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(R2056) Convergence Criteria For Solutions Of A System Of Second Order Nonlinear Differential Equations, Akinwale Olutimo 2023 Lagos State University

(R2056) Convergence Criteria For Solutions Of A System Of Second Order Nonlinear Differential Equations, Akinwale Olutimo

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we investigate the convergence of solutions of certain nonlinear system of two differential equations using a suitable Lyapunov functional with sufficient conditions to establish our new result. An example is given to demonstrate the effectiveness of the result obtained and geometric argument to show that the solutions of the system are better rapidly converging under the criteria obtained.


Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost 2023 Clemson University

Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost

All Dissertations

In confocal single-molecule FRET experiments, the joint distribution of FRET efficiency and donor lifetime distribution can reveal underlying molecular conformational dynamics via deviation from their theoretical Forster relationship. This shift is referred to as a dynamic shift. In this study, we investigate the influence of the free energy landscape in protein conformational dynamics on the dynamic shift by simulation of the associated continuum reaction coordinate Langevin dynamics, yielding a deeper understanding of the dynamic and structural information in the joint FRET efficiency and donor lifetime distribution. We develop novel Langevin models for the dye linker dynamics, including rotational dynamics, based …


New Preconditioned Conjugate Gradient Methods For Some Structured Problems In Physics, Tianqi Zhang 2023 Clemson University

New Preconditioned Conjugate Gradient Methods For Some Structured Problems In Physics, Tianqi Zhang

All Dissertations

This dissertation concerns the development and analysis of new preconditioned conjugate gradient (PCG) algorithms for three important classes of large-scale and complex physical problems characterized by special structures. We propose several new iterative methods for solving the eigenvalue problem or energy minimization problem, which leverage the unique structures inherent in these problems while preserving the underlying physical properties. The new algorithms enable more efficient and robust large-scale modeling and simulations in many areas, including condensed matter physics, optical properties of materials, stabilities of dynamical systems arising from control problems, and many more. Some methods are expected to be applicable to …


Controlled Manipulation And Transport By Microswimmers In Stokes Flows, Jake Buzhardt 2023 Clemson University

Controlled Manipulation And Transport By Microswimmers In Stokes Flows, Jake Buzhardt

All Dissertations

Remotely actuated microscale swimming robots have the potential to revolutionize many aspects of biomedicine. However, for the longterm goals of this field of research to be achievable, it is necessary to develop modelling, simulation, and control strategies which effectively and efficiently account for not only the motion of individual swimmers, but also the complex interactions of such swimmers with their environment including other nearby swimmers, boundaries, other cargo and passive particles, and the fluid medium itself. The aim of this thesis is to study these problems in simulation from the perspective of controls and dynamical systems, with a particular focus …


Exploration And Statistical Modeling Of Profit, Caleb Gibson 2023 East Tennessee State University

Exploration And Statistical Modeling Of Profit, Caleb Gibson

Undergraduate Honors Theses

For any company involved in sales, maximization of profit is the driving force that guides all decision-making. Many factors can influence how profitable a company can be, including external factors like changes in inflation or consumer demand or internal factors like pricing and product cost. Understanding specific trends in one's own internal data, a company can readily identify problem areas or potential growth opportunities to help increase profitability.

In this discussion, we use an extensive data set to examine how a company might analyze their own data to identify potential changes the company might investigate to drive better performance. Based …


Generative Adversarial Game With Tailored Quantum Feature Maps For Enhanced Classification, Anais Sandra Nguemto Guiawa 2023 University of Tennessee, Knoxville

Generative Adversarial Game With Tailored Quantum Feature Maps For Enhanced Classification, Anais Sandra Nguemto Guiawa

Doctoral Dissertations

In the burgeoning field of quantum machine learning, the fusion of quantum computing and machine learning methodologies has sparked immense interest, particularly with the emergence of noisy intermediate-scale quantum (NISQ) devices. These devices hold the promise of achieving quantum advantage, but they grapple with limitations like constrained qubit counts, limited connectivity, operational noise, and a restricted set of operations. These challenges necessitate a strategic and deliberate approach to crafting effective quantum machine learning algorithms.

