Numerical Analysis and Computation Commons^™

Advances In Computational And Statistical Inverse Problems, Dylan Green

Dartmouth College Ph.D Dissertations

Inverse problems are prevalent in many fields of science and engineering, such as signal processing and medical imaging. In such problems, indirect data are used to recover information regarding some unknown parameters of interest. When these problems fail to be well-posed, the original problems must be modified to include additional constraints or optimization terms, giving rise to so-called regularization techniques. Classical methods for solving inverse problems are often deterministic and focus on finding point estimates for the unknowns. Some newer methods approach the solving of inverse problems by instead casting them in a statistical framework, allowing for novel point estimate …

Identifiability For Pde Models Of Fluorescence Microscopy Experiments, Veronica Ciocanel

Biology and Medicine Through Mathematics Conference

No abstract provided.

Multiscale Modeling Of Microtubule Polarity Mechanisms Following Neuronal Axotomy, Hannah Scanlon

Biology and Medicine Through Mathematics Conference

No abstract provided.

Conjugations Of Unitary Operators, I, Javad Mashreghi, Mraek Ptak, William T. Ross

Department of Math & Statistics Faculty Publications

If U is a unitary operator on a separable complex Hilbert space H, an application of the spectral theorem says there is a conjugation C on H (an antilinear, involutive isometry on H) for which CUC= U*. In this paper, we fix a unitary operator U and describe all of the conjugations C which satisfy this property. As a consequence of our results, we show that a subspace is hyperinvariant for U if and only if it is invariant for any conjugation C for which CUC = U*.

Effect Of Recommending Users And Opinions On The Network Connectivity And Idea Generation Process, Sriniwas Pandey, Hiroki Sayama

Northeast Journal of Complex Systems (NEJCS)

The growing reliance on online services underscores the crucial role of recommendation systems, especially on social media platforms seeking increased user engagement. This study investigates how recommendation systems influence the impact of personal behavioral traits on social network dynamics. It explores the interplay between homophily, users’ openness to novel ideas, and recommendation-driven exposure to new opinions. Additionally, the research examines the impact of recommendation systems on the diversity of newly generated ideas, shedding light on the challenges and opportunities in designing effective systems that balance the exploration of new ideas with the risk of reinforcing biases or filtering valuable, unconventional …

Analytical And Numerical Analysis Of The Sirs Model, Catherine Nguyen

Departmental Honors & Graduate Capstone Projects

Mathematical models in epidemiology describe how diseases affect and spread within a population. By understanding the trends of a disease, more effective public health policies can be made. In this paper, the Susceptible-Infected-Recovered-Susceptible (SIRS) Model was examined analytically and numerically to compare with the data for Coronavirus Disease 2019 (COVID-19). Since the SIRS model is a complex model, analytical techniques were used to solve simplified versions of the SIRS model in order to understand general trends that occur. Then by Euler's Method, the Runge-Kutta Method, and the Predictor-Corrector Method, computational approximations were obtained to solve and plot the SIRS model. …

Proof-Of-Concept For Converging Beam Small Animal Irradiator, Benjamin Insley

Dissertations and Theses (Open Access)

The Monte Carlo particle simulator TOPAS, the multiphysics solver COMSOL., and

several analytical radiation transport methods were employed to perform an in-depth proof-ofconcept

for a high dose rate, high precision converging beam small animal irradiation platform.

In the first aim of this work, a novel carbon nanotube-based compact X-ray tube optimized for

high output and high directionality was designed and characterized. In the second aim, an

optimization algorithm was developed to customize a collimator geometry for this unique Xray

source to simultaneously maximize the irradiator’s intensity and precision. Then, a full

converging beam irradiator apparatus was fit with a multitude …

Convergence Estimate Of Minimal Residual Methods And Random Sketching Of Krylov Subspace Methods, Peter Westerbaan

All Dissertations

This study concerns two main issues in numerical linear algebra: convergence estimate of minimal residual methods based on explicit construction of approximate min-max polynomials for in- definite matrices, and development and analysis of Krylov subspace methods using non-orthonormal basis vectors based on random sketching. For a matrix A with spectrum Λ(A), it is well known that the min-max polynomial problem min max |pk (z)| pk ∈Pk, pk (0)=1, z∈Λ(A) is used to bound the relative error of Krylov subspace minimum residual methods or similar methods. For a symmetric positive definite matrix A, the min-max polynomial for the Conjugate Gradient (CG) …

