Applied Mathematics Commons^™

Time-Marching Quantum Algorithm For Simulation Of Nonlinear Lorenz Dynamics, Efstratios Koukoutsis, George Vahala, Min Soe, Kyriakos Hizanidis, Linda Vahala, Abhay K. Ram

Electrical & Computer Engineering Faculty Publications

Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by developing an explicit quantum algorithm that implements the time evolution of a second-order time-discretized version of the Lorenz model. The Lorenz model is a celebrated system of nonlinear ordinary differential equations that has been extensively studied in the contexts of climate science, fluid dynamics, and chaos theory. Our algorithm possesses a recursive structure and requires only a linear number of copies of the initial state …

The Effect Of Electrode Geometry On Excited Species Production In Atmospheric Pressure Air–Hydrogen Streamer Discharge, Shirshak Kumar Dhali, Stuart Reyes

Electrical & Computer Engineering Faculty Publications

When a gas is overvolted at or near atmospheric pressure, it results in a streamer discharge formation. Electrode geometries exert significant impact on the electrical breakdown of gases by altering the spatial profile of the electric field. In many applications the efficient generation of radicals is critical and is determined by the characteristics of the streamer discharge. We examine the effect of electrode geometry on the streamer characteristics and the production of radicals. This is performed for three different electrode geometries: plane–plane, pin–plane, and pin–pin. A two-dimensional rotationally symmetric fluid model is used for the streamer discharge simulation in the …

Bayesian Networks For Safety-Critical Systems, Joseph Mietkiewicz

Theses

This thesis addresses a operational challenge in modern industrial operations: the increasing complexity of systems and the consequent cognitive burden on operators. As industrial technologies advance, the human-computer interface has become the primary conduit for information flow, playing a pivotal role in operational decision-making. However, the proliferation of data often leads to information overload, potentially compromising rather than enhancing operator performance. This research explores an approach to this pressing issue through the application of Bayesian networks as decision support systems in safety- critical scenarios. Our study employs a multi-faceted approach, combining theoretical modeling with empirical testing. Through collaboration with industry …

Investigating The Temperature Effects On Aedes Aegypti And Dengue Virus In Central Argentina: Perspectives From Mathematical Modeling, Morgan H. Jackson

Theses and Dissertations

Dengue virus (DENV) causes over 390 million infections and around 40,000 deaths worldwide each year. DENV is primarily transmitted by the mosquito Aedes aegypti, and both the life cycle of these mosquitoes and DENV transmission are significantly impacted by temperature. In the temperate region of Central Argentina, where dengue outbreaks first began in 2009, outbreaks only occur following new introductions of DENV from other regions. Due to the relationships between temperature and DENV and temperature and Ae. aegypti, the risk of an outbreak changes throughout the year. Here, we develop and analyze mathematical models for both mosquito population dynamics and …

Swarming Segregation: Leveraging Swarm Intelligence And Regionalization As Instruments For School District Desegregation, Jeffrey Wooten

Theses and Dissertations

Even after Brown led to the South briefly having the most diverse schools in the nation, schools throughout the Northeast have remained the most segregated in the nation for decades. While federal jurisprudence has made compelling desegregation pursuant to the Equal Protection Clause more challenging, New Jersey has a particularly favorable landscape to address severe segregation. With a highly diverse, densely populated public enrollment, favorable state constitutional precedent, and a history of successfully compelling desegregation, New Jersey is fertile ground exploring regional desegregation. Scholars, judges, and even plaintiffs in ongoing litigation (Latino Action Network v. N.J.) have called for New …

Maximum Trimmed Likelihood Estimation For Discrete Multivariate Vasicek Processes, Thomas M. Fullerton Jr., Michael Pokojovy, Andrews T. Anum, Ebenezer Nkum

Mathematics & Statistics Faculty Publications

The multivariate Vasicek model is commonly used to capture mean-reverting dynamics typical for short rates, asset price stochastic log-volatilities, etc. Reparametrizing the discretized problem as a VAR(1) model, the parameters are oftentimes estimated using the multivariate least squares (MLS) method, which can be susceptible to outliers. To account for potential model violations, a maximum trimmed likelihood estimation (MTLE) approach is utilized to derive a system of nonlinear estimating equations, and an iterative procedure is developed to solve the latter. In addition to robustness, our new technique allows for reliable recovery of the long-term mean, unlike existing methodologies. A set of …

Towards Understanding Thermal Management In Unsteady Boundary Layer Flow With Ac/Dc Electric Fields, Sara Abdelsalam, M. A. Dagher, Y. A. Elmaboud, A. I. Abdellateef

