Numerical Analysis and Computation Commons^™

Discontinuous Galerkin Methods For Compressible Miscible Displacements And Applications In Reservoir Simulation, Yue Kang

Dissertations, Master's Theses and Master's Reports

This dissertation contains research on discontinuous Galerkin (DG) methods applied to the system of compressible miscible displacements, which is widely adopted to model surfactant flooding in enhanced oil recovery (EOR) techniques. In most scenarios, DG methods can effectively simulate problems in miscible displacements.
However, if the problem setting is complex, the oscillations in the numerical results can be detrimental, with severe overshoots leading to nonphysical numerical approximations. The first way to address this issue is to apply the bound-preserving
technique. Therefore, we adopt a bound-preserving Discontinuous Galerkin method
with a Second-order Implicit Pressure Explicit Concentration (SIPEC) time marching
method to …

New Method For Computing The Euclidean Condition Number With Rim-C, Cody Mccarthy

Dissertations, Master's Theses and Master's Reports

The condition number, being critical to solving linear systems, has many impor-
tant applications. Specifically for robust control analysis, the Euclidean norm has
widespread use over the 1-norm and ∞-norm such as determining a control system’s
stability to uncertainty [1]. Much work has been done with estimating the Euclidean
condition number, but current algorithms for computing said condition number, with
large matrices, tend to run slow as well as requiring a large amount of computa-
tional resources. This report seeks to provide a more time efficient algorithm that
utilizes MATLAB’s eigs, svds, and normest commands as well as the recently …

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

Theses and Dissertations (Comprehensive)

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …

Penalized Interpolating B-Splines And Their Applications, Kylee L. Hartman-Caballero

Theses and Dissertations

One of the most studied data analysis techniques in Numerical Analysis is interpolation. Interpolation is used in a variety of fields, namely computer graphic design and biomedical research. Among interpolation techniques, cubic splines have been viewed as the standard since at least the 1960s, due to their ease of computation, numerical stability, and the relative smoothness of the interpolating curve. However, cubic splines have notable drawbacks, such as their lack of local control and necessary knowledge of boundary conditions. Arguably a more versatile interpolation technique is the use of B-splines. B-splines, a relative of Bézier curves, allow local control through …

Mathematical Analysis Of Eukaryotic Pericentromere, Puranjan Ghimire

Theses and Dissertations

The centromere is crucial for chromosomal stability and their proper segregation during cell division in eukaryotes. Surrounding the centromere are pericentromeres, made of repetitive DNA elements called pericentromeric repeats, varying from 10 in fission yeast to thousands in humans. These repeats form densely packed heterochromatin, where genes are usually silenced. The silencing mechanism across different pericentromeric repeats remains unclear.

Despite variations in sequence and length, pericentromeric repeats are conserved across eukaryotes, indicating their functional importance. This dissertation presents mathematical models to quantify gene silencing in fission yeast and humans. In fission yeast, my model predicts that silencing occurs only with …

Characterizing Probabilities Of Outbreaks Of Dengue In Central Argentina Using A Temperature-Dependent Stochastic Model, Morgan H. Jackson, Elizabet L. Estallo, Cheng Ly, Michael A. Robert

Graduate Research Posters

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 dengue transmission are significantly impacted by temperature. In the temperate region of Central Argentina, where dengue outbreaks first began in 2009, outbreaks of dengue can only occur due to new introductions of DENV from other regions. Due to the relationships between temperature and dengue, the risk of outbreak changes throughout the year.

We develop a stochastic model including temperature-dependent mosquito life history traits and transmission-related parameters. …

Numerical Modeling Of Thermal Runaway In Lithium-Ion Batteries Using Decomposition Kinetics And Inter-Cell Contact Resistance, Shehzad Khan

College of Graduate Studies: Theses & Dissertations

Lithium-ion batteries (LIBs) are central in numerous high-demand applications due to their high energy density and prolonged cycle life. Despite these advantages, their susceptibility to thermal runaway (TR) poses a significant safety risk, with the potential for catastrophic failures. This study focuses on the thermal behavior of prismatic lithium-ion cells, using a finite volume-based partial differential equation (PDE) solver developed in MATLAB and JULIA to model TR behavior. This solver accurately simulates transient behaviors, convection, diffusion, and source terms across various coordinate systems. By engaging in a series of increasing complex case studies, this research aims to identify the critical …

A Comparative Analysis Of A Family Of Advanced Iterative Optimization Methods In Nonlinear Regression, Tanmoy Kumar Debnath

