Numerical Analysis and Computation Commons^™

Boundary Integral Equation Methods For Superhydrophobic Flow And Integrated Photonics, Kosuke Sugita

Dissertations

This dissertation presents fast integral equation methods (FIEMs) for solving two important problems encountered in practical engineering applications.

The first problem involves the mixed boundary value problem in two-dimensional Stokes flow, which appears commonly in computational fluid mechanics. This problem is particularly relevant to the design of microfluidic devices, especially those involving superhydrophobic (SH) flows over surfaces made of composite solid materials with alternating solid portions, grooves, or air pockets, leading to enhanced slip.

The second problem addresses waveguide devices in two dimensions, governed by the Helmholtz equation with Dirichlet conditions imposed on the boundary. This problem serves as a …

Analysis Of Nonequilibrium Langevin Dynamics For Steady Homogeneous Flows, Abdel Kader A. Geraldo

Doctoral Dissertations

First, we propose using rotating periodic boundary conditions (PBCs) [13] to simulate nonequilibrium molecular dynamics (NEMD) in uniaxial or biaxial stretching flow. These specialized PBCs are required because the simulation box deforms with the flow. The method extends previous models with one or two lattice remappings and is simpler to implement than PBCs proposed by Dobson [10] and Hunt [24]. Then, using automorphism remapping PBC techniques such as Lees-Edwards for shear flow and Kraynik-Reinelt for planar elongational flow, we demonstrate expo-nential convergence to a steady-state limit cycle of incompressible two-dimensional
NELD. To demonstrate convergence [12], we use a technique similar …

Null Space Removal In Finite Element Discretizations, Pengfei Jia

All Theses

Partial differential equations are frequently utilized in the mathematical formulation of physical problems. Boundary conditions need to be applied in order to obtain the unique solution to such problems. However, some types of boundary conditions do not lead to unique solutions because the continuous problem has a null space. In this thesis, we will discuss how to solve such problems effectively. We first review the foundation of all three problems and prove that Laplace problem, linear elasticity problem and Stokes problem can be well posed if we restrict the test and trial space in the continuous and discrete finite element …

Flow Dynamics In Cardiovascular Devices: A Comprehensive Review, Venant Niyonkuru, Bosco Jean Ndayishimiye Dr, Anicet Barthélemy Sibomana

Digital Journal of Clinical Medicine

This review explores flow dynamics in cardiovascular devices, focusing on fundamental fluid mechanics principles and normal blood flow patterns. It discusses the role of different structures in maintaining flow dynamics and the importance of stents, heart valves, artificial hearts, and ventricular assist devices in cardiovascular interventions. The review emphasizes the need for optimized designs and further research to enhance knowledge of flow dynamics in cardiovascular devices, advancing the field and improving patient care in cardiovascular interventions.

Modeling Biphasic, Non-Sigmoidal Dose-Response Relationships: Comparison Of Brain- Cousens And Cedergreen Models For A Biochemical Dataset, Venkat D. Abbaraju, Tamaraty L. Robinson, Brian P. Weiser

Rowan-Virtua School of Osteopathic Medicine Faculty Scholarship

Biphasic, non-sigmoidal dose-response relationships are frequently observed in biochemistry and pharmacology, but they are not always analyzed with appropriate statistical methods. Here, we examine curve fitting methods for “hormetic” dose-response relationships where low and high doses of an effector produce opposite responses. We provide the full dataset used for modeling, and we provide the code for analyzing the dataset in SAS using two established mathematical models of hormesis, the Brain-Cousens model and the Cedergreen model. We show how to obtain and interpret curve parameters such as the ED50 that arise from modeling, and we discuss how curve parameters might change …

A Comparison Of Computational Perfusion Imaging Techniques, Shaharina Shoha

Masters Theses & Specialist Projects

Dynamic contrast agent magnetic resonance perfusion imaging plays a vital role in various medical applications, including tumor grading, distinguishing between tumor types, guiding procedures, and evaluating treatment efficacy. Extracting essential biological parameters, such as cerebral blood flow (CBF), cerebral blood volume (CBV), and mean transit time (MTT), from acquired imaging data is crucial for making critical treatment decisions. However, the accuracy of these parameters can be compromised by the inherent noise and artifacts present in the source images.

