Partial Differential Equations Commons^™

A Multiscale Computational Framework Coupling Pulmonary Arterial Blood Flow And Lung Tissue Perfusion, Nigar Sultana, Hangjie Ji, Mette Sofie Olufsen

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Modified Sir Model Used To Investigate The Relationship Between Congenital And Adult Syphilis, Kaleesta R. Waysman

Honors Thesis

A complex SIR model integrating the relationship between adult and congenital syphilis was developed. The goal of the project was to determine the specific population(s) or control strategies that should be enforced, altered, or removed to decrease the number of children experiencing clinical sequelae due to congenital syphilis. Early clinical sequelae include hydrops fetalis, preterm birth, central nervous system infection, hepatosplenomegaly, hyperbilirubinemia, cholestasis, hemolytic anemia, snuffles, osteochondritis, and lesions or rashes in the palms and soles. Late clinical sequelae include interstitial keratitis, hearing loss, Hutchinson teeth, saber shins, Clutton joints, mulberry molars, and saddle nose. After implementing real-world data into …

A Model Of Oocyte Population Dynamics For Fish Oogenesis, Louis Fostier, Frédérique Clément, Romain Yvinec, Violette Thermes

Biology and Medicine Through Mathematics Conference

No abstract provided.

Reaction-Diffusions System Simulated On Irregular Shapes And Surfaces Model Petal Spot Patterns In Monkeyflower Hybrids, Emily Simmons, Arielle M. Cooley, Joshua R. Puzey, Gregory D. Conradi Smith

Biology and Medicine Through Mathematics Conference

No abstract provided.

Exploring The Evolution Of Altruistic Punishment Using A Pde Model For Multilevel Selection, Daniel Cooney

Biology and Medicine Through Mathematics Conference

No abstract provided.

Chemoattractant Distribution In The Drosophila Egg Chamber, Lara Scott

Biology and Medicine Through Mathematics Conference

No abstract provided.

Sperm-Egg Interaction For Fertilization Success, Prajakta P. Bedekar

Biology and Medicine Through Mathematics Conference

No abstract provided.

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 …

Predicting Biomolecular Properties And Interactions Using Numerical, Statistical And Machine Learning Methods, Elyssa Sliheet

Mathematics Theses and Dissertations

We investigate machine learning and electrostatic methods to predict biophysical properties of proteins, such as solvation energy and protein ligand binding affinity, for the purpose of drug discovery/development. We focus on the Poisson-Boltzmann model and various high performance computing considerations such as parallelization schemes.

A Class Of Game-Theoretic And Fokker-Planck Optimal Control Frameworks In Colon And Esophageal Cancer, Mesfer Alajmi Phd

Mathematics Dissertations - Archive

In this dissertation, we first present a new stochastic framework for parameter estimation and uncertainty quantification in colon cancer-induced immune responses. A stochastic process that captures the system's inherent randomness determines the dynamics of colon cancer. The stochastic framework is based on the Fokker-Planck equation, which represents the evolution of the probability density function corresponding to the stochastic process. We formulate an optimization problem that takes individual patient data with randomness present and solves it to obtain the unknown parameters corresponding to the individual tumor characteristics. Furthermore, we perform a sensitivity analysis of the optimal parameter set to identify the …

Pde Model For Protocell Evolution And The Origin Of Chromosomes Via Multilevel Selection, Daniel B. Cooney, Fernando W. Rossine, Dylan H. Morris, Simon A. Levin

Biology and Medicine Through Mathematics Conference

No abstract provided.

Helices In Fluids And Their Applications, Eva M. Strawbridge

Biology and Medicine Through Mathematics Conference

No abstract provided.

De-Coupling Cell-Autonomous And Non-Cell-Autonomous Fitness Effects Allows Solution Of The Fokker-Planck Equation For The Evolution Of Interacting Populations, Steph J. Owen

Biology and Medicine Through Mathematics Conference

No abstract provided.

Mathematical Modeling Of Brain Cancer Growth Using A Level-Set Method, Gbocho M. Terasaki

Biology and Medicine Through Mathematics Conference

No abstract provided.

