Applied Mathematics Commons^™

Macro–Micro-Coupled Simulations Of Bead–Spring Breaking-Reforming Networks, Andrei Medved

Theses and Dissertations

In this work we investigate the dynamic behavior of bead-spring polymer solutions in viscoelastic fluids, which are essential in industries like materials science, biotechnology, and pharmaceuticals. The study leverages GPU-accelerated simulations and detailed modeling of polymer chain dynamics at the mesoscale, which enables efficient analysis of intricate fluid behaviors and the microscale dynamics of polymer chains. Additionally, the research examines the breaking-reforming dynamics of polymer chains, crucial for understanding phenomena such as shear thinning and thickening. The findings have broad applications, from improving inkjet printing and 3D printing technologies to developing new drug delivery systems and biocompatible materials. This work …

Analysis Of The Effect Of Vaccination, Efficient Surveillance And Treatment On The Transmission Dynamics Of Cholera, Loyinmi Adedapo Chris, Ajala Adebisi Shukurat, Alani L. Ijaola

Al-Bahir

In this study, we presented a modified SIR-SI model to investigate the dynamics and potential controls for cholera transmission, with an incident rate equipped with a saturation factor to investigate the combined impact of three vital measures which include effective surveillance, vaccination campaign and proper treatment in case severity. We established among other things, the qualitative analysis of the model to validate the results. Furthermore, the reproduction number (R0) was found to be less than unity (1), through the stability analysis. Additionally, finite different scheme was utilized in solving the differential equations of the model. MATLAB software was used for …

Mathematical Modeling, Analysis, And Simulation Of Patient Addiction Journey, Adan Baca, Diego Gonzalez, Alonso G. Ogueda, Holly C. Matto, Padmanabhan Seshaiyer

CODEE Journal

This paper aims to develop a mathematical model to study the dynamics of addiction as individuals go through their detox journey. The motivation for this work is three fold. First, there has been a significant increase in drug overdose and drug addiction following the COVID-19 pandemic, and addiction may be interpreted as a infectious disease. Secondly, the dynamics of infectious disease could be modeled via compartmental models described by differential equations and one can therefore leverage the existing analytical and numerical methods to model addiction as a disease. Finally, the work helps to inform how mathematical models governed by differential …

The Bioremediation Effect Of Microalgae On Wastewater: A Green Technology Approach, Mohamed Ahmed Reda Hamed Dr, Marwa Abdelfattah Abdallah Dr

Journal of Engineering Research

The present study lays an emphasis on the microalgae-based for simultaneous wastewater bioremediation using Chlorella vulgaris and Micrococcus luteus mixed algal cultures to remove its constituent pollutants, amazing green technology guarantees benefits with the decrease in the formation of dangerous solid sludge. Ten days of fully monitoring laboratory experimental program were performed in batch cultures to investigate the effect of various dominant mixing ratios for attaining wastewater concentrations and different governing temperature ranges on the performance of microalgae treatment. The results revealed that there is a significant impact of both wastewater concentrations and temperature treatment conditions on the capability of …

Unlocking The Potential Of Rooftop Sustainable Systems: Understanding Barriers And Facilitators, Mahmoud Desouki, Taghreed A. El-Haddad

Journal of Engineering Research

Urbanization is reducing green spaces in old cities globally, including Egypt, adversely impacting air quality, climate, and psychological well-being. The rooftop has the potential to offer viable alternatives that provide multiple benefits. They can host sustainable systems, and foster social activities. Despite these advantages, their adoption in cities like Tanta the Egyptian city, one of the world's most densely populated cities with a shrinking per capita green space, remains limited. Most rooftops are often serving as dumping grounds for trash and unused items. This study aims to explore the reasons behind this underutilization to find ways to encourage the use …

Indicators And Evidence Of Environmental Sustainability For Pedestrian In Public Parks (Towards An Approach For Formulating A Guideline Evaluation Model), Nashwa Youssif

Journal of Engineering Research

يتناول البحث أحد المجالات التي فرضت تواجدها في الأونة الأخيرة علي الساحة العلمية والبحثية التي تتعلق بالعلاقة التبادلية التأثير بين الإنسان والفراغ العمراني حيث يتنامي الإهتمام بالخصائص الإنسانيه و مدي توافقها مع هذا الفراغ العمراني.

وتعد مسارات المشاة من أهم الحيزات العمرانية التى تشكل النسيج العمراني وأحد أهم وسائل التواصل الإجتماعي والثقافي والوظيفي نظرآ لإرتباطها بالغالبية العظمي من أفراد المجتمع، ومساعدتها على جذب العديـد من الأنشطة داخل الحدائق العامة. مما يشير إلي ضرورة الإهتمام بتحسين بيئة حركة المشاه كمدخل للتواصل والإستدامة.

