were used to simulate 1,000 marketing outcomes per strategy per year, capturing a broad range of market conditions. Key performance indicators such …

Physics Embedded Neural Network: A Novel Data-Free Numerical Method For Solving Computational Physics Problems, Pawan Gaire

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

A novel approach for solving partial differential equations (PDEs) using neural networks for scientific computing is introduced. The proposed approach, referred to as physics-embedded neural network (PENN), features a unique architecture that incorporates the PDE and boundary conditions information directly within the final fully-connected layer of the feed-forward neural network (NN). The key aspect of PENN is the parallel numerical embedding of a differential equation associated with physical problems within the activation function of the network’s final layer. This integration leads to a new class of computational solvers competitive with classical methods like the Finite Element Method (FEM) and capable …

Using Permutation Groups To Identify Families Of Capacity Achieving Codes, Daniel Welchons

Department of Mathematics: Dissertations, Theses, and Student Research

When communicating over a noisy channel, the probability of message interference sets a maximum possible transmission rate known as the channel capacity. Any family of codes which have rates converging to the channel capacity and arbitrarily low probability of decoding failure is called capacity achieving. Such codes have been known to exist since the birth of information theory, but are difficult to find explicitly. It has recently been shown that the permutation groups of a family of codes can be used to show that the family is capacity achieving on the q-ary erasure channel.

This thesis seeks to apply the …

Using Permutation Groups To Identify Family Of Capacity Achieving Codes, Daniel Joseph Welchons

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

When communicating over a noisy channel, the probability of message interference sets a maximum possible transmission rate known as the channel capacity. Any family of codes which have rates converging to the channel capacity and arbitrarily low probability of decoding failure is called capacity achieving. Such codes have been known to exist since the birth of information theory but are difficult to find explicitly. It has recently been shown that the permutation groups of a family of codes can be used to show that the family is capacity achieving on the q-ary erasure channel.

This this thesis seeks to …

Towards Advancing Streamflow And Peak Flow Prediction With Machine Learning: Identifying Infrastructure At Risk, Sudan Pokharel

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

Due to climate change and its impact, the need for adaptive strategies for natural disaster mitigation and resource management has never been more urgent. Central to this is water resource management, which is essential for sustainable human activities, ecological balance, and the mitigation of natural hazards like floods. Streamflow is a crucial element of water resource management and plays a vital role in planning and building water infrastructure, implementing emergency response plans, supporting flood mitigation initiatives, and regulating agricultural and industrial use. However, accurate prediction of streamflow still remains a challenge due to the complex non-linear and non-stationary interaction between …

Geometric Modeling, Reconstruction And Evaluation Of Maize Leaf Morphology In 3d, Zhaocheng Xiang

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

Maize is a vital crop for global food security, yet quantitative characterization of its three-dimensional (3D) morphology remains a major challenge due to the geometric complexity of curved leaf structures and occlusions during data collection. This work presents an integrated framework for the digital reconstruction, parametric modeling, and functional analysis of maize leaf morphology and canopy architecture, advancing the precision and interpretability of phenotyping and modeling in smart agriculture.

First, we propose a descriptive and parametric model that represents maize leaves through three fundamental components: midrib, cross-section, and blade contour. Each is described by geometric curves and controlled by biologically …

The Feasibility Of Utilizing The Open Dynamic Interaction Network (Odin) App To Assess Rema Data Across 30 Days Among Those Recovering From Alcoholism, Dennis E. Mcchargue, Bilal Khan, Jesscia Phelps, Patrick Duryea, Kimberly A. Tyler, Arthur Andrews, Ellie Reznicek, Lucy Napper, Mohamed Saad, Hsuan-Wee Lee

Department of Psychology: Faculty Publications

About ~4 million people with an alcohol use disorder receive treatment annually, and frequent relapse has produced a rapid revolving door between recovery and use. This paper presents preliminary data from a prospective micro-longitudinal study (30 days) that examines co-evolution of relapse risk processes of people with alcohol use disorders who entered a short-term residential substance use treatment. The primary goal of the current data was to assess the feasibility of using the open dynamic interaction network (ODIN) responsive ecological momentary assessment (rEMA). rEMA collected daily estimates on affect, urges, sober-support engagement, and use. The ODIN app administered twelve questions …

Bidding Strategy For A Wind Power Producer In Us Energy And Reserve Markets, Anne Stratman

