Physical Sciences and Mathematics Commons^™

Squeezing Flow Between Two Parallel Plates Under The Effects Of Maxwell Equation And Viscous Dissipation, Muhammad Bilal, Anwar Saeed, Ayesha Ali

International Journal of Emerging Multidisciplinaries: Mathematics

The unsteady, incompressible electroviscous fluid flow has been investigated with thermal energy transmission across two parallel plates. The upper plate is in motion, while the lower one is stationary. The flow is governed by the Navier-Stokes equations, which are combined with the Maxwell equation. The system of nonlinear PDEs is simplified to a system of ODEs along with their boundary conditions using Von-Karman's transformation. For the problem's analytic solution, the homotopy analysis method (HAM) has been used, and the result is compared to the Runge Kutta method of order four and latest computational technique parametric continuation method (PCM) to determine …

Numerical Solution Of An Inviscid Burger Equation With Cauchy Conditions, Muhammad Zahid

International Journal of Emerging Multidisciplinaries: Mathematics

This article deals with the solution of the Cauchy problem for the Inviscid Burger equation. Various numerical techniques like Upwind non Conservative, Upwind Conservative, Lax Friedrich, Lax Wendorff, and Mac Cormack, are used to solve initial-value problems for the Inviscid Burger equation. Through various model problems, the efficiency and accuracy of the techniques have been shown via the graphical and tabulated form with the exact solution

Homotopy Analysis Method For Free-Convective Boundary-Layer Equation Using Pade ´Approximation: Pade ´Approximation For Free-Convective Boundary-Layer Equation, Raja Mehmood Khan, Naveed Imran

International Journal of Emerging Multidisciplinaries: Mathematics

This paper is devoted to the study of a free-convective boundary layer flow modeled by a system of nonlinear ordinary differential equations. We apply Homotopy Analysis Method (HAM) along with Pade´ approximation to solve free-convective boundary-layer equation. It is observed that the combination of HAM and the Pade´ approximation improves the accuracy and enlarge the convergence domain.

Homotopy Analysis Method For Fourth-Order Time Fractional Diffusion-Wave Equation, Naveed Imran, Raja Mehmood Khan

International Journal of Emerging Multidisciplinaries: Mathematics

This paper is devoted to the study of a fourth-order fractional diffusion-wave equation defined in a bounded space domain. We apply Homotopy Analysis Method (HAM) to obtain solutions of fourth-order fractional diffusion-wave equation defined in a bounded space domain. It is observed that the HAM improves the accuracy and enlarge the convergence domain.

Flow And Heat Transfer Of Power Law Fluid Over Horizontal Stretching Cylinder With Partial Slip Condition And Thermal Radiation, Zakia Shamim, Azeem Shahzad, Tahir Naseem

International Journal of Emerging Multidisciplinaries: Mathematics

The aim of the present study is to investigate the boundary layer flow of power-law fluid over the horizontal stretching cylinder. The temperature-dependent thermal conductivity of the power-law fluid is considered. Combined effects of constant thermal conductivity and viscous dissipation are analyzed in heat transfer. The relevant boundary layer partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by using suitable transformations. These nonlinear ordinary differential equations are solved by the BVP4C method using MATLAB. The accuracy of computed results is checked by comparing them with existing literature. To discuss the effects of flow parameters on velocity and …

Axisymmetric Hydromagnetized Heat Transfer Across A Stretching Sheet With Joule Heating And Radiation, Tahir Naseem, Sajeela Bibi

International Journal of Emerging Multidisciplinaries: Mathematics

This investigation thoroughly analyses magnetohydrodynamics axisymmetric fluid flow and heat transfer over an exponentially stretching sheet in the presence of radiation and Joule heating effects. The governing partial differential equation is obtained and converted into coupled ordinary differential equations using a suitable similarity transformation. This transformation is also used to re-model the governing system to modify ODEs and boundary conditions using the BVP4C MATLAB) package. The effects of the involved physical parameters, such as suction/injection parameter, magnetic parameter, Prandtl number, Eckert number, and radiation parameter on velocity and temperature profiles are shown graphically. The effects of various parameters on Nusselt …

Heat And Mass Transfer Of Viscous Fluid In A Permeable Channel With Reabsorbing Walls, Aamir Shahzad, Aniqa Shah, Shamsul Haq

