Physical Sciences and Mathematics Commons^™

Localized Collocation Meshless Method For Modeling Transdermal Pharmacokinetics In Multiphase Skin Structures, Eduardo Divo

Math Department Colloquium Series

The human skin has a complicated structure with many multi-scale, biophysical effects impacting the propagation of skin-injected substances, such as partitioning, metabolic reactions, adsorption and elimination. An extended version of Fick’s second law governing the process of the compound diffusion in various skin layer is employed in the current work by considering the conservation of mass of the substance and the metabolic reaction of the substance in viable skin. Additionally, a model assuming linear coupling between the substance concentrations that are bound and unbound with blood was developed. Using such a model, a set of coupled partial differential equations are …

How Generative Ai Models Such As Chatgpt Can Be (Mis)Used In Spc Practice, Education, And Research? An Exploratory Study, Fadel M. Megahed, Ying-Ju (Tessa) Chen, Joshua A. Ferris, Sven Knoth, L. Allison Jones-Farmer

Mathematics Faculty Publications

Generative Artificial Intelligence (AI) models such as OpenAI's ChatGPT have the potential to revolutionize Statistical Process Control (SPC) practice, learning, and research. However, these tools are in the early stages of development and can be easily misused or misunderstood. In this paper, we give an overview of the development of Generative AI. Specifically, we explore ChatGPT's ability to provide code, explain basic concepts, and create knowledge related to SPC practice, learning, and research. By investigating responses to structured prompts, we highlight the benefits and limitations of the results. Our study indicates that the current version of ChatGPT performs well for …

Methods, Analyses, And Applications Of Multilayer Temporal Link Prediction In Networks, Xie He

Dartmouth College Ph.D Dissertations

Many applications stem from the possibility of accurately predicting links in various types of networks. In this thesis, we present methods, analyses, and applications for static, temporal, and multilayer networks. The first part of this thesis demonstrates how static network features serve as efficient and accurate predictors for link prediction in temporal networks. It includes an ensemble learning method we developed and presents experimental results on 90 synthetic stochastic block models and 19 real-world datasets. The second part closely follows, showcasing 20 different sampling methods and their effects on nine different link prediction algorithms for 250 real-world networks across 6 …

Generation, Dynamics, And Interaction Of Quartic Solitary Waves In Nonlinear Laser Systems, Sabrina Hetzel

Mathematics Theses and Dissertations

Solitons are self-reinforcing localized wave packets that have remarkable stability features that arise from the balanced competition of nonlinear and dispersive effects in the medium. Traditionally, the dominant order of dispersion has been the lowest (second), however in recent years, experimental and theoretical research has shown that high, even order dispersion may lead to novel applications. Here, the focus is on investigating the interplay of dominant quartic (fourth-order) dispersion and the self-phase modulation due to the nonlinear Kerr effect in laser systems. One big factor to consider for experimentalists working in laser systems is the effect of noise on the …

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.

Modeling And Numerical Analysis Of The Cholesteric Landau-De Gennes Model, Andrew L. Hicks

LSU Doctoral Dissertations

This thesis gives an analysis of modeling and numerical issues in the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs) with cholesteric effects. We derive various time-step restrictions for a (weighted) $L^2$ gradient flow scheme to be energy decreasing. Furthermore, we prove a mesh size restriction, for finite element discretizations, that is critical to avoid spurious numerical artifacts in discrete minimizers that is not well-known in the LC literature, particularly when simulating cholesteric LCs that exhibit ``twist''. Furthermore, we perform a computational exploration of the model and present several numerical simulations in 3-D, on both slab geometries and spherical …

Tools For Biomolecular Modeling And Simulation, Xin Yang

Mathematics Theses and Dissertations

Electrostatic interactions play a pivotal role in understanding biomolecular systems, influencing their structural stability and functional dynamics. The Poisson-Boltzmann (PB) equation, a prevalent implicit solvent model that treats the solvent as a continuum while describes the mobile ions using the Boltzmann distribution, has become a standard tool for detailed investigations into biomolecular electrostatics. There are two primary methodologies: grid-based finite difference or finite element methods and body-fitted boundary element methods. This dissertation focuses on developing fast and accurate PB solvers, leveraging both methodologies, to meet diverse scientific needs and overcome various obstacles in the field.