Department of Electrical and Computer Engineering: Dissertations, Theses, and Student Research

Wind power is one of the world's fastest-growing renewable energy resources and has expanded quickly within the US electric grid. Currently, wind power producers (WPPs) may sell energy products in US markets but are not allowed to sell reserve products, due to the uncertain and intermittent nature of wind power. However, as wind’s share of the power supply grows, it may eventually be necessary for WPPs to contribute to system-wide reserves. This paper proposes a stochastic optimization model to determine the optimal offer strategy for a WPP that participates in the day-ahead and real-time energy and spinning reserve markets. The …

Approximation Via Degree Reduction Of Nonlinearities With Applications To Turbulent Flows, Flame Fronts, And Magnetohydrodynamics, Matthew Enlow

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

We perform an analytical and computational investigation on the effectiveness of a locally bounded truncation function, which we call a calming function, when applied to the nonlinear terms of several dissipative partial differential equations. In particular, the 3D Navier-Stokes equations of incompressible fluid flow, the 2D Kuramoto-Sivashinsky equations of laminar flame fronts, and the 2D MHD-Boussinesq equations of magnetohydrodynamics. Each of these equations have open questions about the global existence and uniqueness of their solutions. These calming functions effectively reduce the algebraic degree of select nonlinear terms, thus one can verify global wellposedness for these "calmed systems." More specifically, in …

A Cohomological Perspective To Nonlocal Operators, Nicholas White

Honors Program: Senior Projects (Public)

Nonlocal models have experienced a large period of growth in recent years. In particular, nonlocal models centered around a finite horizon have been the subject of many novel results. In this work we consider three nonlocal operators defined via a finite horizon: a weighted averaging operator in one dimension, an averaging differential operator, and the truncated Riesz fractional gradient. We primarily explore the kernel of each of these operators when we restrict to open sets. We discuss how the topological structure of the domain can give insight into the behavior of these operators, and more specifically the structure of their …

Inhabiting Numbers: Weaving, Polyphony, And Embodied Mathematics, Kristine Barrett

Textile Society of America: Symposium Proceedings

Inhabiting Numbers: Polyphony as Woven Sound explores connections between vocal polyphony and textile practices, specifically weaving and spinning. Rather than consider music and weaving as separate from one another, the following paper presents the ways in which they are deeply intertwined and mutually constitutive forms of cultural expression. The technical modes of thinking produced through repetition inherent in both—particularly as practices utilizing complex mathematical structures—produce ways of thinking unique to each. Through practice, I suggest these technical modes of making transit across different materials and mediums—in both explicit and implicit ways. The music created through the interweaving of multiple voices …

Quantitative Verification For Massive Linear Systems, Qing Liu

School of Computing: Dissertations, Theses, and Student Research

The verification of linear systems has been an active area of research for decades. Reachability analysis is a key component in verification problems. It involves computing the system’s reachable set, the set of reachable states in the state space from a given set of initial states. Most verification methods primarily focus on qualitative verification, which answers whether or not a system may violate specified safety conditions. This paper extends this qualitative verification to quantitative verification by introducing a novel approach, employing probabilistic stars (Probstars) to compute reachable sets, which augment traditional star sets by integrating Gaussian-distributed random variables with …

Modeling The Population Dynamics And Movement Of Zebra Mussels, Alexanderia Lacy, Yu Jin, David Strayer, Suzanne Lenhart

Department of Mathematics: Faculty Publications

Zebra mussels have caused significant damage in many lakes and rivers. By using a hybrid population model with discrete-time equations and ordinary differential equations, we represent the zebra mussel’s life cycle, growth, and population movement. The dynamics of the larvae (unsettled and settled larvae) are represented during the summer months in a system of two ordinary differential equations, while the juvenile, small adult, and large adult stages are represented by a discrete model with yearly time steps. The goal is to investigate the effects of zebra mussel movement between three different spatial locations and possible control measures. Zebra mussel data …

Regular Ideals, Ideal Intersections, And Quotients, Jonathan H. Brown, Adam H. Fuller, David R. Pitts, Sarah A. Reznikoff

Department of Mathematics: Faculty Publications

Let B ⊆ A be an inclusion of C^∗ -algebras. We study the relationship between the regular ideals of B and regular ideals of A.We show that if B ⊆ A is a regular C^∗ -inclusion and there is a faithful invariant conditional expectation from A onto B, then there is an isomorphism between the lattice of regular ideals of A and invariant regular ideals of B. We study properties of inclusions preserved under quotients by regular ideals. This includes showing that if D ⊆ A is a Cartan inclusion and J is a regular ideal in A, …

