Numerical Analysis and Computation Commons^™

Eulerian Smoke Simulation With Multiple Fields, Diyang Zhang

Dartmouth College Master’s Theses

Fluid simulation is a cornerstone of computer graphics, enabling the realistic depiction of dynamic phenomena such as smoke, fire, and other gaseous behaviours. This thesis focuses on advancing Eulerian smoke simulation techniques, with a particular emphasis on grid-based simulations that capture intricate vortical structures and fine visual details.

We propose several detail-preserving frameworks that incorporate various scalar and vector fields within the simulation pipeline, including velocity, impulse, and Lamb vectors, along with their decompositions and transformed representations. By mathematically analyzing the properties of impulse, we derive its scalar fields decomposition (ImpSFD), which introduces an alternative numerical interpretation, and Vortex-Particles in …

Integrating Sentiment Analysis In Predictive Models: A Comparative Study On Game Popularity On Steam, Khaleefa Alhemeiri

CMC Senior Theses

Over the past decades, the gaming industry has managed to evolve into a multi-billion-dollar enterprise. Gaming platforms such as Steam foster unprecedented amounts of engagement among players worldwide daily. In this thesis, we investigate the effect of incorporating sentiment-driven metrics, specifically YouTube view counts and positive reviews, into predictive models for game popularity. In addition, by comparing our linear regression sentiment-based approach to the Bayesian hierarchical folded normal model used by De Luisa et al. (2021), we can understand the many differences, strengths, and limitations of each methodology. In our thesis, we focus on three games. Each is of varying …

Regularized Methods For Tensor Recovery And Processing, Katherine J. Henneberger

Theses and Dissertations--Mathematics

The rapid growth of high-dimensional data has exposed the limitations of traditional vector and matrix-based methods for data analysis. These methods often struggle with computational inefficiencies, loss of critical cross-dimensional correlations, and challenges inherent in high-dimensional data. Tensors—multidimensional arrays—offer a robust framework for modeling and analyzing complex data. Tensor methods have proven valuable in tasks such as dimensionality reduction, feature extraction, and data compression, underpinning advancements in machine learning, computer vision, signal processing, and remote sensing.

This thesis focuses on two challenges in tensor analysis: tensor recovery and tensor processing. Tensor recovery addresses the reconstruction of incomplete or corrupted tensors. …

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 …

Predicting Real Estate Prices Using Deep Learning Regression Models On Socio Spatial Data, Gentle Engworo

Graduate Theses/Dissertations

ABSTRACT

Cities keep their own kind of ledger. Every block, bus stop, corner store, and year that slips by leaves a small entry about what homes are worth. That ledger is what we call socio-spatial data: simple facts about what a home is (its age), where it sits (latitude/longitude), how easy it is to get around (distance to the nearest MRT station), what’s nearby (number of convenience stores), and when it sold (transaction date). This thesis asks a practical question in that everyday language: given these common clues, can we predict home prices more accurately and explain why? Using 414 …

Rapid Inference Of Atmospheric Feature Parameters From Light Curves Using Bayesian Neural Networks, Eugenio A. Diaz

Honors Undergraduate Theses

Mapping atmospheres using rotationally modulated light curves offers insights into cloud structures and dynamics. Current retrieval methods, primarily based on Markov Chain Monte Carlo (MCMC) techniques like Aeolus, can infer atmospheric features but are computationally prohibitive for large datasets. This project proposes a neural network (NN) framework for the rapid, variational inference of atmospheric structure from light curves, particularly those of brown dwarfs. The primary approach focuses on training a Bayesian NN (BNN) to perform regression, predicting the spot parameters that describe the object's surface brightness map. Given the scarcity of suitable observational training data, the BNN is trained on …

Ultrasonic Sensor-Based Sound Synthesis Using Raspberry Pi Pico W, Niraj Jaishwal

Williams Honors College, Honors Research Projects

At the intersection of Human Computer Interaction and digital art, this project transforms simple motion into musical expression. It explores an interactive real-time sound synthesis system using ultrasonic sensors to generate continuous audio. The objective is to design a system that maps physical distances into musical parameters such as pitch and amplitude, which will create a responsive audio environment. Two ultrasonic sensors are used in combination with the Raspberry Pi Pico W microcontroller running CircuitPython and Adafruit Audio Hat for real-time sound output. One sensor controls the pitch of the generated tone, while the other controls volume. This enables expressive …

Modified Equations Of Conformal Symplectic Exponential Time Differencing Methods, Taylore M. Keesler

Honors Undergraduate Theses

Planetary orbits, pendulums, and hurricanes are everyday examples of nonlinear systems, often studied using differential equations. However, their exact solutions can not always be computed, and thus, we use numerical methods to approximate their solutions. Certain methods are better suited to preserve special properties of the system like energy and geometry. Through previous numerical simulations, a conformal symplectic method proves more effective in this preservation. To understand why, we find the modified equation of a nonlinear system with damping, which is a differential equation for which the numerical solution is exact. Through backward error analysis, we obtain these modified equations, …

Cfd Analysis Of Hydrodynamic Cavitation Through An Orifice: Influence Of Different Inlet Pressures And Number Of Orifice Holes, Lemthong Chanphavong, Vongsavanh Chanthaboune, Keophousone Phonhalath

ASEAN Journal on Science and Technology for Development

Hydrodynamic cavitation (HC) is considered an energy-efficient process with high potential for utilization in many chemical processes. This study presents a computational fluid dynamics (CFD) analysis of cavitating flow through an orifice with a constant flow area. The Reynolds-Averaged Navier-Stokes (RANS) equations, coupled with turbulence and cavitation models, are employed to capture the complex flow behaviors. The effects of inlet pressures and number of orifice-holes on cavitation behavior are investigated. Result of the numerical simulation is validated with the existing experimental data from the literature. The CFD study revealed that cavitation initiates just behind the inlet edge of the orifice …

Application Of Semantic Segmentation To An Automatic Target Recognition Problem, Bruce W. Rush Jr.