Applications Of Survival Estimation Under Stochastic Order To Cancer: The Three Sample Problem, Sage Vantine

Honors Program Theses and Research Projects

Stochastic ordering of probability distributions holds various practical applications. However, in real-world scenarios, the empirical survival functions extracted from actual data often fail to meet the requirements of stochastic ordering. Consequently, we must devise methods to estimate these distribution curves in order to satisfy the constraint. In practical applications, such as the investigation of the time of death or the progression of diseases like cancer, we frequently observe that patients with one condition are expected to exhibit a higher likelihood of survival at all time points compared to those with a different condition. Nevertheless, when we attempt to fit a …

Scaled And Graduated Learning In Deep Relu Networks And Reconstructing Depp Inelastic Scattering Kinematics, Abdullah Ayar Farhat

Mathematics & Statistics Theses & Dissertations

To address computational challenges in learning deep neural networks, properties of deep RELU networks were studied to develop a multi-scale learning model. The multi-scale model was compared to the multi-grade learning models. Unlike the deep neural network learned from the standard single-scale, single-grade model, the multi-scale neural networks use low scale information from all hidden layers, and thusly provide a robust approximation method that requires fewer parameters, lower computational time, and is resistant to noise. It is shown that the multiscale method is not subject to issues arising from the vanishing gradient problem. This allows very deep multi-scale networks to …

Analyzing The Influence Of Design And Operating Conditions On Combustion And Emissions In Premixed Turbulent Flames: A Comprehensive Review, Medhat Elkelawy Prof. Dr. Eng., E. A. El Shenawy Prof. Dr., Hagar Alm-Eldin Bastawissi, Ibrahim Ali Mousa Eng., Mohamed M. Abdel-Raouf Ibrahim Dr. Eng.

Journal of Engineering Research

Recently, premixed combustion has dominated the field of combustion research worldwide. The current work is a review that addresses the effects of design and operating regimes on the combustion and emission characteristics of premixed turbulent flames. The study accounts for recent developments aimed at overcoming combustor operability issues that influence emissions and flame stability. Various experimental setups have been utilized in investigations, with results pertaining to performance and emissions concerning premixed turbulent flames. Thus, the objective of this paper is to provide a comprehensive review of the effects of swirl vane angles and equivalence fuel-air ratios for tests conducted both …

Building For Safety: Design Considerations For Refuge Areas In Tall Buildings From Quality Management Perspective, Enass. A. Salama, Heba. M. Gaber, Ahmed. M. Selim

Journal of Engineering Research

New El Alamein City is one of the largest urban projects in Egypt, and the largest project on the north coast. Tall buildings (super high-rise buildings) are considered the prevailing trend by architectural designers to obtain the maximum view of the Mediterranean Sea. The provision of safety evacuation in emergencies for these buildings’ occupants is a crucial challenge from the Quality management point of view. In contrast, there are no sufficient architectural design guidelines for the tall buildings provided by the Egyptian code for protecting buildings from fire, especially the design of the refuge areas. This study aims to investigate …

Effect Of Organic Compounds Additives For Biodiesel Fuel Blends On Diesel Engine Vibrations And Noise Characteristics, Medhat Elkelawy Prof. Dr, Eng., Hagar Alm-Eldin Bastawissi Prof. Dr. Eng., E. A. El Shenawy Prof. Dr., Mahmoud Soliman Eng.

Journal of Engineering Research

The extensive consumption of petroleum fuel directly correlates with both hazardous exhaust emissions affecting human health and contributing to global warming. Initially, biodiesel fuels were proposed as a viable alternative to address these issues. This perspective finds support in numerous published studies that highlight how the significant catalytic effect of nanoparticles allows for their integration into biodiesel blends, resulting in improved combustion characteristics, reduced exhaust emissions, and enhanced performance. This study investigates the impact of additives on biodiesel fuel properties and its effects on engine performance metrics such as brake power, brake thermal efficiency, exhaust gas concentration, engine vibration, and …

Investigation Into The Impact Of Ammonia Hydroxide On Performance And Emissions In Compression Ignition Engines Utilizing Diesel/Biodiesel Blends, Medhat Elkelawy Prof. Dr, Eng., Hagar Alm-Eldin Bastawissi, Mohammed Osama Elsamadony Dr. Eng., Abdallah Salem Abdalhadi

