Applied Mathematics Commons^™

Mathematical Modelling Of Hybrid Photonic Structures For Holographic Sensors, Jack Lyons

Doctoral

This thesis outlines a mathematical framework for modelling the formation of holographic gratings in hybrid photopolymer based nanocomposites with the aim of optimising their holographic recording properties for optical sensing applications. Thus, the second aim of the work is to model the change in optical properties of the grating in response to exposure to a target analyte. This work has been a collaborative research project between the School of Mathematics & Statistics at Technological University Dublin and the Centre for Industrial and Engineering Optics that have done extensive experimental work with holographic gratings recorded in photopolymer materials.

In recent years, …

Dunbar’S Number In Motion: Agent-Based Simulations Of Friendship Formation, Christopher R. Cooke, Cameron D. Lutz

Northeast Journal of Complex Systems (NEJCS)

By contrasting Lévy flight and random walk strategies in simulated agents, we discern the effect of movement behavior on the total duration of social interactions. Our agent-based simulation results approximate empirically observed Dunbar social circle formation using simple behavioral rules of interaction and compatibility to mimic exogenous attribute-based friendship formation. We simulate the complexities of social interactions among agents with unique attributes and a time budget for social engagement over a one-year period. Two distinct simulations were conducted to evaluate the behavioral contributions of Lévy flight and random walk movement patterns on cumulative interaction duration and the formation of Dunbar …

Optimization Of The Cross-Section Of Generic Flexible Bridges, Manal Kamal Zaki, Mina M. Helmy, Mark M. Tawadros

Journal of Engineering Research

This paper investigates the behavior of flexible bridges prone to aerodynamic instabilities due to wind. Optimal cross-sections that reduce aerodynamic forces are recommended. This is achieved by studying a variety of bridge sections with different widths of upper and lower sloping edges in addition to studying the upper and lower cramps of the deck. The wind velocities are also parameterized. Computations are developed based on the powerful computational fluid dynamics (CFD) method known as FLUENT and embedded in ANSYS software. For parametric study, a design of experiments (DOE) is performed based on the response surface methodology (RSM) combined with the …

Using Nanotechnology To Achieve Sustainability In Interior Residential Spaces, Neveen Youssef Azmy, Esraa Tarek Abu-El Azm, Ahmed Ahmed Rizk, Walaa Abou El-Haggag Mehanna

Journal of Engineering Research

Major scientific and technological developments characterize the present time. One notable achievement is the nano revolution, which has greatly influenced various areas of life Nanotechnology is characterized by using very small particles of materials, either alone or by processing them to create new materials with remarkable properties. Hence, nanotechnology offers promising economic solutions and products to achieve a reliable and sustainable environment. Architecture has great potential to benefit from this technology to achieve sustainability and improve indoor environment quality. Given the proliferation of residential buildings in urban areas, where people spend most of their time, it is necessary to integrate …

Evaluating Lidar Technology In Iphone Mobiles For 2d Mapping Applications, Nasr Mohammady Saba, Salem Salama Saleh

Journal of Engineering Research

Abstract- LiDAR (Light Detection and Ranging) technology has revolutionized mapping applications, offering enhanced precision and accuracy in spatial data collection. The integration of LiDAR technology in the latest iPhone models, beginning with the iPhone 12 Pro, has introduced new capabilities for 2D data measurement and plan creation directly on the mobile device. The iPhone 12 Pro and 12 Pro Max models support LiDAR techniques within their mobile phone cameras, enhancing the performance of various applications such as Measurements and Photos. LiDAR operates by emitting pulsed light waves into the surrounding space, which bounce off nearby objects and return to the …

Experimental And Numerical Investigation For Optimum Design Of Hydraulic Steel Gates, Basma Hassan Mohamed Eng, Ahmed Mohamed Anwer Dr, Hanan Eltobgy Prof., Gamal Helmy El-Saeed Prof

Journal of Engineering Research

Conventionally, steel gates are widely used in hydraulic structures for their superior mechanical properties in sustaining hydrostatic pressure. Maintenance and operational costs should be considered while studying the feasibility of these gates. In the current research, three prototype steel gates with different configurations were prepared and examined experimentally. The three gates have the same surface dimensions of (width x height) equal to (1.0 x 1.25 m). The first steel gate represents a typical traditional gate made of skin plate and stiffened laterally using standard steel channels and will be kept for comparison. The second gate represents a standard thicker plate …

Performance And Emissions Characteristics Of Multi-Cylinder Direct Injection Diesel Engine Fuelled With Diesel/Biodiesel And Toluene Additives, Hagar Alm-Eldin Bastawissi, Medhat Elkelawy Prof. Dr. Eng., Mohammed Osama Elsamadony Dr. Eng., Moustafa Ghazaly Eng.

