Applied Mathematics Commons^™

Asymptotic Expansion Of A Maier-Saupe Type Potential Near The Nematic-Isotropic Transition Point In Liquid Crystals, Ryan P. Oneill, Giangvuthanh Nguyen, Xiang Xu

OUR Journal: ODU Undergraduate Research Journal

In this paper we study a Maier-Saupe type bulk potential (Maier & Saupe, 1959) in the Landau-de Gennes free energy in the Q-tensor theory modeling nematic liquid crystal configurations. This potential was originally introduced in Katriel et al. (1986), which is considered as a natural enforcement of a physical constraint on the eigenvalues of symmetric, traceless Q-tensors. More specifically, we present a rigorous derivation of the asymptotic expansion of this singular potential near the nematic-isotropic transition point up to the 4-th order.

Evaluation Of Virtual Distance Learning And Teaching In The Architectural Design Studio Experience Of Professors And Students Of The College Of Architecture And Planning - Qassim University - Kingdom Of Saudi Arabia., Abdulaziz Ibrahim Alhrabi

Journal of Engineering Research

The paper deals with the evaluation of distance learning of the architectural design studio during the Corona pandemic, and the extent to which distance learning and teaching were achieved between the professor and the student. The paper aims to share and evaluate the experience of distance learning and teaching of the architectural design studio, in the College of Architecture and Planning at Qassim University. The research problem is that the Corona virus crisis generates many ideas for educational programs and media, but there is a deficiency in knowledge of many programs that achieve the continuity of the educational process remotely, …

Nano Topology And Decision Making In Medical Applications, Samir Mukhtar, Mohamed Shokry, Manar Omran

Journal of Engineering Research

Nano Topology is one of the essential topics that receive special attention from some athletes in the field of General Topology, Operations Research, and Computer Science, because it has a vital role in the generalizing most of the various mathematical concepts. Recently, many efforts have been made to study many types of Nano Topology, as the previous studies lacked real applications in Engineering, Medicine, Pharmacy, and Social Sciences. In this paper, we present some different applications of these studies. The paper is divided into two parts: Firstly, we study the theory of The Nano Topology and investigate its relation with …

Optimal Site Layout Planning For Construction Projects Over Waterways, Rana M. Azzam, Nashwa Mohamed Yossef Prof, Adel I. Eldosouky Prof

Journal of Engineering Research

Construction site layout planning is an important part of a project's success. An effective construction layout plan can enhance the performance of the construction process by improving productivity, ensuring safety, and reducing costs. Given the importance of bridges over a waterway and the lack of interest in previous research for planning a construction site over a waterway. This paper concentrates on the problems of site planning for such projects, including the problem of limited site space. The study indicated that constructing an offshore terminal is one of the primary requirements for projects with limited space being carried out on a …

Developing Paths In Areas Of Distinguished Value Between Preservation And Extinction (A Case Study Of The Railway Axis In The Maadi Area), Kamal Mahmoud Elgabalawy

Journal of Engineering Research

Abstract: proportion of the place, and thus the loss of the distinctive general character of the area, which leads to its extinction. These areas are of distinguished value, with all the thought and culture they carry of society over time. Among the areas classified as having distinguished value is the Maadi suburb, which is located in the south of Cairo Governorate, where boundaries and foundations for preserving them have been set through the Central Administration for Studies, Research, and Policies of the National Coordination Organization. The Ministry of Culture, approved by the Supreme Council for Planning and Urban Development by …

Review Of Wood Drying Technologies, Mohamed Salah Elmetwaly, Lotfy Hassan Rabie Saker, Mohamed Sameh Salem

Journal of Engineering Research

Abstract- This article provides a comprehensive review of drying optimization in data centers by examining the limitations of drying methods and discussing advances proposed by scientists through whom we can provide a comparison between different drying systems with an emphasis on improving energy efficiency and thermal performance. Wood drying under atmospheric pressure has many advantages, including the ability to dry at lower temperatures (by reducing the likelihood of some drying defects), significantly reduced drying times, color preservation, increased energy efficiency, better control of volatile organic compound emissions, and the ability to dry very large cross sections. Previous studies have achieved …

"Towards A Methodology For Studying The Impact Of Integrating Motion Systems In The External Envelope Of A Building On Natural Lighting Inside The Building– (An Applied Study On A Government School In Greater Cairo)", Nashwa Youssif

Journal of Engineering Research

يدرك المصمم ما للعناصر البيئية ولا سيما الإضاءة الطبيعية من دور فاعل في الوصول إلى تصميم ناجح يحقق أفضل أداء إستخدامي، فالإضاءة الطبيعية تذهب إلى صميم عمل المعماري فيستعين بها للإيحاء بشكل الفراغات ولونها وملمس سطوحها.

