Applied Mathematics Commons^™

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 …

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 …

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 …

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 …

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 …

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 …

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

All Dissertations

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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 …

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 …

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 …

The Role Of Sensing Modalities In Shaping Collective Motion And Group Behavior, Poorendra P. Ramlall

Doctoral Dissertations and Master's Theses

Collective behavior refers to the coordinated movements that emerge from simple interactions between individuals within a group. Traditionally, researchers have modeled these interactions assuming individuals can sense their surroundings in all directions, like having eyes all around their heads. While this is a useful simplification, it does not capture the diverse ways animals actually sense the world. In this thesis, we take inspiration from the natural world, particularly from animals like bats and dolphins that use a combination of hearing and sight to navigate their environments. We explore how combining these sensory cues in a three-dimensional space affects the way …

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 …

Radially Symmetric Positive Solutions Of The Dirichlet Problem For The P-Laplace Equation, Bo Yang

Faculty Articles

We consider the p-Laplace boundary value problem with the Dirichlet boundary condition. A new lower estimate for positive solutions of the problem is obtained. As an application of this new lower estimate, some sufficient conditions for the existence and nonexistence of positive solutions for the p-Laplace problem are obtained.

Uniformly Distributing Points On A Sphere, Flavio Arrigoni

Rose-Hulman Undergraduate Mathematics Journal

In this paper, we are going to present and discuss different procedures for distributing points on a sphere's surface. Furthermore, we will assess their quality with three different distribution tests. The MATHEMATICA package that we created for testing and plotting the points is publicly available.

Modeling Virus Diffusion On Social Media Networks With The Smirq Model, Justin Browning, Arnav Mazumder, Gowri Nanda

Rose-Hulman Undergraduate Mathematics Journal

As social networking services become more complex and widespread, users become increasingly susceptible to becoming infected with malware and risk their data being compromised. In the United States, it costs the government billions of dollars annually to handle malware attacks. Additionally, computer viruses can be spread through schools, businesses, and individuals’ personal devices and accounts. Malware affecting larger groups of people causes problems with privacy, personal files, and financial security. Thus, we developed the probabilistic SMIRQ (pSMIRQ) model that shows how a virus spreads through a generated network as a way to track and prevent future viruses. Our model is …

Approximating Equilibria In Restricted Games, Jack W. Doyle

Rose-Hulman Undergraduate Mathematics Journal

We consider optimal play in restricted games with linear constraints, and use ϵ-equilibria to find near-equilibrium states in these games. We present three mathematical optimization formulations -- a mixed-integer linear program (MILP), a quadratic program with linear constraints (QP), and a quadratically constrained program (QCP) -- to both approximate and identify these states. The MILP has a short runtime relative to the QP and QCP for large games (a factor 100 faster for |S|=9) and exhibits linear growth in run time, but provides only relatively weak upper bound. The QP and QCP provide a tight bound and the precise value …

Resonant Solutions Of The Non-Linear Schrödinger Equation With Periodic Potential, Arein Duaibes, Yulia Karpeshina

Mathematics Faculty Publications

The goal is construction of stationary solutions close to non-trivial combinations of two plane waves at high energies for a periodic non-linear Schrödinger Equation in dimension two. The corresponding isoenergetic surface is described for any sufficiently large energy k2. It is shown that the isoenergetic surface corresponding to k2 is essentially different from that for the zero potential even for small potentials. We use a combination of the perturbative results obtained earlier for the linear case and a method of successive approximation.