Journal of Engineering Research

This study explores the impact of using a diesel, biodiesel, and toluene additive fuel blend in a multi-cylinder direct injection diesel engine, focusing on both performance and emissions characteristics. Biodiesel, made from renewable sources like vegetable oils, is often added to diesel to reduce reliance on fossil fuels and improve combustion due to its higher oxygen content. In this work, a 45% biodiesel blend (B45) led to significant reductions in particulate matter (PM) emissions by up to 40% compared to conventional diesel. Additionally, carbon monoxide (CO) and hydrocarbon (HC) emissions decreased by up to 30% and 25%, respectively, due to …

Effect Of Dual-Fuelled Cng And Gasoline On Spark Ignition Engine Performance And Emissions Behaviors At Different Loads, Medhat Elkelawy Prof. Dr, Eng., M.M. Bassuoni Prof. Dr., Hagar Alm-Eldin Bastawissi, Saied I. Haiba Eng.

Journal of Engineering Research

Engine emissions are one of numerous factors that have detrimentally affected the environment, such as global warming, which is the result of growing exhaust gases, practically carbon dioxide (CO2). These emissions have substantially influenced researchers to develop strategic initiatives to minimize the carbon contents of fuels. The purpose of this research is to investigate the characteristics of internal combustion (SI) engines fueled by gasoline and compressed natural gas (CNG) blends. The experiments are performed using a HONDA 4-stroke, single-cylinder, and air-cooled SI engine. Five CNG concentrations are evaluated, the concentrations range from 0.5 to 2.5 L/min with a 0.5 L/min …

A Quantitative Analysis Of The Commercial-Additive Effects On Diesel Engine Combustion And Emissions Characteristics, Medhat Elkelawy Prof. Dr. Eng., Hagar Alm-Eldin Bastawissi Prof. Dr. Eng., E. A. El Shenawy Prof. Dr., Mahmoud Mohamed Soliman Mahmoud Mohamed Mahmoud Soliman

Journal of Engineering Research

Petroleum fuel prices fluctuate in response to global political and economic issues. Government regulations should be followed when it comes to engine emissions, as these dangerous pollutants have a negative impact on the environment. One such effect is global warming, which raises global temperatures. The purpose of this study is to develop the additives for use as a fuel mix with diesel fuel, which will be used to feed the diesel engine of a single cylinder, four strokes. The engine will be tested experimentally with varying loads at fixed speed of 1500 rpm, using blends of [(5% PRETSONE additive + …

Design And Implementation Of A Low-Cost Educa-Tional Robot For Engineering Curriculums, Diana Refaat Henry Jacob, Ashraf Mohamed Hafez, Mohamed Tarek Elawa

Journal of Engineering Research

The role of educational robots is becoming increasingly important. Many commercial educational robots differ in their abilities and price. In general, the cost of these robots presents the main cause of their limited use in the teaching process, especially in countries with limited financial resources. This work attempts to solve this problem by designing and implementing an educational robot with a limited budget. The robot was initially intended to serve higher education students' needs, especially in engineering curriculums but can be extended to other application areas. This work presents robot hardware functional blocks, mechanical struc-ture design, and 3D printing implementation. …

A Greening The Diesel: Vegetable Oil Biodiesel Blends For Cleaner Emissions And Improved Direct Injection Diesel Engine Performance, Medhat Elkelawy Prof. Dr, Eng., Hagar Alm-Eldin Bastawissi, E. A. El Shenawy Prof. Dr., Mustafa Mohamed Ouda

Journal of Engineering Research

In this study, we conducted comprehensive experiments to assess and compare the performance of pure diesel fuel against biodiesel produced from corn oil in various blend ratios (15/85, 30/70, 45/55, and 60/40) in a conventional four-stroke, direct-injection diesel engine, fuel is injected directly into the combustion chamber at the end of the compression stroke, allowing for efficient combustion and power generation over four distinct phases: intake, compression, power, and exhaust. Each fuel blend was tested at an engine speed of 16,000 rpm across different load conditions (low, medium, and high). Key performance metrics, including volumetric fuel consumption, exhaust smoke, and …

Improved Minimum Variance Channel Estimation Techniques For Ofdm Systems, Kwame S. Ibwe

Tanzania Journal of Engineering and Technology (TJET)

Orthogonal frequency division multiplexing (OFDM) systems face challenges in channel estimation due to noise, variability, and the doubly dispersive nature of wireless channels, which degrade performance. To address these challenges, a multichannel minimum variance double dispersive channel estimator is proposed. The method employs a hybrid approach that combines subspace and minimum variance techniques, optimizing the filter bank output power under a signal-to-noise ratio (SNR) constraint. This design preserves the desired signal while effectively suppressing disturbances, achieving robust performance with reduced computational complexity compared to existing methods. Simulation results demonstrate that the proposed estimator outperforms subspace and asymptotic methods in terms …

Mathematics In Everyday Life: Exploring Practical Applications And Real-World Impact, Priyant Banerjee, Arshad Bhat

Himalayan Research Papers Archive

Mathematics is an essential part of daily life and influences decisions and problem-solving in various aspects of life. This study explores how mathematical concepts are embedded in daily activities such as financial management, cooking, travel planning, and technological interactions. We will show how arithmetic, algebra, geometry, and statistics are applied in real life to improve decision-making, efficiency, and productivity. Findings indicate that people with higher mathematical literacy solve problems more efficiently, especially in budgeting, as accurate calculations minimize financial mistakes and facilitate long-term financial planning. In cooking, proportional reasoning ensures the accuracy of recipes, thus providing consistent culinary results. Travel …