Journal of Engineering Research

In recent times, there has been a surge in scientific endeavors aimed at combating global warming. Various methods have been employed to address this issue, including the substitution of fossil fuels with more environmentally sustainable alternatives and the combination of different fuel types. This can be achieved through the integration of innovative injection systems and the simultaneous combustion of alternative fuels alongside fossil fuels, or by modifying fuel injection systems such as in the PCCI, RCCI, or HCCI systems. In a particular research investigation, a blend of ammonia hydroxide and diesel, with volume percentages of 7.5% and 92.5% respectively, was …

Enhancing Diesel Engine Performance By Directly Injecting Blends Of Ammonium Hydroxide And Including Liquid Petroleum Gas As A Partially Premixed Charge, Medhat Elkelawy Prof. Dr, Eng., Hagar Alm-Eldin Bastawissi, Mohammed Osama Elsamadony Dr. Eng., Abdallah Salem Abdalhadi

Journal of Engineering Research

Recently, scientists have made significant strides in addressing or mitigating environmental issues. Researchers have adopted various approaches to tackle these issues, such as replacing fossil fuels with more environmentally friendly alternatives or blending multiple fuel types. This can be achieved by either integrating these two trends through the use of new injection systems and simultaneous combustion of alternative fuels with fossil fuels or by modifying fuel injection systems, exemplified by the PCCI, RCCI, or HCCI systems. Consequently, these methods have proven effective in reducing environmental pollutants, enhancing thermal efficiency, and decreasing specific fuel consumption. In this study, ammonia hydroxide and …

Experimental Investigation On Combustion And Emission Characteristics Of Co-Combustion Of Pulverized Biomass With Diesel Fuel In An Industrial Burner, Medhat Elkelawy Prof. Dr, Eng., Hagar Alm-Eldin Bastawissi, Ahmed Abou El-Yazied Prof. Dr., Saad El-Malla Dr. Eng.

Journal of Engineering Research

This study presents the combustion and emission results obtained from a laboratory furnace equipped with a 35 kW industrial burner that utilizes co-combustion of pulverized biomass and diesel fuel. The experiment compared the co-combustion of pulverized biomass and diesel fuel with diesel fuel alone. Three different loading ratios of pulverized biomass from residual beet samples were used. Temperatures were measured at various positions inside the furnace to analyze combustion performance. It was observed that increasing the biomass loading ratios led to higher flame temperatures and improved combustion compared to diesel fuel alone. The concentrations of pollutants such as Co, HC, …

Cfd Study On Two-Phase Flow Patterns In A Pipe With 90º Elbow In Different Operating Conditions, Hagar Alm-Eldin Bastawissi, Mohammed Ahmed Khafagy, E. A. El Shenawy Prof. Dr., Ahmed M. Salem Dr

Journal of Engineering Research

Recently, CFD has offered a technological solution for modelling multi-phase flow in which we can make endless simulations with reduced expenses and effort in high accuracy results; we shall also mention that experimental studies have limitations for safety considerations when experimenting with flow in high temperature or pressure values or medium nature as in nuclear or chemical flows.In this paper, we used the ANSYS FLUENT CFD program to simulate the two-phase flow in a pipe to study the effect of attaching a 90-degree elbow fitting to the piping system, seeking to find out the change in the pattern and resulting …

تقنيات الاضاءة الصناعية وتأثيرها فى الفراغ السكنى على السلوك الانسانى, Samah Kamal Elfeky, Walaa Ahmad Nour, Lobna Abdelfatah Agha

Journal of Engineering Research

* Lighting is considered of main items in daily life begining from natural Lighting to industrial lighting. with all of it's different shapes . it is considerdone of the most important data that point Blank spaces and works to show architectural spaces, aesthetic values through being sharp and weak, ensure borders show texture or hide Features, suggest wideness, narrowness of space as the most beautiful design don't see beautiful without good lighting which designed carefully.Due to diversity of human activities, architictums spaces and it is wideness. Increased dependence on industrial Lighting to strengthen Job of performance, beauty of internal, external …

Exploring Human Aging Proteins Based On Deep Autoencoders And K-Means Clustering, Sondos M. Hammad, Mohamed Talaat Saidahmed, Elsayed A. Sallam, Reda Elbasiony