This dissertation revolves around an exploration of these challenges, presenting innovative strategies that tailor quantum algorithms and processes to seamlessly integrate with commercial quantum platforms. A …


Effects Of A Protection Zone In A Reaction-Diffusion Model With Strong Allee Effect., Isaac Johnson 2023 University of Louisville

Effects Of A Protection Zone In A Reaction-Diffusion Model With Strong Allee Effect., Isaac Johnson

Electronic Theses and Dissertations

A protection zone model represents a patchy environment with positive growth over the protection zone and strong Allee effect growth outside the protection zone. Generally, these models are considered through the corresponding eigenvalue problem, but that has certain limitations. In this thesis, a general protection zone model is considered. This model makes no assumption on the direction of the traveling wave solution over the Strong Allee effect patch. We use phase portrait analysis of this protection zone model to draw conclusions about the existence of equilibrium solutions. We establish the existence of three types of equilibrium solutions and the necessary …


Low Reynolds Number Locomotion Near Interfaces In Two-Fluid Media, Avriel Rowena Mae Cartwright 2023 Florida Institute of Technology

Low Reynolds Number Locomotion Near Interfaces In Two-Fluid Media, Avriel Rowena Mae Cartwright

Theses and Dissertations

Microorganisms often swim within complex fluid environments composed of multiple materials with very different properties. Biological locomotion, including swimming speed, is significantly impacted by the physical composition and rheology of the surrounding fluid environment, as well as the presence of phase boundaries and free interfaces, across which physical properties of the fluid media may vary greatly. Through computational simulations, we first investigate the classical Taylor’s swimming sheet problem near interfaces within multi-fluid environments using a two-fluid immersed boundary method. The accuracy of the methodology is illustrated through comparisons with analytical solutions. Our simulation results indicate that the interface dynamics and …


Memory Network-Based Interpreter Of User Preferences In Content-Aware Recommender Systems, Nhu Thuat TRAN, Hady W. LAUW 2023 Singapore Management University

Memory Network-Based Interpreter Of User Preferences In Content-Aware Recommender Systems, Nhu Thuat Tran, Hady W. Lauw

Research Collection School Of Computing and Information Systems

This article introduces a novel architecture for two objectives recommendation and interpretability in a unified model. We leverage textual content as a source of interpretability in content-aware recommender systems. The goal is to characterize user preferences with a set of human-understandable attributes, each is described by a single word, enabling comprehension of user interests behind item adoptions. This is achieved via a dedicated architecture, which is interpretable by design, involving two components for recommendation and interpretation. In particular, we seek an interpreter, which accepts holistic user’s representation from a recommender to output a set of activated attributes describing user preferences. …


Experimental Analysis Of Nonlinear Wave Propagation In Bistable Mechanical Metamaterials With A Defect, Samuel R. Harre 2023 University of Nebraska-Lincoln

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, …


Game-Theoretic Approaches To Optimal Resource Allocation And Defense Strategies In Herbaceous Plants, Molly R. Creagar 2023 University of Nebraska-Lincoln

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 …


Understanding Collective Performance: Human Factors And Team Science, Joseph Keebler 2023 Embry-Riddle Aeronautical University

Understanding Collective Performance: Human Factors And Team Science, Joseph Keebler

Math Department Colloquium Series

This talk will focus on modern issues with team science. Joe will discuss a variety of projects he's been involved with aimed at improving teamwork in complex sociotechnical systems including military, aviation, and healthcare. He will discuss major theoretical facets of teamwork and provide evidence-based best practices that were utilized to improve teams in applied settings.