An Agent-Based Model Of Microglia And Neuron Interaction: Implications In Neurodegenerative Disease, Cheyenne Ty, Amanda Case, Emmanuel Mezzulo, Abigail Penland, Kamila Larripa

Spora: A Journal of Biomathematics

Whether immune cells protect or harm the brain is an open question depending on context, and their role is implicated in multiple diseases such as Alzheimer's disease, dementia, and other neurological disorders. Microglia, a specific type of immune cell in the central nervous system, play a key role in homeostasis, and genes associated with an elevated risk of Alzheimer's disease correspond with deficiencies in their behavior. We created an agent-based model that incorporates inflammatory signaling, chemotaxis, and phagocytosis of damaged neurons and allows the exploration of crucial pathways in the maintenance of brain health. We specifically investigated pathways related to …

On Solving Differential Equations Describing The Ecology Of Shallow Lakes: A Comparison Of Classical And Modern Computational Methods Through Python, Vruddhi Kapre, Jeffrey R. Anderson, Alessandro Maria Selvitella

Spora: A Journal of Biomathematics

In this exposition paper, we describe some computational methodologies to solve numerically differential equations modeling the shallow lake ecosystem, with particular focus on the dynamics of the phosphorus. We describe in detail Python implementations of classical algorithms, like Runge-Kutta, and more modern approaches, including physics-informed neural networks.

On The Sharpness Of A Korn’S Inequality For Piecewise H1 Space And Its Applications, Qingguo Hong, Young Ju Lee, Jinchao Xu

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we investigate the sharpness of a Korn's inequality for piecewise H1 space and its applications. We first revisit a Korn's inequality for the piecewise H1 space based on general polygonal or polyhedral decompositions of the domain. We express the Korn's inequality with minimal jump terms. Then we prove that such minimal jump conditions are sharp for achieving the Korn's inequality. The sharpness of the Korn's inequality and explicitly given minimal conditions can be used to test whether any given finite element spaces satisfy Korn's inequality, immediately as well as to build or modify nonconforming finite elements for …

Long-Time Asymptotics For The Kadomtsev–Petviashvili I Equation With Small Initial Data, Samir Donmazov

Theses and Dissertations--Mathematics

We study the initial value problem for the Kadomtsev--Petviashvili I (KP I) equation (u_t + 6uu_x + u_xxx)_x = 3u_yy with small initial data belonging to a subspace of the energy space for the KP I equation. We establish the long-time asymptotics for solutions of the KP I equation using the inverse scattering transform formalism developed by Zhou. Within this framework, the inverse problem for the KP I equation is formulated as a nonlocal Riemann--Hilbert problem (RHP) in two spatial dimensions. As part of the asymptotic analysis, we determine the long-time behavior of the …

Collision Avoidance And Vegetation As Drivers Of Collective Motion In Australian Plague Locusts, Nathan S. Hasegawa

HMC Senior Theses

The Australian plague locust (Chortoicetes terminifera) is an agricultural and ecological pest that causes tens of millions of dollars in crop damage each year. In this thesis, we develop mathematical models of hopper bands, dense formations of juvenile locusts that move across a vegetated field and destroy plants in their path. We develop agent-based and PDE models of hopper bands moving through vegetation to examine how recently discovered behavior where locusts slow down to avoid collisions with other locusts may influence the shape, speed, and destructiveness of hopper bands. We find that collision avoidance may cause locusts to …

Multi-Valued Variational Inequalities For Variable Exponent Double Phase Problems: Comparison And Extremality Results, Siegfried Carl, Vy Khoi Le, Patrick Winkert

Mathematics and Statistics Faculty Research & Creative Works

We prove existence and comparison results for multi-valued variational inequalities in a bounded domain Ω of the form (Formula presented.) where A:W1,H(Ω)→W1,H(Ω)∗ given by (Formula presented.) for u∈W1,H(Ω), is the double phase operator with variable exponents and W1,H(Ω) is the associated Musielak–Orlicz Sobolev space. First, an existence result is proved under some weak coercivity condition. Our main focus aims at the treatment of the problem under consideration when coercivity fails. To this end we establish the method of sub–super-solution for the multi-valued variational inequality in the space W1, H(Ω) based on appropriately defined sub- and super-solutions, which yields the existence …

Caves, Calculus, And Climate Change: Measuring And Modeling The Discharge Of Biz Falls In Mammoth Cave National Park, Ava Lich

Mahurin Honors College Capstone Experience/Thesis Projects

Climate change poses a significant global challenge, with increasing levels of atmospheric carbon dioxide as a primary driver of rising temperatures and environmental disruptions. Karst systems, such as those in South-Central Kentucky, play a role in sequestering atmospheric CO₂ through the dissolution of limestone, a process that forms unique landscapes while mitigating climate impacts. This study investigates the discharge dynamics of Cascade River in Great Onyx Cave to enhance understanding of the relationship between hydrology and carbon sequestration in karst environments. A barrel weir equipped with pressure transducers was employed to collect and measure water flow, and Torricelli’s law was …