Spatial Patterning Of Predator-Prey Distributions Arising From Prey Defense, Evan C. Haskell, Jonathan Bell

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Meshless Approach To Computational Pharmacokinetics, Anthony Matthew Khoury

Doctoral Dissertations and Master's Theses

The meshless method is an incredibly powerful technique for solving a variety of problems with unparalleled accuracy and efficiency. The pharmacokinetic problem of transdermal drug delivery (TDDD) is one such topic and is of significant complexity. The locally collocated meshless method (LCMM) is developed in solution to this topic. First, the meshless method is formulated to model this transport phenomenon and is then validated against an analytical solution of a pharmacokinetic problem set, to demonstrate this accuracy and efficiency. The analytical solution provides a locus by which convergence behavior are evaluated, demonstrating the super convergence of the locally collocated meshless …

Assess The Impacts Of Human Mobility Change On Covid-19 Using Differential Equations With Google Community Mobility Data, Nao Yamamoto

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Deep Learning With Physics Informed Neural Networks For The Airborne Spread Of Covid-19 In Enclosed Spaces, Udbhav Muthakana, Padmanabhan Seshaiyer, Maziar Raissi, Long Nguyen

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Attraction-Repulsion Taxis Mechanisms In A Predator-Prey Model, Evan C. Haskell

Biology and Medicine Through Mathematics Conference

No abstract provided.

Mathematical Modeling Of Gliding Motility And Its Regulation In Myxococcus Xanthus, Yirui Chen

Biology and Medicine Through Mathematics Conference

No abstract provided.

Parameter Estimation For Tear Film Thinning, Rayanne Luke

Biology and Medicine Through Mathematics Conference

No abstract provided.

483— Effectiveness Of Mmr Vaccination In Orthodox Jewish Neighborhoods, Meenu Mundackal

GREAT Day Posters

Measles is a highly contagious disease, where large outbreaks arise by direct contact between susceptible (unvaccinated) and infectious individuals. Many Orthodox Jewish neighborhoods were affected by measles from 2018-2019. To quantify the vaccination effort on this susceptible population, a retrospective analysis was used to study the NYC and Rockland County populations using a differential equations model. A subsequent model, known as a realistically-structured network model, studied only the NYC population, in relation to typical household size. Vaccination strategies were applied to three cohorts: unvaccinated family members, members with 1 prior MMR dose, and members with 2 prior MMR doses. The …

Image Restoration Using Automatic Damaged Regions Detection And Machine Learning-Based Inpainting Technique, Chloe Martin-King

Computational and Data Sciences (PhD) Dissertations

In this dissertation we propose two novel image restoration schemes. The first pertains to automatic detection of damaged regions in old photographs and digital images of cracked paintings. In cases when inpainting mask generation cannot be completely automatic, our detection algorithm facilitates precise mask creation, particularly useful for images containing damage that is tedious to annotate or difficult to geometrically define. The main contribution of this dissertation is the development and utilization of a new inpainting technique, region hiding, to repair a single image by training a convolutional neural network on various transformations of that image. Region hiding is also …

Multidisciplinary Education And Research In Biomathematics For Solving Global Challenges, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Transport Phenomena In Field Effect Transistors, Ryan M. Evans, Arvind Balijepalli, Anthony Kearsley

Biology and Medicine Through Mathematics Conference

No abstract provided.

Spatial Spread Of Defective Interfering Particles And Its Role In Suppressing Viral Load, Qasim Ali Qa, Ruian Ke

Biology and Medicine Through Mathematics Conference

No abstract provided.

Numerically Solving A System Of Pdes Modeling Chronic Wounds Treated With Oxygen Therapy, Stefan Stryker

Mahurin Honors College Capstone Experience/Thesis Projects

Chronic wounds such as diabetic foot ulcers are the leading cause of non-traumatic amputations in developed countries. For researchers to better understand the physiology of these wounds, a mathematical model describing oxygen levels at the wound site can be used to help predict healing responses. The model utilizes equations that are modified from work by Guffey (2015) that consists of four variables – oxygen, bacteria, neutrophils, and chemoattractant within a system of partial differential equations. Our research focuses on numerically solving these partial differential equations using a finite volume approach. This numerical solver will be important for future research in …

High Performance Computation Of Cardiac Models In Real-Time Using Webgl, Abouzar Kaboudian, Flavio H. Fenton

Biology and Medicine Through Mathematics Conference

No abstract provided.

An Interdisciplinary Approach To Computational Neurostimulation, Madison Guitard

Biology and Medicine Through Mathematics Conference

No abstract provided.

Shear Driven Micro-Fluidic Pump For Cardiovascular Applications, Nihad E. Daidzic

Aviation Department Publications

A valveless shear-driven micro-fluidic pump design (SDMFP) for hemodynamic applications is presented in this work. One of the possible medical and biomedical applications is in-vivo hemodynamic (human blood circulation) support/assist. One or more SDMFPs can be inserted/implanted into vascular lumens in a form of a stent/duct in series and/or in parallel (bypass duct) to support blood circulation in-vivo. A comprehensive review of various micro-pump designs up to about mid 2000’s is given in [1,2]. Many of micropump designs considered are not suitable for in-vivo or even in-vitro medical/biomedical applications.

Operating principles, design, and SDMFP features are given in [3]. A …