College of Graduate Studies: Theses & Dissertations

Synthetic Aperture Radar (SAR) is an active remote sensing system commonly used in aerial reconnaissance. SAR penetrates cloud cover and vegetation by recording reflected energy pulses. The resulting information content is difficult to interpret due to vast clutter data and sparse target data. The time-consuming process of analyzing SAR imagery can be greatly reduced by implementing an Automatic Target Recognition (ATR) algorithm. Convolutional Neural Networks (CNN) are capable of extracting identification features from SAR data content. Further research in this field indicates that high performing models are insufficiently robust due to high clutter correlation among classes in the Moving and …

Modeling Energetic Electron Precipitation: Radiation Belt Loss, Its Drivers, And Atmospheric Impacts, Zhi Gu Li

Graduate Theses, Dissertations, and Problem Reports (ETD)

Energetic electrons in the terrestrial outer radiation belt present significant hazards to spacecraft systems and human operations in space. The intensity of these electrons can vary rapidly and dramatically during geomagnetic storms, governed by a complex competition between acceleration and loss processes. Among these, precipitation into the atmosphere via resonant wave-particle interaction acts as a key loss mechanism. This dissertation focuses on improving the quantification of energetic electron precipitation using physics-based modeling constrained by low-altitude satellite observations.

We begin by developing and validating the Drift-Diffusion model, which simulates low-altitude electron dynamics while accounting for azimuthal drift, pitch-angle diffusion, and atmospheric …

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 …

(R2100) Optimality Conditions Of A Topsis Optimization Model And Its Application On Interval-Valued Data, Sudipta Roy, Sandip Chatterjee

Applications and Applied Mathematics: An International Journal (AAM)

The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is widely used in the field of multi-criteria decision analysis. Despite its popularity and widespread application, little attention has been given to the mathematical foundation that underlies the TOPSIS algorithm. The existing literature on this subject is far from comprehensive, leaving many aspects of the algorithm unexplored. This paper aims to address this gap in the literature by delving into the optimization problem associated with TOPSIS. Unlike traditional interval analysis theory, which only covers a limited scope, our approach extends to a broader range of scenarios and offers …

(R2113) A Numerical Method For Solving Linear First-Order Volterra Integro-Differential Equations With Integral Boundary Condition, Zelal Temel, Musa Cakir

Applications and Applied Mathematics: An International Journal (AAM)

We investigate an efficient numerical method for the linear first-order Volterra integro-differential equations with integral boundary condition. To solve this problem, boundaries are determined for its derivative and the solution. The numerical solutions of the problem are modeled over a uniform mesh using the composite right-side rectangle concept for the integral component and the implicit difference rules for the differential component. Next, the stability and convergence of the numerical approach are discussed. The numerical experiments are presented confirming the accuracy of the proposed scheme.

Question-Attentive Review-Level Explanation For Neural Rating Regression, Trung Hoang Le, Hady Wirawan Lauw

Research Collection School Of Computing and Information Systems

Recommendation explanations help to improve their acceptance by end users. Explanations come in many different forms. One that is of interest here is presenting an existing review of the recommended item as the explanation. The challenge is in selecting a suitable review, which is customarily addressed by assessing the relative importance or “attention” of each review to the recommendation objective. Our focus is improving review-level explanation by leveraging additional information in the form of questions and answers (QA). The proposed framework employs QA in an attention mechanism that aligns reviews to various QAs of an item and assesses their contribution …

Modelling Saccharomyces Cerevisiae For The Production Of Fermented Beverages, Paul A. Valle Dr., Yolocuauhtli Salazar Dr., Luis N. Coria Dr., Oscar N. Soto Dr., Jesus B. Paez Dr.

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Bayesian Networks And Machine Learning For Predicting Breast Cancer Growth From In Vitro Cell Count Data, Widodo Samyono

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Seshaiyer: Understanding Non-Linear Dynamics Of Interacting Subpopulations And Implicit Human Behavior Using Physics-Informed Neural Networks, Naima Aubry-Romero, Alonso Ogueda-Oliva, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

An Introduction To The Time-Independent Schrödinger Equation And Methods To Solve It, Vu Giang, Alex Gnech

OUR Journal: ODU Undergraduate Research Journal

The Time-Independent Schrödinger Equation is a linear elliptic PDE that describes quantum-mechanical systems. Its significance in the science of submicroscopic phenomena, particularly quantum mechanics, is as central as Newton’s laws of motion are to classical mechanics. This study uses various methods, including novel neural networks and finite difference schemes, to solve the one-dimensional two-body equation.

(Si13-02) Approximate Solution Of Fuzzy Volterra Integro-Differential Equations Using Numerical Techniques, Asiya Ansari, Najmuddin Ahmad

Applications and Applied Mathematics: An International Journal (AAM)

To determine the approximate solution to fuzzy Volterra integro-differential equations, the Adomian Decomposition Method (ADM), Modified Adomian Decomposition Method (MADM), Variational Iteration Method (VIM), and Homotopy Perturbation Method (HPM) are proposed in this study. We present two examples to support the methodology, and the results are presented in tables to demonstrate the method’s efficiency and correctness. Wolfram Mathematica 11.3 is used to perform the computations.