A Mathematical Model For Frogeye Leaf Spot Epidemics In Soybean, Chayu Yang, Jin Wang

Department of Mathematics: Faculty Publications

We propose a new mathematical model based on differential equations to investigate the transmission and spread of frogeye leaf spot, a major soybean disease caused by the fungus Cercospora sojina. The model incorporates the primary and secondary transmission routes of the disease as well as the intrinsic dynamics of the pathogen in the contaminated soil. We conduct detailed equilibrium and stability analyses for this model using theories of dynamical systems. We additionally conduct numerical simulations to verify the analytical predictions and to implement the model for a practical application.

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

Department of Mathematics: Dissertations, Theses, and Student Research

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 …

Experimental Analysis Of Nonlinear Wave Propagation In Bistable Mechanical Metamaterials With A Defect, Samuel R. Harre

Department of Mechanical and Materials Engineering: Dissertations, Theses, and Student Research

Mechanical metamaterials built up of compliant units can support the propagation of linear and nonlinear waves. A popular architecture consists of a one-dimensional chain of bistable elements connected by linear springs. This type of chain can support nonlinear transition waves that switch each element from one stable state to the other as they propagate along the chain. One way to manipulate the propagation of such waves is via introduction of a local inhomogeneity, i.e., a defect in the otherwise periodic chain. Recent analytical and numerical work has shown that based on its initial velocity, a transition wave may be reflected, …

Differentiating By Prime Numbers, Jack Jeffries

Department of Mathematics: Faculty Publications

It is likely a fair assumption that you, the reader, are not only familiar with but even quite adept at differentiating by x. What about differentiating by 13? That certainly didn’t come up in my calculus class! From a calculus perspective, this is ridiculous: are we supposed to take a limit as 13 changes? One notion of differentiating by 13, or any other prime number, is the notion of p-derivation discovered independently by Joyal [Joy85] and Buium [Bui96]. p-derivations have been put to use in a range of applications in algebra, number theory, and arithmetic geometry. Despite the wide range …

Convolutional Neural Network-Based Gene Prediction Using Buffalograss As A Model System, Michael Morikone

Complex Biosystems Program: Dissertations and Student Research

The task of gene prediction has been largely stagnant in algorithmic improvements compared to when algorithms were first developed for predicting genes thirty years ago. Rather than iteratively improving the underlying algorithms in gene prediction tools by utilizing better performing models, most current approaches update existing tools through incorporating increasing amounts of extrinsic data to improve gene prediction performance. The traditional method of predicting genes is done using Hidden Markov Models (HMMs). These HMMs are constrained by having strict assumptions made about the independence of genes that do not always hold true. To address this, a Convolutional Neural Network (CNN) …

Nuclear Dimension Of Graph C∗-Algebras With Condition (K), Gregory Faurot, Christopher Schafhauser

Department of Mathematics: Faculty Publications

We prove that for any countable directed graph E with Condition (K), the associated graph C^*-algebra C^*(E) has nuclear dimension at most 2. Furthermore, we provide a sufficient condition producing an upper bound of 1.

A Variational Theory For Integral Functionals Involving Finite-Horizon Fractional Gradients, Javier Cueto, Carolin Carolin, Hidde Schönberger

Department of Mathematics: Faculty Publications

The center of interest in this work are variational problems with integral functionals depending on nonlocal gradients with finite horizon that correspond to truncated versions of the Riesz fractional gradient. We contribute several new aspects to both the existence theory of these problems and the study of their asymptotic behavior. Our overall proof strategy builds on finding suitable translation operators that allow to switch between the three types of gradients: classical, fractional, and nonlocal. These provide useful technical tools for transferring results from one setting to the other. Based on this approach, we show that quasiconvexity, which is the natural …

Exploring The Presence Of Nonlinear Deterministic Dynamics In Commodity Prices, Sagar Dahal

Department of Agricultural Economics: Dissertations, Theses, and Student Research

Determining whether commodity prices (and volatility) are driven by linear stochastic processes or low-dimensional nonlinear deterministic dynamics (“chaos”) is crucial for policymaking, forecasting, production, storage, investment, risk management, and hedging decisions. Previous studies that used Lyapunov exponents and correlation dimensions to identify chaotic structures in price series may be unreliable in practical applications because these methods rely on asymptotic properties that require large, noiseless data which is often not available. We applied nonlinear time series analysis approaches to empirically detect the underlying market dynamics using the daily futures prices of ten agricultural commodities. We used phase space reconstruction to reconstruct …

Idempotent Completions Of Equivariant Matrix Factorization Categories, Michael K. Brown, Mark E. Walker

Department of Mathematics: Faculty Publications

We prove that equivariant matrix factorization categories associated to henselian local hypersurface rings are idempotent complete, generalizing a result of Dyckerhoff in the non- equivariant case.