Domain Decomposition Methods For Fluid-Structure Interaction Problems Involving Elastic, Porous, Or Poroelastic Structures, Hemanta Kunwar

All Dissertations

We introduce two global-in-time domain decomposition methods, namely the Steklov-Poincare method and Schwarz waveform relaxation (SWR) method using Robin transmission conditions (or the Robin method), for solving fluid-structure interaction systems involving elastic, porous, or poroelastic structure. These methods allow us to formulate the coupled system as a space-time interface problem and apply iterative algorithms directly to the evolutionary problem. Each time-dependent fluid and the structure subdomain problem is solved independently, which enables the use of different time discretization schemes and time step sizes in the subsystems. This leads to an efficient way of simulating time-dependent multiphysics phenomena. For the fluid-porous …

Representation Learning For Generative Models With Applications To Healthcare, Astronautics, And Aviation, Van Minh Nguyen

Theses and Dissertations

This dissertation explores applications of representation learning and generative models to challenges in healthcare, astronautics, and aviation.

The first part investigates the use of Generative Adversarial Networks (GANs) to synthesize realistic electronic health record (EHR) data. An initial attempt at training a GAN on the MIMIC-IV dataset encountered stability and convergence issues, motivating a deeper study of 1-Lipschitz regularization techniques for Auxiliary Classifier GANs (AC-GANs). An extensive ablation study on the CIFAR-10 dataset found that Spectral Normalization is key for AC-GAN stability and performance, while Weight Clipping fails to converge without Spectral Normalization. Analysis of the training dynamics provided further …

Analysis And Construction Of Artificial Neural Networks For The Heat Equations, And Their Associated Parameters, Depths, And Accuracies., Shakil Ahmed Rafi

Graduate Theses and Dissertations

This dissertation seeks to explore a certain calculus for artificial neural networks. Specifically we will be looking at versions of the heat equation, and exploring strategies on how to approximate them.

Our strategy towards the beginning will be to take a technique called Multi-Level Picard (MLP), and present a simplified version of it showing that it converges to a solution of the equation (^∂/_∂t u_d ) (t, x) = (∇² _x u_d)(t, x).

We will then take a small detour exploring the viscosity super-solution properties of solutions to such …

Thermogravimetric Analysis And Chemical Kinetics Of Waste Tires, Mahir Mohammed Said

Tanzania Journal of Engineering and Technology (TJET)

The focus of this paper is to analyse the pyrolysis reaction of waste tires. The pyrolysis was studied experimentally using thermal and chemical kinetics. The tires were pyrolyzed using thermogravimetry at a temperature range of 200 to 600°C, with heating rates of 10, 20, and 50°C/min. The activating energy was observed to increase with increased temperature. The highest activating energy was 101.02 kJ/mol at a heating rate of 50°C/min.

Causes And Consequences Of Inefficient Drilling And Blasting In Mine Development Headings: A Case Study Of Hard Rock Gold Mining Operations In Northern Tanzania, George Bennett

Tanzania Journal of Engineering and Technology (TJET)

Despite the introduction of the perimeter blasting technique at the Tulawaka Gold Mine, the mine continued to suffer from an overbreak of mine development headings, with an average overbreak of 24% every 22 m, which is approximately twice the acceptable 10% overbreak. The causes of this problem include ineffective drilling practices and uneven and excessive charging of explosives, resulting in a slightly high powder factor of 3.94 kg/m3 instead of 3.8 kg/m3, as per the design. The problem of overbreak resulted in ore dilution, a longer mine development cycle time and additional costs of approximately US$ 45 per cut, especially …

Design And Optimization Of An Azeotropic Distillation Pilot Plant For The Production Of Pure Ethanol, Samwel V. Manyele

Tanzania Journal of Engineering and Technology (TJET)

This study aimed to design an azeotropic distillation plant using Aspen Plus® V10 software and determine optimal process conditions for producing pure ethanol greater than 95% from pre-concentrated near-azeotropic ethanol-water solution. The non-random two-liquid Redlich-Kwong thermodynamic model was the base method for property analysis and performance prediction. Modelling and simulation of the converged process were conducted for fixed column variables (R = 5, N = 12 and p = 1 atm). Plant operating parameters were varied in the range of 0 to 1 for the pre-heater vapour fraction, 2 to 10 for the column feed plates (NFP), 2 to 6 …

Optimization Pump As Turbine Coupled To A Self-Excited Induction Generator Using Multi-Objective Genetic Algorithm, Emanuel J. Nyirenda

Tanzania Journal of Engineering and Technology (TJET)