Asymptotic Formula For Scattering Problems Related To Thin Metasurfaces, Zachary Jermain

LSU Doctoral Dissertations

The goal of this work is to develop an asymptotic formula for the behavior of a scattered electromagnetic field in the presence of a thin metamaterial known as a metasurface. By using a carefully chosen Green’s function and the single and double layer potentials we analyze the perturbed scattering problem in the presence of the metamaterial and a background scattering problem. By using Lippman-Schwinger type representation formulas for the two fields we develop the asymptotic formula for the perturbed field. From here we prove the asymptotic formula holds up to a specific error term based on the size of the …

Parallel Multigrid In Time For Chaotic Dynamical Systems, David Alan Vargas

Mathematics & Statistics ETDs

Despite the fact that Parallel-in-Time (PinT) methods are predicted to become necessary to fully utilize next-generation exa- and zettascale machines, there are currently no known practical methods which scale well with the length of the time-domain for chaotic problems, due to exponential dependence of the condition number on the fastest chaotic timescale. I present modifications to the coarse-grid equations along with a novel rediscretization approach which together greatly improve convergence of the multigrid reduction in time (MGRIT) algorithm and allow the first known PinT speedup for a chaotic PDE. The novel Local Shadowing Relaxation (LSR) is presented as an alternative …

Employing Interactive Architecture Techniques In Architectural Design Methodologies To Retrieve Ancient Egyptian Identity, Dina Elwy Aly Hamed Hussein Dr. Lobna Abd-Allah Abd-Elfattah Agha , Dr. Azza Sobhi Ragab Elsakka

Journal of Engineering Research

Architectural projects often rely on modern technologies like smart architecture and environmental treatments, neglecting the principles and philosophy that reflect civilization, ideas, culture, and traditions. This leads to short-lived buildings that depend on these technologies without any purpose of preserving them. Technicians must constantly renew technology to improve production and without benefits, as threats of superior artificial intelligence have been warned, that autonomous machines may perform tasks without programmers understanding how to reach this level. Instead of relying solely on environmental or smart technology, we should make technology serve the design idea rather than relying solely on it. Considering this, …

The Effect Of Lighting In Color In The Interior Space Of The Residential Unit, Abd Elbary Eldininy Abd Elbary Eldininy

Journal of Engineering Research

ABSTRACT: Humanity is spending more and more time indoors, both at work and at home - with studies showing that we now spend 87% of our lives indoors. Residential environ ments both positively affect the mood and well-being of its occupants, just as places with poor and uncomfortable lighting and colors can make life miserable. This is why we are interested in this issue. The importance of knowing the issues of lighting and colors in order to obtain a well thought-out interior design. The interior designer has the ability to control in the quality of lighting of various types, artificial …

Green Facade Strategy To Mitigate Heat Islands, Arch. Aya Gamal Abdel Hamid Muhammad Prof. Mai Wahba Madkour... Dr. Rania Elghamry Ashmawy Tolba Elakab

Journal of Engineering Research

In the beginning of the twentieth century and the occurrence of the economic crisis that accompanied by a climate crisis, that one of its indicators the rise in temperatures and the formation of hot zones, especially in crowded cities, including Cairo in particular, as it is considered one of the crowded cities in the world, and this noticeable rise in temperatures in Some areas where hot zones form are called heat islands. This results because of the nature of the urban environment, which has a high building density, little natural landscape, and human and industrial activities that has a negative …

Light Structure Building Technology Towards Sustainable Environmental Design, Sally El-Sayed Prof. Dr. Mai Wahba Madkour2, Prof. Dr. Marwa Ahmed Kamer El-Dawla3

Journal of Engineering Research

The building and construction industry is one of the most important sectors globally , as it plays a vital role in providing housing and infrastructure that meets the needs of various communities , However , this industry is considered one of the largest contributors of negative environmental impacts in terms of consuming huge amounts of natural resources in an unsustainable manner and a subsequent increase in energy consumption .Therefore, it was necessary to find solutions and explore for new and sustainable construction methods to alleviate these problems .This research paper will focus on the use of light buildings and their …

Available Building Technology As A Tool For Developing Construction And Structure Systems., J. Q. . Nader Ibrahim Ismael

Journal of Engineering Research

The research aims to study the impact of available building technology in each era in the development of the constructional thought and implementation techniques used and its impact on the development of different types of buildings, through the emergence of different types of buildings and the development of buildings types in terms of shape and height, through the development of building materials used Whether construction materials or finishing materials, as well as used construction techniques and equipment, and the impact of all on the development of construction thought and construction systems through different eras . The research also represents an …