Analysis Of Syndrome-Based Iterative Decoder Failure Of Qldpc Codes, Kirsten D. Morris, Tefjol Pllaha, Christine A. Kelley

Department of Mathematics: Faculty Publications

Iterative decoder failures of quantum low density parity check (QLDPC) codes are attributed to substructures in the code’s graph, known as trapping sets, as well as degenerate errors that can arise in quantum codes. Failure inducing sets are subsets of codeword coordinates that, when initially in error, lead to decoding failure in a trapping set. In this paper we examine the failure inducing sets of QLDPC codes under syndrome-based iterative decoding, and their connection to absorbing sets in classical LDPC codes.

Computation Of The Basic Reproduction Numbers For Reaction-Diffusion Epidemic Models, Chayu Yang, Jin Wang

Department of Mathematics: Faculty Publications

We consider a class of k-dimensional reaction-diusion epidemic models (k = 1; 2; • • • ) that are developed from autonomous ODE systems. We present a computational approach for the calculation and analysis of their basic reproduction numbers. Particularly, we apply matrix theory to study the relationship between the basic reproduction numbers of the PDE models and those of their underlying ODE models. We show that the basic reproduction numbers are the same for these PDE models and their associated ODE models in several important scenarios. We additionally provide two numerical examples to verify our analytical results.

Pull-Push Method: A New Approach To Edge-Isoperimetric Problems, Sergei L. Bezrukov, Nikola Kuzmanovski, Jounglag Lim

Department of Mathematics: Faculty Publications

We prove a generalization of the Ahlswede-Cai local-global principle. A new technique to handle edge-isoperimetric problems is introduced which we call the pull-push method. Our main result includes all previously published results in this area as special cases with the only exception of the edge-isoperimetric problem for grids. With this we partially answer a question of Harper on local-global principles. We also describe a strategy for further generalization of our results so that the case of grids would be covered, which would completely settle Harper’s question.

When Are The Natural Embeddings Of Classical Invariant Rings Pure?, Melvin Hochster, Jack Jeffries, Vaibhav Pandey, Anurag K. Singh

Department of Mathematics: Faculty Publications

Consider a reductive linear algebraic group G acting linearly on a polynomial ring S over an infinite field; key examples are the general linear group, the symplectic group, the orthogonal group, and the special linear group, with the classical representations as inWeyl’s book: For the general linear group, consider a direct sum of copies of the standard representation and copies of the dual; in the other cases, take copies of the standard representation. The invariant rings in the respective cases are determinantal rings, rings defined by Pfaffians of alternating matrices, symmetric determinantal rings and the Plücker coordinate rings of Grassmannians; …

Listening For Common Ground In High School And Early Collegiate Mathematics, Gail Burrill, Henry Cohn, Yvonne Lai, Dev P. Sinha, Ji Y. Son, Katherine F. Stevenson

Department of Mathematics: Faculty Publications

Solutions to pressing and complex social challenges require that we reach for common ground. Only through cooperation among people with a broad range of backgrounds and expertise can progress be made on issues as challenging as improving student success in mathematics. In this spirit, the AMS Committee on Education held a forum in May 2022 entitled The Evolving Curriculum in High School and Early Undergraduate Mathematical Sciences Education.¹ This article is a report on that forum by the authors listed above, who were among the organizers and presenters.

Theory Of Invariant Manifold And Foliation And Uniqueness Of Center Manifold Dynamics, Bo Deng

Department of Mathematics: Faculty Publications

Here we prove that the dynamics on any two center-manifolds of a fixed point of any C^k,1 dynamical system of finite dimension with k ≥ 1 are C^k-conjugate to each other. For pedagogical purpose, we also extend Perron’s method for differential equations to diffeomorphisms to construct the theory of invariant manifolds and invariant foliations at fixed points of dynamical systems of finite dimensions.