Series Expansions Of Lambert W And Related Functions, Jacob Imre 2023 Western University

Series Expansions Of Lambert W And Related Functions, Jacob Imre

Electronic Thesis and Dissertation Repository

In the realm of multivalued functions, certain specimens run the risk of being elementary or complex

to a fault. The Lambert $W$ function serves as a middle ground in a way, being non-representable by elementary

functions yet admitting several properties which have allowed for copious research. $W$ utilizes the

inverse of the elementary function $xe^x$, resulting in a multivalued function with non-elementary

connections between its branches. $W_k(z)$, the solution to the equation $z=W_k(z)e^{W_k(z)}$

for a "branch number" $k \in \Z$, has both asymptotic and Taylor series for its various branches.

In recent years, significant effort has been dedicated to exploring …


Differentiating By Prime Numbers, Jack Jeffries 2023 University of Nebraska-Lincoln

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 …


A Primer On The Legendre Transformation, Steven J. Kilner, David L. Farnsworth 2023 Monroe County Community College

A Primer On The Legendre Transformation, Steven J. Kilner, David L. Farnsworth

Articles

Guidance is offered for understanding and using the Legendre transformation and its associated duality among functions and curves. The genesis of this paper was encounters with colleagues and students asking about the transformation. A main feature is simplicity of exposition, while keeping in mind the purpose or application for using the transformation.


Dynamic Rotation Of Maxwellian Fluid With Fluctuating Thermal Conductivity, Yasir Iqbal, Iqra Batool, Zia Ur Rehman 2023 Department of Mathematics, University of Wah, Wah Cantt 47040, Pakistan

Dynamic Rotation Of Maxwellian Fluid With Fluctuating Thermal Conductivity, Yasir Iqbal, Iqra Batool, Zia Ur Rehman

International Journal of Emerging Multidisciplinaries: Mathematics

This investigation examined the behavior of an overhead-connected Maxwell (UCM) fluid within a rotating framework, with consideration for variations in thermal conductivity based on temperature. The heat deportation process was simulated by incorporating a non-Fourier heat flux term, accounting for thermal relaxation effects. The governing set of partial differential equations underwent decomposition through boundary layer approximations, followed by employing similarity transformations to convert them into self-similar forms. To investigate the effect of the rotation criterion ($\lambda$), Prandtl number (Pr), Deborah number ($\beta$), parameter ($\epsilon$), and dimensionless thermal relaxation time ($\gamma$), an advanced three-stage Lobatto IIIa numerical method was applied. The …


Thermodynamic Laws Of Billiards-Like Microscopic Heat Conduction Models, Ling-Chen Bu 2023 University of Massachusetts Amherst

Thermodynamic Laws Of Billiards-Like Microscopic Heat Conduction Models, Ling-Chen Bu

Doctoral Dissertations

In this thesis, we study the mathematical model of one-dimensional microscopic heat conduction of gas particles, applying both both analytical and numerical approaches. The macroscopic law of heat conduction is the renowned Fourier’s law J = −k∇T, where J is the local heat flux density, T(x, t) is the temperature gradient, and k is the thermal conductivity coefficient that characterizes the material’s ability to conduct heat. Though Fouriers’s law has been discovered since 1822, the thorough understanding of its microscopic mechanisms remains challenging [3] (2000). We assume that the microscopic model of heat conduction is a hard ball system. The …


Long-Acting Cabotegravir And The Emergence Of Drug-Resistant Hiv, Katharine Gurski 2023 Howard University

Long-Acting Cabotegravir And The Emergence Of Drug-Resistant Hiv, Katharine Gurski

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Utilizing Non-Negative Least Squares For Data-Driven Discovery Of Dynamics, Tracey G. Oellerich 2023 George Mason University

Utilizing Non-Negative Least Squares For Data-Driven Discovery Of Dynamics, Tracey G. Oellerich

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Effect Of Under-Reporting, Vaccine Efficiency And Social Behavior On Epidemic Progression, Samiran Ghosh, Samiran Ghosh 2023 Illinois State University

Effect Of Under-Reporting, Vaccine Efficiency And Social Behavior On Epidemic Progression, Samiran Ghosh, Samiran Ghosh

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


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