Basic Science Engineering

Unsteady boundary layer flow induced by alternating current (AC) or direct current (DC) electric field through a porous layer is investigated numerically. The finite difference method based on Crank-Nicolson is applied to solve the nonlinear system. The governing equations are built with fractional shear stress and the Cattaneo heat flux model, and time fractional derivatives are computed using the Caputo fractional derivative. The numerical results are presented to demonstrate the effects of varying parameters on momentum and thermal boundary layer. The results reveal that the time delay in the velocity profile occurs for larger values of both the velocity fractional …

Bound Preserving Discontinuous Galerkin Methods For Euler Equations And Nonequilibrium Flows, Fangyao Zhu

Dissertations, Master's Theses and Master's Reports

This dissertation is composed of four chapters in which we will closely examine the high order bound preserving discontinuous Galerkin methods for solving partial differential equations, specifically non-equilibrium chemical reacting flows and Euler equations under gravitational fields. A shared requirement between the two is the necessity for positive values of both density and pressure. Due to this physical nature of the two systems, constructing a positivity preserving scheme become very essential in our research.

For non-equilibrium flows where multi-reactions and multi-species are involved, we are also required to keep the bounds of the mass fraction of each species in between …

Learning Paradigms For Rhythm Detection And Generation Using Mathematical Models, Biophysical And Artificial Neural Networks, Prianka Bose

Dissertations

Humans possess an inherent ability to recognize evenly-spaced rhythms, known as isochronous rhythms, owing to the brain's predisposition to entrain to external auditory stimuli with regular temporal intervals. The central focus of this research is to understand how the brain learns and retains rhythmic time intervals in the context of music. This dissertation studies rhythm detection and generation through mathematical models, biophysical networks, and artificial neural networks, addressing both isochronous and non-isochronous patterns.

A primary focus of the thesis is on isochronous rhythms. In particular, given a perturbation to an isochronous rhythm such as a tempo change or phase shift …

Mathematical Modelling And Analysis For The Co-Infection Of Viral And Bacterial Diseases: A Systematic Review Protocol, Timothy Kiprono Yano, Ebenezer Afrifa-Yamoah, Julia Collins, Ute Mueller, Steven Richardson

Research outputs 2022 to 2026

Introduction Breaking the chain of transmission of an infectious disease pathogen is a major public health priority. The challenges of understanding, describing and predicting the transmission dynamics of infections have led to a wide range of mathematical, statistical and biological research problems. Advances in diagnostic laboratory procedures with the ability to test multiple pathogens simultaneously mean that co-infections are increasingly being detected, yet little is known about the impact of co-infections in shaping the course of an infection, infectivity, and pathogen replication rate. This is particularly true of the apparent synergistic effects of viral and bacterial co-infections, which present the …

The Faithfulness Of An Extension Of Lawrence-Krammer-Bigelow Representation On The Group Of Conjugating Automorphisms $C_N$ In The Cases $N=3$ And $N=4$, Mohamad Nasser

BAU Journal - Science and Technology

Let $C_n$ be the group of conjugating automorphisms. V. Bardakov defined a representation $\rho$ of $C_n$, which is an extension of Lawrence-Krammer-Bigelow representation of the braid group $B_n$. Bardakov proved that the representation $\rho$ is unfaithful for $n \geq 5$. The cases $n=3,4$ remain open. M. N. Nasser and M. N. Abdulrahim made attempts towards the faithfulness of $\rho$ in the case $n=3$. In this work, we prove that $\rho$ is unfaithful in the both cases $n=3$ and $n=4$.

Modeling Of Light Filamentation For Nonlinear Imaging And Waveguiding, Nicholas Bagley

Mathematics Theses and Dissertations

Ultrashort pulses are capable of extremely high powers; in addition to enabling various applications in defense, sensing, and imaging, they provide a useful arena in which to study nonlinear optical phenomena that are observable only at high intensities. Due to these effects, which can include ionization and thermal blooming, simulation of ultrashort pulse propagation is a complicated multiphysics problem. We provide an overview of techniques used to simulate the propagation of ultrashort pulses in the nonlinear regime, including the formation of light filaments due to the competition of Kerr self-focusing and defocusing (e.g. via plasma generation). We discuss both carrier-resolved …

An Optimization Framework For Data Enrichment: A First Principles Approach To Designing Optimal Smoothers And Splines, Griffin Michael Kearney