Journal of Engineering Research

Aging significantly affects human health and the overall economy, yet understanding of the underlying molecular mechanisms remains limited. Among all human genes, almost three hundred and five have been linked to human aging. While certain subsets of these genes or specific aging-related genes have been extensively studied. There has been a lack of comprehensive examination encompassing the entire set of aging-related genes. Here, the main objective is to overcome understanding based on an innovative approach that combines the capabilities of deep learning. Particularly using One-Dimensional Deep AutoEncoder (1D-DAE). Followed by the K-means clustering technique as a means of unsupervised learning. …

Homotopy Perturbation Laplace Method For Boundary Value Problems, Mubashir Qayyum, Khadim Hussain

International Journal of Emerging Multidisciplinaries: Mathematics

Most of the real situations are typically modeled as differential equations (DEs). Accurate solutions of such equations is one of the objective of researchers for the analysis and predictions in the physical systems. Typically, pure numerical approaches are utilized for the solution of such problems. These methods are usually consistent, but due to discretization and round-off errors, accuracy can be compromised. Also, pure numerical schemes may be computationally expensive and have large memory requirement. Due to this reason, current manuscript proposed a hybrid methodology by combining homotopy perturbation method (HPM) with Laplace transformation. This scheme provides excellent accuracy in less …

A Cohomological Perspective To Nonlocal Operators, Nicholas White

Honors Theses

Nonlocal models have experienced a large period of growth in recent years. In particular, nonlocal models centered around a finite horizon have been the subject of many novel results. In this work we consider three nonlocal operators defined via a finite horizon: a weighted averaging operator in one dimension, an averaging differential operator, and the truncated Riesz fractional gradient. We primarily explore the kernel of each of these operators when we restrict to open sets. We discuss how the topological structure of the domain can give insight into the behavior of these operators, and more specifically the structure of their …

Mathematically Modeling How Trapping Regimes That Target Specific Crayfish Life Stages Impact Removal Efficacy, Rini Pattison

Seaver College Research And Scholarly Achievement Symposium

The red swamp crayfish, Procambarus clarkii, is an invasive species introduced into several streams within the Santa Monica Mountains (SMM) in Southern California. Crayfish predation decimates native aquatic species. Thus, the Mountains Restoration Trust (MRT) and Environmental Restoration Group have worked to remove crayfish through regular trapping in Malibu Creek.

To aid conservation efforts, former SURB students William Milligan and Dev Patel developed mathematical models of crayfish removal efficacy. Milligan created a differential equation model of how crayfish removal affects local newt populations. Patel expanded Milligan’s crayfish model by creating a discrete model of the crayfish life cycle that newly …

Cell Motion And Multicellular Organization: A Mathematical Model For Pattern Formation In The Dictyostelium Discoideum Slug, Henry Tullis, Emily Evans, John Dallon

Library/Life Sciences Undergraduate Poster Competition 2024

Understanding multicellular behavior is key to biology and medicine

• Embryonic development requires coordinated cell motion, differentiation
• Wound healing also relies on emergent multicellular processes
• Dictyostelium discoideum (Dd) has been identified as a model organism for biomedical research, partly because it is a simple example of multicellularity
• Understanding Dd can improve, inform approaches to these tricky problems

Strengthen Establishment Of Application-Supported Major Science And Technology Infrastructure To Enhance Basic Capacity Of Science And Technology For High-Quality Development, Congli Huang, Feite Zhou, Xiang Xu, Lingling Zhang

Bulletin of Chinese Academy of Sciences (Chinese Version)

From “Two Bombs and One Satellite” to Five-hundred-meter Aperture Spherical Radio Telescope (FAST), from ground zero to the center stage of the world, China has unswervingly followed the path of independent innovation with distinctive characteristics. After the development of nearly half a century, breakthroughs have been made in several key areas. The position, implication, and classification of major scientific and technological infrastructures are constantly changing under the new situation. Based on an in-depth investigation of major scientific and technological infrastructure such as high-efficiency and low-carbon gas turbine research facility, it is believed that the construction of application-supported major scientific and …

Characterization Of Biological Particles Using An Integrated Hyperspectral Imaging And Machine Learning, Kaeul Lim, Arezoo Ardekani