As a way of accelerating the deployment of affordable and clean renewable energy generation technologies, applying a pump working as a turbine coupled to a self-excited induction generator is gaining popularity in various areas including energy recovery and micro hydro systems. However, it is currently challenging to predict the performance of the PAT-SEIG system and there is no agreed-upon rule on the selection of the appropriate system to be installed at a particular site. This paper has presented multi-objective optimization to select the best operating point of the PAT-SEIG system. The results show that the peak efficiencies for the PAT …

Evaluation Of Cybersecurity In Remote Working Settings For Mobile Network Operators, Victoria Mahabi

Tanzania Journal of Engineering and Technology (TJET)

Cybersecurity has increasingly been a primary concern to people as technology advances and allows them to work remotely. This study thus evaluated the cybersecurity posture for organisations that have opted for remote working culture, whereas emerging cyber threats, practices to combat them, and appropriate guidelines for managing cyber threats were discussed. The study used a descriptive design with a quantitative approach from 118 information technology personnel working for Tanzania's three major mobile network operators (MNOs). SPSS analysed the collected data. The study revealed that predominant cyber-threats affecting MNOs in remote working include human errors, phishing attacks, malicious domains, denial of …

Sol-Gel Synthesis And Microstructure Characterization Of Nio-Tio2 Semiconductor, Godlisten N. Shao

Tanzania Journal of Engineering and Technology (TJET)

NiO-TiO2 is a fascinating p-n semiconducting binary metal oxide with unique electronic and optical properties. The NiO-TiO2 has been synthesized using complicated preparation methods and expensive precursors that hamper their large-scale production. The present study reports the preparation of NiO-TiO2 semiconductor with improved physicochemical properties. NiO-TiO2 samples were prepared through one-pot sol-gel synthesis process followed by sintering of the as-synthesized materials at temperatures ranging from 600 to 1000 °C. The role of thermal treatment and NiO content on the microstructures was exquisitely studied. The microstructure of the NiO-TiO2 samples was examined by Raman spectroscopy, XRD, XRF, SEM-EDAX, high resolution TEM, …

General Hydrogeochemical Characterization Of Groundwater In Coastal Aquifers Of Kilwa Kisiwani Oceanic Island, South East Tanzania, Simon R Melchioly

Tanzania Journal of Engineering and Technology (TJET)

The main objective of this study was to determine the hydrogeochemical processes controlling the groundwater chemistry on the Island and assess its suitability for human consumption and irrigation. The methodology used in the study include hydrogeological assessment of the study area and laboratory analysis for general physico-chemical parameters of groundwater. Other parameters such as Soluble sodium percentage (SSP) or % Na+, Sodium Adsorption Ratio (SAR), Magnesium adsorption ratio (MAR), Residual sodium carbonate (RSC), hydrochemical facies classification, and Water Quality Index (WQI) were calculated using empirical formulae. The effects of salinization of groundwater were classified using the chloride-Bicarbonate (Cl/HCO3) and the …

Optimal Load Shedding During Service Restoration In Electrical Secondary Distribution Network Based On Reinforcement Learning, Rukia J. Mwifunyi

Tanzania Journal of Engineering and Technology (TJET)

Increased stress in traditional power systems results in blackouts due to voltage instability attributed to a mismatch between available capacity and load demand, especially in distribution networks. Service restoration schemes are designed to return power supply to the affected parts of the networks. The availability of insufficient supply is a complex problem that requires operational experience or an automatic system. The stochastic nature of load demand significantly impacts service restoration as it results in increased restored demand in case a fault occurs during off-peak hours and helps reduce overload if the fault occurs during peak hours. The study adopts an …

Study Of The Effects Of Thermal Aging Coupled With Shot-Peening Treatment Of Carbonitrided Din 1.6587 Low Alloy Steel On Retained Austenite And Residual Stresses, Richard J. Katemi

Tanzania Journal of Engineering and Technology (TJET)

This work investigated the effects of thermal aging and shot-peening of carbonitrided 1.6587 steel grade on retained austenite and residual stresses. After carbonitriding samples contained maximum of 0.87% carbon, 0.34% nitrogen and 50 mass. -% retained austenite. Thermal aging conditions investigated were -30°C, 90°C and 150°C while the aging period were 14, 96 and 720 hours. After thermal aging, some of the samples were subjected to shot-peening treatment using standard cut wire shots StD – G3 - 0.6 mm VDFI 8001 with intensity in the range of 0.25 to 0.30 mmA and coverage of 1.00 to 1.24 x 98%. It …