Dissertations - ALL

We develop a general framework for state estimation in systems modeled with stochastic dynamics and noisy measurements. Our approach is based on maximum likelihood estimation and employs a variety of techniques from optimization theory including the calculus of variations and discrete optimization to derive optimality conditions for many different types of problems. We make no rigid assumptions on the form of the mapping from measurements to state-estimate or on the distributions of the random processes, making the framework more general than existing techniques such as splines, Kalman smoothing or Gaussian Process Regressions, which are subject to limiting restrictions and modeling …

Safety And Optimality Monitors For Learning-Enabled Systems Using Conformal Prediction, Jackson Cox

McKelvey School of Engineering Graduate Student Theses & Dissertations

The use of machine learning to create data-driven plant models and controllers has led to an increased need for safety and optimality monitors for model-based systems. System plant models are subject to uncertainty due to learning constraints such as unseen data and overfitting or physical constraints such as unknown dynamics and noise. This uncertainty is detrimental to safety-critical systems and must be properly regulated. To curb this uncertainty, we create prediction sets using the guarantees provided by Conformal Prediction. With a user-specified high probability, these prediction sets contain the true plant system states for an entire prediction horizon, which we …

Traveling Waves In Biological Population Models, Ahlam Alzahrani

Theses and Dissertations

In this thesis, we examine the existence of traveling waves in population models. We begin by exploring conditions under which traveling waves exist, even when the migration probability lacks a density function or, if the density function exists, it may be discontinuous. To address this, we impose certain conditions that ensure the monotonicity of the evolution operator, enabling the application of the Monotone Iteration Method. Next, we explore the existence of monotone traveling waves in a general class of integral-difference population models that depend on both the previous state and long-term memory, allowing for the consideration of multiple past states. …

Mathematical Modelling Of Disease Outbreak, Favour Christian, Matthew Molloy

SURE Journal: Science Undergraduate Research Experience Journal

Establishing a model framework for more research necessitates a thorough understanding of the causes, distribution, prevalence, and evolution of infectious illnesses. The main mathematical concept used in this modelling simulation is ordinary differential equations (ODEs). The purpose of this study was to investigate the significance of the many criteria linked to a zombie virus spread. The zombie framework provides an accessible and relatively simple representation of the nature of infectious disease spread, allowing for tractable assumptions and the development of more complex situations.

The models are designed around a zombie outbreak in which the zombie virus is spread through a …

The Mathematical Laws Of Morphology And Biomechanics Through Ontogeny, Wijesooriya Kisal Wijesooriya

The Journal of Purdue Undergraduate Research

No abstract provided.

Where To Build Food Banks: A Machine Learning Approach, Gavin Ruan

The Journal of Purdue Undergraduate Research

Over 44 million Americans currently suffer from food insecurity, of whom 13 million are children. Food insecurity has been shown to cause a wide range of both physical and developmental issues. Across the United States, thousands of food banks and pantries serve as vital sources of food and other forms of aid for food-insecure families. By optimizing food bank locations, food banks and their resources would become more accessible to families who desperately require it. The aim of this paper is to build a machine learning framework that is able to optimize food bank locations and to consider factors such …

Operations On Submodules With The Multiplicative And Quotient Properties, Jiekai Pang

Mathematics & Statistics ETDs

Inspired by the works of Petro, Epstein, Vassilev, and Morre, this thesis aims to study the generalized definitions of the semiprime operation, weakly prime operation, and standard closure operation on rings, that is, the multiplicative operation, weakly multiplicative operation, and standardly multiplicative operation on submodules. Then, we will use Matlis duality to induce the dual notions of these definitions on submodules of Matlis-dualizable Artinian modules. In order to understand the dual notion of the standardly multiplicative operation, that is, the standardly quotient operation, we will classify the operations on the injective hull of residue field of the ring K[[x,y]]/(xy) which …

Theory And Algorithms To Learn, Propagate, And Exploit Uncertainty For Stochastic Optimal Control Of Dynamical Systems, Vignesh Sivaramakrishnan

Electrical and Computer Engineering ETDs

Non-Gaussian uncertainty frequently arises in learning and control problems involving stochastic dynamical systems, particularly in autonomous vehicles, UAVs, satellites, and robotics. In this dissertation, we propose a new framework that leverages characteristic functions that provides a frequency-domain representation of random variables. The dissertation is structured into three key areas. First, we address model-based stochastic optimal control for linear systems with non-Gaussian noise, demonstrating that characteristic functions can be used to enforce chance constraints and control systems toward desired distributions. Second, we explore data-driven stochastic control, utilizing empirical characteristic functions to handle systems with unknown disturbances. In addition, we derive several …