ومن هنا تتمثل مشكلة البحث في نقص الدراسات حول تقييم العلاقة بين معايير الاستدامة التصميمية والنظم البيئية لمسارات المشاة …

The Feasibility Of Utilizing The Open Dynamic Interaction Network (Odin) App To Assess Rema Data Across 30 Days Among Those Recovering From Alcoholism, Dennis E. Mcchargue, Bilal Khan, Jesscia Phelps, Patrick Duryea, Kimberly A. Tyler, Arthur Andrews, Ellie Reznicek, Lucy Napper, Mohamed Saad, Hsuan-Wee Lee

Department of Psychology: Faculty Publications

About ~4 million people with an alcohol use disorder receive treatment annually, and frequent relapse has produced a rapid revolving door between recovery and use. This paper presents preliminary data from a prospective micro-longitudinal study (30 days) that examines co-evolution of relapse risk processes of people with alcohol use disorders who entered a short-term residential substance use treatment. The primary goal of the current data was to assess the feasibility of using the open dynamic interaction network (ODIN) responsive ecological momentary assessment (rEMA). rEMA collected daily estimates on affect, urges, sober-support engagement, and use. The ODIN app administered twelve questions …

Hypogene Speleogenesis In Carbonates By Cooling Hydrothermal Flow: The Case Of Mt. Berenike Caves, Israel, Roi Roded, Boaz Langford, Einat Aharonov, Piotr Szymczak, Micka Ullman, Shemesh Yaaran, Boaz Lazar, Amos Frumkin

International Journal of Speleology

The Berenike hypogenic cave system near Lake Kinneret, Israel, provides a valuable case study for investigating the recently proposed Confined-Cooling-Flow (CCF) speleogenesis model. Field and speleological surveys, along with existing research, are used to provide a thorough analysis. The CCF model relies on a simple thermo-hydro-chemical scenario, involving the rise of CO2-rich hydrothermal fluids discharging into a confined layer. The cooling of these CO2-rich fluids turns them into aggressive solutions due to the inverse relation between temperature and solubility of carbonates (retrograde solubility). Previous geochemical and numerical analyses of the CCF model predict localized and persistent dissolution and speleogenesis on …

Delta-Shaped Approximation Based Homotopy Analysis Method For Nonlinear Poisson-Type Partial Differential Equations, Cyril Ocloo

Dissertations

This research aims to solve nonlinear Poisson-type partial differential equations (PDEs) by the approach of the homotopy analysis method (HAM) incorporated with approximate particular solutions (APS) using Delta-shaped basis (DSB) approximations.

With the inclusion of the h auxiliary parameters, we tackle nonlinear problems by studying the mathematical characteristics of the h curve. This is to ensure the numerical convergence of the HAM.

In the solution process, we use the homotopy analysis method to convert a nonlinear PDE into linear inhomogeneous PDEs, which are solved using the method of approximate particular solutions with DSB.

A proper value of the h is …

On Weak Solutions And The Navier-Stokes Equations, Aryan Prabhudesai

Mathematical Sciences Undergraduate Honors Theses

In this paper, I will discuss a partial differential equation that has solutions that are discontinuous. This example motivates the need for distribution theory, which will provide an interpretation of what it means for a discontinuous function to be a “solution” to a PDE. Then I will give a detailed foundation of distributions, including the definition of the derivative of a distribution. Then I will introduce and give background on the Navier-Stokes equations. Following that, I will explain the Millennium Problem concerning global regularity for the Navier-Stokes equations and share mathematical results regarding weak solutions. Finally, I will go over …

Localized Hermite Method Of Approximate Particular Solutions, Kwesi Acheampong

Dissertations

A localized Hermite method of approximate particular solutions (LHMAPS) is presented in this dissertation. This method is designed to improve the accuracy of the localized method of approximate particular solutions (LMAPS) for solving partial differential equations. LMAPS is a strong-form method that defines local radial basis function approximations to the solution values at a group of collocation points before applying the differential operator to this approximation function. Based on the LMAPS's local scheme, LHMAPS seeks Hermite-type local approximations based on both function values and derivatives. Numerical experiments validate the superior accuracy of the proposed method to the LMAPS by solving …

Computation Of Moving Interface Flows In Biophysical Applications, Mohammad Murshed

Masters Theses and Doctoral Dissertations

This dissertation is concerned with the modeling, simulation, and analysis of moving interface problems involving viscous fluids and solid structures. The main computational technique employed in this work is the immersed boundary method, a widely known numerical method for fluid-structure interaction (FSI). In this technique, the fluid equations are solved in an Eulerian grid and the structure is treated as a network of Lagrangian nodes. The communication between the fluid and structure dynamics is established by the use of the Dirac delta function. Utilizing the immersed boundary method, we have studied three biophysical applications. In the first application, we computed …

Efficient First-Order Methods For Some Smooth Nonlinear Optimization Problems, Yunheng Jiang

All Dissertations

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First-Order Algorithms For Convex Smooth Optimization Problems With Homogeneous Linear Constraints, Yidan Guo

All Dissertations

The purpose of this dissertation is to explore the first-order methods that can be used to solve an approximate solution for convex smooth problems with homogeneous linear constraints. It consists of three interconnected research projects.