This thesis focuses on addressing the challenges associated with parameter estimation in dynamic contrast agent magnetic resonance perfusion imaging. Specifically, we aim …

Reducing Communication In The Solution Of Linear Systems, Neil S. Lindquist

Doctoral Dissertations

There is a growing performance gap between computation and communication on modern computers, making it crucial to develop algorithms with lower latency and bandwidth requirements. Because systems of linear equations are important for numerous scientific and engineering applications, I have studied several approaches for reducing communication in those problems. First, I developed optimizations to dense LU with partial pivoting, which downstream applications can adopt with little to no effort. Second, I consider two techniques to completely replace pivoting in dense LU, which can provide significantly higher speedups, albeit without the same numerical guarantees as partial pivoting. One technique uses randomized …

Deep Virtual Pion Pair Production, Dilini Lakshani Bulumulla

Physics Theses & Dissertations

This experiment investigates the deep virtual production of both σ− and ρ− mesons, with a particular focus on the microscopic structure of the σ mesons. While the ρ meson is an ordinary qq¯ pair, the σ meson is composed of not only the typical qq¯ pair, making it a topic of controversy for nearly six decades. Although the existence of the σ− meson is now well established, its microscopic structure remains poorly understood. The primary objective of this thesis is to contribute to the understanding of the σ meson by analyzing its deep virtual production. The main focus of this …

Mathematics Behind Machine Learning, Rim Hammoud

Electronic Theses, Projects, and Dissertations

Artificial intelligence (AI) is a broad field of study that involves developing intelligent
machines that can perform tasks that typically require human intelligence. Machine
learning (ML) is often used as a tool to help create AI systems. The goal of ML is
to create models that can learn and improve to make predictions or decisions based on given data. The goal of this thesis is to build a clear and rigorous exposition of the mathematical underpinnings of support vector machines (SVM), a popular platform used in ML. As we will explore later on in the thesis, SVM can be implemented …

She Is An Expert In This Research Field: The Signal Of Recent Publications' Relevance, Gil Zeevi, Osnat Mokryn

Northeast Journal of Complex Systems (NEJCS)

Assessing the expertise of researchers has garnered increased interest recently. This heightened focus arises from the growing emphasis on interdisciplinary science and the subsequent need to form expert teams. When forming these teams, the coordinators need to assess expertise in fields that are often very different from theirs. The conventional reliance on signals of success, prestige, and academic impact can unintentionally perpetuate biases within the assessment process. This traditional approach favors senior researchers and those affiliated with prestigious institutions, potentially overlooking talented individuals from underrepresented backgrounds or institutions. This paper addresses the challenge of determining expertise by proposing a methodology …

Pathogen Emergence As Complex Biological Invasion: Lessons From Dynamical Systems Modeling, Sudam Surasinghe, Marisabel Rodriguez, Victor Meszaros, Jane Molofsky, Salvador Almagro-Moreno, Brandon Ogbunugafor

Northeast Journal of Complex Systems (NEJCS)

Infectious disease emergence has become the target of cross-disciplinary efforts
that aim to understand and predict the shape of outbreaks. The many challenges
involved with the prediction of disease emergence events is a characteristic that in-
fectious diseases share with biological invasions in many subfields of ecology (e.g.,
how certain plants are able to successfully invade a new niche). Like infectious
diseases, biological invasions by plants and animals involve interactions between
agents (pathogens and plants in their respective cases) and a recipient niche. In
this study, we examine the problem of pathogen emergence through the lens of a
framework first …

Solving The Cable Equation, A Second-Order Time Dependent Pde For Non-Ideal Cables With Action Potentials In The Mammalian Brain Using Kss Methods, Nirmohi Charbe

Master's Theses

In this thesis we shall perform the comparisons of a Krylov Subspace Spectral method with Forward Euler, Backward Euler and Crank-Nicolson to solve the Cable Equation. The Cable Equation measures action potentials in axons in a mammalian brain treated as an ideal cable in the first part of the study. We shall subject this problem to the further assumption of a non-ideal cable. Assume a non-uniform cross section area along the longitudinal axis. At the present time, the effects of torsion, curvature and material capacitance are ignored. There is particular interest to generalize the application of the PDEs including and …

Said-Ball Polynomials For Solving Linear Systems Of Ordinary Differential Equations, Mubark Al-Subaai Dr., Ahmes Saleh Kherd

Emirates Journal for Engineering Research

Said-Ball polynomials with collocation method are used to numerically solve a system of linear ordinary differential equations. The matrix forms of Said-Ball polynomials of the solution, derivatives, and conditions are done. The linear system of ordinary differential equations with appropriate conditions is reduced to the linear algebraic equations system with unknown Said-Ball coefficients. Solving the resulting system determines the coefficients of Said-Ball polynomials. By Substituting these values in the polynomial, we get the problem's exact and approximate solutions. The obtaining numerical results show the proposed method's accuracy and reliability when compared with the other works and exact solutions

Temporality-Induced Chaos In The Kuramoto Model, Keanu Mason Rock, Hamza Dirie, Sean P. Cornelius

Northeast Journal of Complex Systems (NEJCS)