وهناك العديد من الأساليب الحديثة التي تساعد المعماري علي إتخاذ قراراته التصميمية الخاصة بتصميم المبنى وكيفية الإستفادة من الإضاءة الطبيعية داخل المباني، وهذه الأساليب تهدف إلى زيادة إحترام البيئة وتفترض تحسينات في النظم البيئية من العزل الحراري وإستغلال مصادر الطاقة الطبيعية والإهتمام بنظم الإضاءة الطبيعية والمواد البنائية.

وتعد تقنية دمج الأنظمة الحركية بالغلاف الخارجي للمبنى مع الإستفادة من الإضاءة الطبيعية داخل هذا …

An Efficient Fourier Caching Algorithm For Walk On Spheres, Zihong Zhou

Dartmouth College Master’s Theses

Walk on Spheres (WoS) is a grid-free Monte Carlo method for solving elliptic partial differential equations (PDEs).
Rather than discretizing the domain, WoS leverages the mean-value principle to obtain Monte Carlo estimates by recursively averaging the solution over the largest contained sphere, terminating upon reaching the boundary.
Unfortunately, WoS requires many independent estimates to achieve noise-free results.

We propose an acceleration technique for WoS, inspired by irradiance caching methods, that computes the solution at a sparse set of locations, and extrapolates these cached values to local neighborhoods. A key insight is that WoS can be extended to compute not only …

Production Box Cost Estimating Relationships For Dod Avionics, Carla J. Cisneros, Edward D. White, Brandon M. Lucas, Jonathan D. Ritschel, Robert D. Fass, Shawn M. Valentine

Faculty Publications

The authors use historical information obtained from the Cost Assessment Data Enterprise to estimate recurring production unit cost for DoD avionics via cost estimating relationships (CERs). The specific modeled responses include mean unit cost, median unit cost, and the 100th production unit cost (T100) utilizing learning curve theory. For T100, the authors adopt both a multiplicative and an additive error for CER comparison. Recommended CERs consist of the mean unit cost and the T100 utilizing a multiplicative error. Moreover, results reveal that weight has a significant effect on cost as well as a potential underaccounting of real price change or …

(Si13-07) Optimal Range For Value Of Two-Person Zero-Sum Game Models With Uncertain Payoffs, Sana Afreen, Ajay Kumar Bhurjee

Applications and Applied Mathematics: An International Journal (AAM)

Game theory deals with the decision-making of individuals in conflicting situations with known payoffs. However, these payoffs are imprecisely known, which means they have uncertainty due to vagueness in the data set of most real-world problems. Therefore, we consider a two-person zero-sum game model on a larger scale where the payoffs are imprecise and lie within a closed interval. We define the pure and mixed strategy as well as value for the game models. The proposed method computes the optimal range for the value of the game model using interval analysis. To derive some important results, we establish some lemmas …

(Si13-09) Numerical Methods For Solving Nonlinear Fisher Equation Using Backward Differentiation Formula, Vikash Vimal, Rajesh Kumar Sinha, Liju Pannikkal

Applications and Applied Mathematics: An International Journal (AAM)

This paper examines the numerical solution of the nonlinear Fisher equation that is used to find the growth of tumour cells in the brain. By employing new methods that transform nonlinear partial differential equations (PDE) into nonlinear ordinary differential equations (ODE) through spatial discretization. The stability of the resulting nonlinear system is evaluated using Lyapunov’s criteria. Implicit stiff solvers, including various orders of backward differentiation formulas, are used to address the ODE system. The efficiency of these numerical methods is demonstrated through two examples, and a comparison with existing methods from the literature is conducted. Compared to traditional methods, the …

(Si13-06) Analysis Of Some Unified Integral Equations Of Fredholm Type Associated With Multivariable Incomplete H And I-Functions, Rahul Sharma, Vinod Gill, Naresh Kumar, Kanak Modi, Yudhveer Singh

Applications and Applied Mathematics: An International Journal (AAM)

In this research paper, we examine various effective methods for addressing the problem of solving Fredholm-type integral equations. Our investigation commences by applying the principles of fractional calculus theory. We employ series representations and products of multivariable incomplete H-functions and multivariable incomplete I-functions to solve these integrals. The outcomes derived from our analysis possess a general nature and hold the potential to yield numerous results.