In the first project, we study the problem of computing the projection of a given vector onto the kernel of a symmetric positive semi-definite matrix. The complexity of an algorithm for computing a numerical solution is evaluated by the total number of matrix-vector multiplications required for computing an approximate solution. Such problems arise commonly in consensus optimization, in which the total number of matrix-vector multiplications …

Scalable Solution Of Time-Dependent Pdes Through Component-Wise Exponential Integrator, Chelsea Drum

Dissertations

Exponential integrators, such as exponential Runge-Kutta or Rosenbrock methods, are designed specifically for the time integration of stiff systems of ordinary differential equations (ODEs) and allow the use of larger time steps than other general-purpose ODE solvers. However, these methods rely on computing matrix function-vector products that are traditionally computed using a Krylov projection, such as Lanczos or Arnoldi iteration, that involves substantial computational expense at high spatial resolution. Krylov Subspace Spectral (KSS) methods' frequency-dependent approach, designed to circumvent stiffness in linear problems, computes these products with greater scalability. We propose the combination of such KSS methods with exponential integrators …

Optimization Strategies For Political Redistricting, Blake Splitter

All Dissertations

Political redistricting has remained a hot-button issue in the United States for several decades. Every ten years, most states need to redraw their districts to account for changing populations. Sometimes, these district plans can be drawn with the malevolent intention of aiding one political party over another. This dissertation summarizes four distinct methods of drawing these districts using computer algorithms while keeping several objectives in mind. We test these approaches on the case study state of South Carolina, since it provides a sufficiently challenging problem for us to test various algorithms. We find that many of these approaches improve upon …

Multi-Scale Ocean Modeling Using The Discontinuous Galerkin Method, Yao Gahounzo

Boise State University Theses and Dissertations

Ocean models often employ the hydrostatic assumption for large-scale applications when the horizontal scale is larger than the depth. Nonetheless, the non-hydrostatic effects are of great importance in submesoscale studies, such as modeling the physical processes of ice-ocean interactions. Most non-hydrostatic ocean models used in ice-ocean interaction studies are low-order finite-difference and finite-volume methods, often with significant dispersive errors. Therefore, there is a need for a high-order ocean model for ice-ocean interaction applications.

The first part of this thesis focuses on deriving the boundary conditions at the ice-ocean interface and incorporating them into the high-order discontinuous Galerkin (DG) method-based ocean …

Effects Of A Protection Zone In A Reaction-Diffusion Model With Shifting Bounded Habitat And Allee Effect., Davis Henderson

Electronic Theses and Dissertations

We consider a reaction-diffusion equation that models a population in a shifting bounded habitat with a protection zone and the Allee effect. We assume that the population growth function exhibits the strong Allee effect and has a positive integral within the protection zone (indicating population persistence) and a negative integral in the surrounding patches (indicating population decay). We prove that the existence of steady-state solutions to this system depends on the length of the protection zone. It is demonstrated that there exists some value H* such that, for a protection zone of size H*, there exists a solution and, for …

Frameworks For The Techno-Economic Assessment Of Membrane-Based Bioprocessing Platforms, Juan Jose Romero Conde

All Dissertations

This dissertation describes developing and implementing computational frameworks for simulating and optimizing purification processes in the biopharmaceutical industry. The framework performs techno-economic analyses to establish value propositions for new process alternatives, especially membrane technologies. Initially, the focus is developing a framework capable of simulating monoclonal antibody (mAb) capture using membrane and resin media in multi-column chromatography (MCC) platforms for continuous manufacturing. Subsequently, the impact of capture MCC is compared against other intensification strategies in established mAb manufacturing facilities. Finally, the framework application expands to simulate the purification of adeno-associated virus (AAV) vectors for gene therapy.

Chapter 2 details the framework …

Visualization Of Species Tree Likelihood Under The Multispecies Coalescent Model, Jaimasan Sutton

Mathematics & Statistics ETDs

A commonly used tool for evolutionary biologists is a phylogenetic tree that represents the ancestry of a set of species and the evolution of traits. Statistical models can be used to predict the probabilities of gene trees which represent ancestral relationships of genes sampled from species. Because of this, we are able to represent the likelihood of a species tree, which represents the evolutionary history of a set of species, as a function of the counts of gene tree topologies, where each gene tree represents the ancestry of a specific genetic locus for multiple species. Because we can represent these …