Switched dynamical systems have been extensively studied in engineering literature in the context of system control. In these systems, the dynamical laws change between different subsystems depending on the environment, a process that is known to produce emergent behaviors---notably chaos. These dynamics are analogous to those of temporal networks, in which the network topology changes over time, thereby altering the dynamics on the network. It stands to reason that temporal networks may therefore produce emergent chaos and other exotic behaviors unanticipated in static networks, yet concrete examples remain elusive. Here, we present a minimal example of a networked system in …

Extending The Spectral Difference Method With Divergence Cleaning (Sddc) To The Hall Mhd Equations, Russell J. Hankey, Kuangxu Chen, Chunlei Liang

Northeast Journal of Complex Systems (NEJCS)

The Hall Magnetohydrodynamic (MHD) equations are an extension of the standard MHD equations that include the “Hall” term from the general Ohm’s law. The Hall term decouples ion and electron motion physically on the ion inertial length scales. Implementing the Hall MHD equations in a numerical solver allows more physical simulations for plasma dynamics on length scales less than the ion inertial scale length but greater than the electron inertial length. The present effort is an important step towards producing physically correct results to important problems, such as the Geospace Environmental Modeling (GEM) Magnetic Reconnection problem. The solver that is …

(R1951) Numerical Solution For A Class Of Nonlinear Emden-Fowler Equations By Exponential Collocation Method, Mohammad Aslefallah, Saeid Abbasbandy, Şuayip Yüzbaşi

Applications and Applied Mathematics: An International Journal (AAM)

In this research, exponential approximation is used to solve a class of nonlinear Emden-Fowler equations. This method is based on the matrix forms of exponential functions and their derivatives using collocation points. To demonstrate the usefulness of the method, we apply it to some different problems. The numerical approximate solutions are compared with available (existing) exact (analytical) solutions to show the accuracy of the proposed method. The method has been checked with several examples to show its validity and reliability. The reported examples illustrate that the method is reasonably efficient and accurate.

(R1987) Hermite Wavelets Method For System Of Linear Differential Equations, Inderdeep Singh, Manbir Kaur

Applications and Applied Mathematics: An International Journal (AAM)

In this research paper, we present an accurate technique for solving the system of linear differential equations. Such equations often arise as a result of modeling in many systems and applications of engineering and science. The proposed scheme is based on Hermite wavelets basis functions and operational matrices of integration. The demonstrated scheme is simple as it converts the problem into algebraic matrix equation. To validate the applicability and efficacy of the developed scheme, some illustrative examples are also considered. The results so obtained with the help of the present proposed numerical technique by using Hermite wavelets are observed to …

Hydrodynamic And Physicochemical Interactions Between An Active Janus Particle And An Inactive Particle, Jessica S. Rosenberg

Dissertations, Theses, and Capstone Projects

Active matter is an area of soft matter science in which units consume energy and turn it into autonomous motion. Groups of these units – whether flocks of birds, bacterial colonies, or even collections of synthetically-made active particles – may exhibit complex behavior on large scales. While the large-scale picture is of great importance, so is the microscopic scale. Studying the individual particles that make up active matter will allow us to understand how they move, and whether and under what circumstances their activity can be controlled.

Here we delve into the world of active matter by studying colloidal-sized (100 …

Distributed Control Of Servicing Satellite Fleet Using Horizon Simulation Framework, Scott Plantenga

Master's Theses

On-orbit satellite servicing is critical to maximizing space utilization and sustainability and is of growing interest for commercial, civil, and defense applications. Reliance on astronauts or anchored robotic arms for the servicing of next-generation large, complex space structures operating beyond Low Earth Orbit is impractical. Substantial literature has investigated the mission design and analysis of robotic servicing missions that utilize a single servicing satellite to approach and service a single target satellite. This motivates the present research to investigate a fleet of servicing satellites performing several operations for a large, central space structure.

This research leverages a distributed control approach, …

A Guide To Uncertainty And Global Sensitivity Analysis In Lumped-Parameter Models Of The Cardiovascular System, Raheem Gul, Aamir Shahzad, Syed Muhammad Jawwad Riaz

International Journal of Emerging Multidisciplinaries: Mathematics

In this paper, a general 5-steps framework of uncertainty analysis (UA) and sensitivity analysis (SA) in lumped parameter models of the cardiovascular system (partial or complete) is presented. In order to conduct proper UA and SA, a high number of model simulations is required. Therefore, lumped parameter (0D) models of the cardiovascular system (CVS) are suitable for UA and SA as compared to high or multi-dimensional models (3D,2D,1D). As an example, a linear elastic lumped-parameter model of arm arteries is considered and a 5-steps framework is applied to quantify the impact of input parameters on output variables. The framework uses …