(Si13-04) System Of Variational Inclusions Involving Cayley Operator And Yosida Approximation Operator With Xor Operations, Mohd Iqbal, Tirth Ram

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider and study a new class of system of variational inclusions called a system of variational inclusions involving Cayley operator and Yosida approximation operator with XOR operation. We have shown that our problem is equivalent to a fixed point equation. Based on fixed point formulation, an iterative algorithm is designed to obtain existence and convergence result for our problem.

(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.

Human Capital At Home: Evidence From A Randomized Evaluation In The Philippines, Noam Angrist, Sarah Kabay, Dean S. Karlan, Lincoln Lau, Kevin M. Wong

Education Division Scholarship

Children spend most of their time at home in their early years, yet efforts to promote human capital at home in many low- and middle-income settings remain limited. We conduct a randomized controlled trial to evaluate an intervention which encourages parents and caregivers to foster human capital accumulation among their children between ages 3 and 5, with a focus on math and phonics skills. Children gain 0.52 and 0.51 standard deviations relative to the control group on math and phonics tests, respectively (p<0.001). A year later effects persist, but math gains dissipate to 0.15 (p=0.06) and phonics to 0.13 (p=0.12). Effects appear to be mediated largely through instructional support by parents and not other parent investment mechanisms, such as more positive parent-child interactions or additional time spent on education at home beyond the intervention. Our results show that parents can be effective conduits of educational instruction even in low-resource settings.

Data-Driven Mathematical Modeling And Simulation Of Migration Dynamics During The Russian-Ukrainian War, Danielle Sitalo, Alonso Ogueda-Oliva, Padmanabhan Seshaiyer

Spora: A Journal of Biomathematics

In this work, we employ a governing system of ordinary differential equations (ODEs) to create a mathematical model for getting insights into the dynamics of migration of Ukrainians evacuating due to war. A suitable assumption on coefficients of this model results in the well-known logistic growth. Additionally, stability analyses of equilibrium solutions for these ODEs are performed, and we employ parameter estimation techniques to identify coefficients using online datasets via both a least-squares approach as well as a physics informed neural network approach. Our findings indicate that over time, the daily influx of Ukrainian refugees to Poland stabilizes at a …

Malware Classification Through Abstract Syntax Trees And L-Moments, Anthony J. Rose, Christine M. Schubert Kabban, Scott R. Graham, Wayne C. Henry, Christopher M. Rondeau

Faculty Publications

The ongoing evolution of malware presents a formidable challenge to cybersecurity: identifying unknown threats. Traditional detection methods, such as signatures and various forms of static analysis, inherently lag behind these evolving threats. This research introduces a novel approach to malware detection by leveraging the robust statistical capabilities of L-moments and the structural insights provided by Abstract Syntax Trees (ASTs) and applying them to PowerShell. L-moments, recognized for their resilience to outliers and adaptability to diverse distributional shapes, are extracted from network analysis measures like degree centrality, betweenness centrality, and closeness centrality of ASTs. These measures provide a detailed structural representation …

Optimization And Machine Learning Techniques For Analyzing Spatiotemporal Dynamics, Dipak Prasad Dulal

All ETDs from UAB

In a numerical context, the tensor CP decomposition challenge can be reformulated into a series of least squares subproblems, which can be addressed using the renowned Alternating Least Square algorithm (ALS). The ALS algorithm is often characterized by a 'swamp phenomenon' that slows down its convergence, especially when dealing with extensive data structures. One of the goals of our research is to find ways to speed up the convergence of the ALS algorithm. This thesis discusses the use of Canonical Polyadic decomposition techniques and machine learning models in various data-driven domains, such as COVID-19, higher-order images and videos (e.g. RGB …