Graduate Industrial Research Symposium

Hyperspectral imaging (HSI) is a promising modality in medicine with many potential applications. This study focuses on developing a label-free lipid nanoparticle characterization method using a convolutional neural network (CNN) analysis of HSI images. The HSI data, hypercube, consists of a series of images acquired at different wavelengths for the same field of view, providing continuous spectra information for each pixel. Three distinct liposome samples were collected for analysis. Advanced image preprocessing and classification methods for HSI data were developed to differentiate liposomes based on their material compositions. Our machine learning-based classification method was able to distinguish different liposome types …

Resource Optimization For Air Mobility Under Emergency Situations, Yongxin (Jack) Liu

Math Department Colloquium Series

This project aims to improve air traffic management in emergencies. We first developed a GRU neural network to forecast weather-related airport capacity constraints using historical data, underscoring the value of real-time data analysis. We then optimized emergency evacuation air travel using Particle Swarm Optimization, demonstrating the ability to quickly aggregate evacuation flight resources cost-effectively. Finally, we provided a hybrid model combining a genetic algorithm with a neural network for evacuation planning, we show that neural network can be integrated accelerate genetic algorithms for efficient and performance assured system optimization.

Stability Of Predator-Prey Model For Worm Attack In Wireless Sensor Networks, Rajeev Kishore, Padam Singh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we propose a predator-prey mathematical model for analyzing the dynamical behaviors of the system. This system is an epidemic model, and it is capable of ascertaining the worm's spreading at the initial stage and improving the security of wireless sensor networks. We investigate different fixed points and examine the stability of the projected model.

Existence And Uniqueness Of Solutions Of Sobolev Type Second Order Integrodifferential Equation, Kamalendra Kumar, Manish Nath Tripathi

Applications and Applied Mathematics: An International Journal (AAM)

The primary concern of this article is to establish the existence, uniqueness and continuous dependence on initial data of mild solutions of second order mixed integrodifferential equations of Sobolev type in Banach spaces. For this objective, we employ the idea of strongly continuous cosine family of operators, the modified version of Banach theorem and Grownwall’s inequality. The model is demonstrated to elucidate the abstract conclusion.

A Novel Fuzzy Time Series Forecasting Method Based On Probabilistic Fuzzy Set And Cpbd Approach, Krishna Kumar Gupta, Suneet Saxena

Applications and Applied Mathematics: An International Journal (AAM)

Probabilistic fuzzy set is used to model the non-probabilistic and probabilistic uncertainties simultaneously in the system. This study proposes a cumulative probability-based discretization and probabilistic fuzzy set based novel fuzzy time series forecasting method. It also proposes a novel discretization approach based on cumulative probability to tackle the probabilistic uncertainty in partitioning of datasets. Gaussian probability distribution function has been used to construct probabilistic fuzzy set. The advantage of the proposed work is that it addresses the uncertainties due to randomness and fuzziness simultaneously and also improves accuracy rate in time series forecasting. A proposed forecasting method is applied on …

Utilization Of Caputo Fractional Derivative In Mhd Nanofluid Flow With Soret And Thermal Radiation Effects, Harshad Patel, Gopal Nanda

Applications and Applied Mathematics: An International Journal (AAM)

In existence of heat diffusion and thermal radiation, an analytical equation is found for unsteady MHD flow past an exponentially accelerating vertical plate in optically thick water based nanofluid. The governing equations are made dimensionless by similarity transformation. A definition of Caputo fractional derivative is applied to generalize governing system of partial differential equations. Laplace transform techniques are applied and obtained the analytical solutions of proposed problems. For a physical point of view, numerical results are obtained using MATLAB software and presented via graphs. From the results, it is concluded that magnetic fields tend to reduce velocity. It is also …

Effects Of Magnetic Field And Chemical Reaction On A Time Dependent Casson Fluid Flow, Akhil Mittal, Harshad Patel, Ramesh Patoliya, Vimalkumar Gohil

Applications and Applied Mathematics: An International Journal (AAM)

This research paper deals with the effect of chemical reactions and magnetic fields on the hydrodynamics fluid flow of Casson fluid. The novelty of this work is the inclusion of time-dependent flow across a vertical plate with a stepped concentration at the surface in a porous media. The stated phenomenon is modeled in the PDE system and is adapted in the ODE system through similarity transformation. The LT (Laplace Transform) and ILT (Inverse LT) are used to obtain the analytical results for regulating dimension-free movement, thermals, and concentration expression. The exact expression of shear rate, heat exchange rate, and mass …