College of Graduate Studies: Theses & Dissertations

Classical statistical supervised learning optimization techniques like the Gauss-Newton Iterative Method (GNIM), Weighted Gauss-Newton Iterative Method (WGNIM), Reweighted Gauss-Newton Iterative Method (RGNIM), and Levenberg-Marquart (LM) algorithm extend the nonlinear least squares method. The WGNIM improves model fitting by controlling heteroscedasticity in the linear and nonlinear models. A comparative analysis of the GNIM, WGNIM, RGNIM, and LM methods for fitting nonlinear models is presented. A step-wise diagnosis for structural multicollinearity in the reweighted linearized model is investigated via the Variance Inflation Factor (VIF) to determine variance inflation in the sequence of estimators for the model parameters. Under restricted multicollinearity levels in …

Mathematical Modeling Of Coupled Heat And Mass Transfer In Metal-Hydride Hydrogen Storage Systems, Muhammad Hasnain

College of Graduate Studies: Theses & Dissertations

As a promising clean energy carrier hydrogen has recently gained significant interest, but its efficient and safe storage is a major challenge. Compared to the gaseous state and liquid state, metal hydrides (MH) offer a potentially more effective storage approach for hydrogen. However, the main challenge in this approach is the low thermal conductivity of the MH bed that leads to low heat transfer and ultimately to higher charging and discharging times. The purpose of this work is to develop an in-house comprehensive heat and mass transfer model for hydrogen sorption in MH reactors to simulate the dynamic behavior of …

A Novel Scheme Based On Bessel Operational Matrices For Solving A Class Of Nonlinear Systems Of Differential Equations, Atallah El-Shenawy, Mohamed El-Gamel, Muhammad E. Anany

Mansoura Engineering Journal

The system of ordinary differential equations arises in many natural phenomena, especially in the field of disease spread. In this paper, a perfect spectral technique is introduced to solve systems of nonlinear differential equations. The technique enhanced the Bessel collocation technique by converting the series notation of unknown variables and their derivatives to matrix relations. The Newton algorithm is developed to solve the resulting nonlinear system of algebraic equations. The effectiveness of the scheme is proved by the convergence analysis and error bound as demonstrated in Theorem 1. The scheme of solution is tested to clarify the efficiency and the …

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 …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Simulation Of Multi-Variable Converters Using The Linear Interpolation Method, Miraziz Vorisovich Sagatov

Chemical Technology, Control and Management

In this work, based on the theory of barycentric coordinates and simplexes, a linear interpolation method is proposed for modeling and controlling the operation of multiparameter converters. It has been determined that the linear interpolation method minimizes the structural diagram of a computing device, which makes it possible to more accurately determine the metrological characteristics of multiparameter measuring transducers and offer effective methods and means for processing primary measurement information. A theorem has been proven about a linear interpolating polynomial of a function of many variables, which will allow us to judge the property of linearization of multidimensional quantities from …

Applications Of Survival Estimation Under Stochastic Order To Cancer: The Three Sample Problem, Sage Vantine

Honors Program Theses and Research Projects

Stochastic ordering of probability distributions holds various practical applications. However, in real-world scenarios, the empirical survival functions extracted from actual data often fail to meet the requirements of stochastic ordering. Consequently, we must devise methods to estimate these distribution curves in order to satisfy the constraint. In practical applications, such as the investigation of the time of death or the progression of diseases like cancer, we frequently observe that patients with one condition are expected to exhibit a higher likelihood of survival at all time points compared to those with a different condition. Nevertheless, when we attempt to fit a …

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 …

Motion Simulation And Risk Assessment Of Dropped Objects In Offshore Operations, Hanqi Yu

LSU New Orleans Theses and Dissertations

Subsea pipelines are a cost-effective and reliable way to transport hydrocarbons in offshore oil and gas development. However, dropped objects can pose hazards and cause damage to pipelines. This dissertation briefly introduces the hazards and hidden dangers caused by dropped containers, discusses motion simulation methods for different object shapes, and reviews risk assessment procedures for handling dropped objects in offshore operations. Ongoing research at the University of New Orleans' towing tank on dropped container models is also discussed. Using ANSYS Fluent, we simulate trajectories of container models and calculate relevant hydrodynamic coefficients for different dropped angles. We then apply risk …

(R2058) Mhd Stagnation Point Flow Of Nanofluid With Buoyancy Effect Through A Porous Shrinking Sheet, Timothy L. Oyekunle, Mojeed T. Akolade, Samson A. Agunbiade, Paul O. Adeniran

Applications and Applied Mathematics: An International Journal (AAM)

The current investigation seeks to identify the response of buoyancy and heat source mechanisms on chemically reacting and magnetized nanofluid. The stagnation point flows through the shrinking porous surface assumed as an air-based fluid conveying nanoparticles under Buongiorno’s model. This article contributes to the existing literature with the introduction of nonlinear convection of the nanofluid, triggered by the heat source, which accelerates the temperature of the fluid particles, thus resulting in airflow upstream. Subject to these conditions, the mathematical model is presented in PDE systems. An approach of similarity variable is employed to arrive at the ODE systems, which is …

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 …

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 …

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. …