Performance Studies Of An Axial Flow Waterjet Pump Using An Unsteady Reynolds-Averaged Navier-Stokes Model, Stephen E. Monroe, Junfeng Wang, Chunlei Liang

Northeast Journal of Complex Systems (NEJCS)

In this study, an Unsteady Reynolds-Averaged Navier-Stokes (URANS) model is demonstrated its suitability for studying the flow and performance of open marine propellers and waterjet pumps. First, the accuracy of the URANS model is validated by studying turbulent flow past counter-rotating propellers (CRPs). Specifically, experimental data from Miller (1976) is employed for comparison against the URANS results. Subsequently, URANS is used to study the flow and performance of an Office of Naval Research (ONR) axial flow waterjet pump (AxWJ-2). Due to the large number of degrees of freedom for both simulations, parallel computations over 80 cores are performed. For the …

Representation Theory Arising From Groups In Physics, Jaxon Green

Master's Theses

A representation is a group homomorphism whose image is a group of invertible matrices. Representations and their associated matrices are analyzed through well-established techniques from linear algebra. We characterize representations by a unique decomposition into irreducible representations just as we characterize the decomposition of matrices into their eigenspaces. Through the study of these representations, we uncover mathematical relationships that underlie groups with physical applications. Due to physical symmetries, we study how the irreducible representations of groups that embody the actions of even the most basic rotations are utilized in the computation of irreducible representations groups that reflect more complicated mechanics, …

Solving Fractional Differential Equations On A Quantum Computer: A Variational Approach, Fong Yew Leong, Dax Enshan Koh, Jian Feng Kong, Siong Thye Goh, Jun Yong Khoo, Wei Bin Ewe, Hongying Li, Jayne Thompson, Dario Poletti

Research Collection School Of Computing and Information Systems

We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap history states. The proposed algorithm is not only efficient in terms of time complexity but also has lower memory costs compared to classical methods. Our results indicate that solution fidelity is insensitive to the fractional index and that gradient evaluation costs scale economically with the number of time steps. As a proof of concept, we apply our algorithm to solve a range of fractional partial differential equations commonly encountered in engineering …

A Micromagnetic Study Of Skyrmions In Thin-Film Multilayered Ferromagnetic Materials, Nicholas J. Dubicki

Dissertations

Magnetic skyrmions are topologically protected, localized, nanoscale spin textures in non-centrosymmetric thin ferromagnetic materials and heterostructures. At present they are of great interest to physicists for potential applications in information technology due to their particle-like properties and stability. In a system of multiple thin ferromagnetic layers, the stray field interaction was typically treated with various simplifications and approximations. It is shown that extensive analysis of the micromagnetic equations leads to an exact representation of the stray field interaction energy in the form of layer interaction kernels, a so-called 'finite thickness' representation. This formulation reveals the competition between perpendicular magnetic anisotropy …

Certifying Stability In Runge-Kutta Schemes: Algebraic Conditions And Semidefinite Programming, Austin Juhl

Dissertations

Numerical stability is a critical property for a time-integration scheme. In the context of Runge-Kutta methods applied to stiff differential equations, A-stability is one of the most basic and practically important notions of stability. Dating back to the work of Dahlquist, it has been known that A-stability is equivalent to the Runge-Kutta stability function satisfying a particular convex feasibility problem. Specifically, up to a transformation, the stability function lies in the convex cone of positive functions. In recent years, sum-of-squares optimization and semidefinite programming have become valuable tools in developing rigorous certificates of stability in dynamical systems. Therefore, it is …

Large Deviation Theory In Stochastic Processes: Applications To Biological Modeling, Moshe C. Silverstein

Dissertations

This dissertation delves into developing and applying stochastic models to analyze complex biological systems. It leverages Large Deviation Theory (LDT) to gain insights into these systems, focusing on two key examples: neural networks and calcium signaling dynamics. Traditional deterministic methods frequently fail to capture biological processes' randomness and inherent variability. Meanwhile, many stochastic approaches struggle to be mathematically tractable or provide accessible insights. The approach introduced in this study provides rigorous mathematical frameworks to enhance understanding of these stochastic behaviors while remaining tractable and insightful.