Increasing Occupancy Rates In Coastal Tourism Development At The Regional Level In Support Of A Sustainable Quality Of Life In Egypt, عبدالرحمن محمد عبدالقادر موسي

Journal of Engineering Research

إن استغلال الفراغات التي تمثل أكثر من 80% من مساحة المنتجعات السياحية الساحلية في الأنشطة الرياضية والترفيهية والثقافية والاجتماعية وتوفير الخدمات المختلفة عن طريق دعم الخدمات الإلكترونية التي تساعد الزائرين في قضاء وقت أكبر بتلك القري السياحية، مع تعلم السباحة وركوب الدرجات والتجديف والتسلق وركوب الخيل دعما لجودة الحياة ، حيث التمتع بالهواء المتجدد القادم من البحر بعيدا عن التلوث والضوضاء، ولزيادة الاستفادة والدعم يتم توفير وحدات فندقة لغير الملاك لزيادة الزوار والاتفاق مع المدارس والجامعات لتنشيط تلك الرحلات للشواطئ وممارسة الأنشطة المميزة لهؤلاء الشباب والاستفادة من الخدمات الجيدة والفراغات الصحية والهواء المتجدد وتعلم الرياضات الشاطئية المفيدة وذلك الاتجاه من …

Green Architecture Strategies To Achieve Sustainability In Buildings, Azza Sobhi Ragab Elsakka J. Q. Assos., Menna Ashraf Saeid Ali

Journal of Engineering Research

في الوقت الحالي توجد حاجة مُلحة لتطبيق معايير الاستدامة التي تعني المحافظة على الموارد الحالية و استخدامها بحيث لا تقل استفادة الأجيال القادمة من تلك الموارد ، و للاستدامة عدة جوانب لتطبيقها أحد تلك التطبيقات هي العمارة الخضراء ، العمارة الخضراء مرت بعدة مراحل بدءاً من القرن السابع عشر ( منذ العصر العثماني الاسلامي ) من خلال وجود بعض الأساليب الغير مباشرة في التصميم التي توفر التهوية و الإضاءة الطبيعية و حتى عصرنا هذا، حيث وُجد تقييم لأداء المبنى الأخضر من حيث أسلوب التصميم و الإنشاء بحيث لا يؤثر على البيئة تأثير سلبي و ما زال التطوير مستمر في إنشاء …

Enhancing Daylight Using Sustainable Natural Lighting Techniques In Modern Architecture, سارة حسني شعلان أ.م.د/ لبني عبد الفتاح أغا

Journal of Engineering Research

Natural lighting is one of the basic criteria for the architectural design process. It is one of the most important data that contributes to the design of architectural spaces and the manifestation of aesthetic values. In light of the global technological development and the scientific and information revolution, the role of the architect comes in highlighting the importance of natural lighting and its positive role in human biology, and reducing effort and psychological pressure in the event of Its use is an alternative to artificial lighting, as it increases human efficiency and achievement at work, in addition to giving a …

The Impact Of Green Infrastructure On Urban Heat Island Phenomenon In Existing Cities, Neveen Youssef Azmy Basant Elsayed Abu-Farrag, Walaa Abou El-Haggag Mehanna

Journal of Engineering Research

Rapid urbanization and overpopulation, along with a lack of green space, led to an increase in air temperature, lowering the rate of thermal comfort in dense urban areas, decreasing air quality, and increasing the urban heat island (UHI) phenomenon, particularly in existing cities. As a result, the research aims to reduce the UHI effect and improve the thermal performance of existing Egyptian cities by adopting green infrastructure (GI) principles and demonstrating their effectiveness on the UHI phenomenon. This research concentrates on the UHI phenomenon as one of the environmental issues facing urbanization and includes a review of green infrastructure (GI) …