A stochastic model for a random biological neural network is constructed that addresses the dependencies …

Efficient Numerical Methods For Monge-Ampere Type Equations, Jake S. Brusca

Dissertations

Current numerical methods for Monge-Ampere-type equations and Optimal Transport problems face challenges when handling higher dimensions and large-scale data. This dissertation aims to develop and analyze efficient, highly parallelizable numerical algorithms for solving the Monge-Ampere equation to address these issues. Two approaches are employed:

(1) The discretization method is enhanced by introducing an integral repre-sentation of the Monge-Ampere operator. This integral can be discretized using higher-order quadrature, yielding a more efficient, higher-order monotone scheme that allows for narrower stencils. An additional advantage of this discretization is its natural extension to arbitrary dimensions.

(2) The nonlinear solvers for this scheme are …

Diagrams In Involutive Residuated Lattices, Isis A. Gallardo

Electronic Theses and Dissertations

First, we show that every distributive lattice-ordered pregroup can be embedded into a functional algebra over an integral chain, thereby improving the existing Cayley/Holland style embedding theorem. Using this result, we demonstrate that the variety of all dis tributive lattice-ordered pregroups is generated by the functional algebra on the integers. Additionally, we prove that the equational theory of this variety is decidable.

Next, we establish that DLP is equal to the join of its subvarieties LP_n, where 𝑛 ∈ ℤ⁺, consisting of 𝑛-periodic ℓ-pregroups. We also prove that every algebra in LP_n can be embedded …

Evaluation Of Business-Driven Reference Architecture For Big Data Analytics Implementation By Public Sector Organizations In Resource-Constrained Setting: A Case Study Of Uganda, Matendo Didas

Tanzania Journal of Engineering and Technology (TJET)

Big Data Analytics (BDA) is a new area at the nexus of agenda, public sector organizations, and government business. It may satisfy the growing need for trustworthy, cost-effective services in the public sector for better, more informed decision-making processes. BDA has been proposed on the planning schedules of several public sector organizations and the government. Therefore, from the previous work, using Uganda as a case study, specifically the Uganda Bureau of Statistics (UBOS), Ministry of Health (MoH), and Ministry of Education and Sports (MoES), this study aims to evaluate a designed Business-Driven Reference Architecture for Big Data Analytics Implementation (BRABDAI) …

Exploring The Transformation Of Sustainable Collective Spaces: A Study From Mlalakuwa Informal Settlement, Jacob Lutta

Tanzania Journal of Engineering and Technology (TJET)

A major challenge in collective space transformation is addressing the complexity of informal urbanisation in developing countries. Using a case study approach, this paper examines the concerns related to a particular informal settlement's sustainable collective space transformation. One of the key findings is that the absence of formal rules and regulations in the development of informal settlements in combination with land-grabbing leads to the absence of open spaces that could be used collectively. It is observed that sustainability in urban development is another body of critical thought that integrates several streams of current urban elements and embodies various conceptions of …

Investigation Of Heavy Metal Composition And Associated Health Risks From Selected Groundwater Wells In Temeke, Dar-Es-Salaam, Justin M. Jeremiah

Tanzania Journal of Engineering and Technology (TJET)

Water quality continues to be the challenge to residents in Dar es Salaam due to various anthropogenic activities in the city. This study was conducted to assess groundwater quality by determining concentrations of heavy metals. Both probability and Nonprobability sampling techniques were used to collect samples from 40 groundwater wells in 24 wards of Temeke municipal and analysed using Microwave Plasma Atomic Emission Spectrometer (Agilent 4210 MP-AES) at the Geochemistry Laboratory of the University of Dar es Salaam. Results indicated varying heavy metal concentrations ranging from 0.71 ± 0.08 to 6.64 ± 0.21 mg/l for As, 0.02 ± 0.01 to …

Development And Testing Of Small-Scale Flash Dryer For Maize Bran, Eden Ngowi

Tanzania Journal of Engineering and Technology (TJET)

Sun drying is the most common technique used to dry various food products due to its economic convenience. However, it is not effective owing to its unreliable nature leading to microbial deterioration and aflatoxin contamination of food. In Tanzania, about 1.3 million tonnes of maize bran are at risk of deterioration annually due to improper drying. The aim of this study was to design, fabricate and test an efficient small-scale flash dryer for maize bran. Using principles of material and energy balance, a small-scale flash dryer with a throughput of 500 kg of dry product per hour was designed resulting …