International Journal of Emerging Multidisciplinaries: Mathematics

An analytical investigation is made to determine the heat and mass transfer mechanism of non-isothermal highly viscous uid in a longnarrow porous channel. The walls of the channel are maintained at the same temperature. The mathematical model is developed by using the continuity, momentum, energy and diffusion equations. Analytical solutions are establish to get the expressions of velocity field, pressure distribution, mass ow rate, wall shear stress, temperature profile, mass concentration distribution as well as the heat transfer rate (Nusselt number) and mass transfer rate (Sherwood number) with involved physical parameters. Numerical results are graphically sketched to describe the role …

Theory And Computations For The System Of Integral Equations Via The Use Of Optimal Auxiliary Function Method, Laiq Zada, Falak Naz, Rashid Nawaz

International Journal of Emerging Multidisciplinaries: Mathematics

This paper extends the application of Optimal Auxiliary Function Method (OAFM) to the system of integral equations. The system of Volterra integral equations of second kind are taken as test examples. The results obtained by proposed method are compared with different methods i.e., Biorthogonal systems in a Banach space Fixed point, the implicit Trapezoidal rule in conjunction with Newton's method, and Relaxed Monte Carlo method (RMCM). The results revealed that OAFM is more efficient, simple to apply, and fast convergent. The auxiliary functions used in the method control its convergence. The values of arbitrary constants involved in the auxiliary functions …

Three Dimensional Mhd Viscous Flow Under The Influence Of Thermal Radiation And Viscous Dissipation, Sana Akbar, Muhammad Sohail

International Journal of Emerging Multidisciplinaries: Mathematics

The present study elucidates the results on the mathematical modeling and numerical study for the viscous flow demeanor past over the plane horizontal surface stretched nonlinearly in two sideways. Furthermore, a comprehensive analysis on the effects of magnetic field, thermal radiation and viscous dissipation are considered and observed. Cartesian coordinate system is employed for modelling the flow equations. In this research water act as a traditional thermal fluid. Three distinct nanoparticles namely Gold (Au), Aluminum (Al) and Silver (Ag) are suspended. Numerical and analytical solution for the resulting differential equations demonstrates the flow demeanor for velocity and temperature distribution are …

The Effect Of Habitat Fragmentation On Plant Communities In A Spatially-Implicit Grassland Model, Mika T. Cooney, Benjamin R. Hafner, Shelby E. Johnson, Sean Lee

Rose-Hulman Undergraduate Mathematics Journal

The spatially implicit Tilman-Levins ODE model helps to explain why so many plant species can coexist in grassland communities. This now-classic modeling framework assumes a trade-off between colonization and competition traits and predicts that habitat destruction can lead to long transient declines called ``extinction debts.'' Despite its strengths, the Tilman-Levins model does not explicitly account for landscape scale or the spatial configuration of viable habitat, two factors that may be decisive for population viability. We propose modifications to the model that explicitly capture habitat geometry and the spatial pattern of seed dispersal. The modified model retains implicit space and is …

Permitted Sets And Convex Coding In Nonthreshold Linear Networks, Steven Collazos, Duane Nykamp

Mathematics Publications

Hebbian theory proposes that ensembles of neurons form a basis for neural processing. It is possible to gain insight into the activity patterns of these neural ensembles through a binary analysis, regarding neurons as either active or inactive. The framework of permitted and forbidden sets, introduced by Hahnloser, Seung, and Slotine (2003), is a mathematical model of such a binary analysis: groups of coactive neurons can be permitted or forbidden depending on the network's structure.

In order to widen the applicability of the framework of permitted sets, we extend the permitted set analysis from the original threshold-linear regime. …

Entropy Analysis Of Sutterby Nanofluid Flow Over A Riga Sheet With Gyrotactic Microorganisms And Cattaneo–Christov Double Diffusion, M. Faizan, F. Ali, K. Loganathan, A. Zaib, C. A. Reddy, Sara I. Abdelsalam

Basic Science Engineering

In this article, a Riga plate is exhibited with an electric magnetization actuator consisting of permanent magnets and electrodes assembled alternatively. This exhibition produces electromagnetic hydrodynamic phenomena over a fluid flow. A new study model is formed with the Sutterby nanofluid flow through the Riga plate, which is crucial to the structure of several industrial and entering advancements, including thermal nuclear reactors, flow metres and nuclear reactor design. This article addresses the entropy analysis of Sutterby nanofluid flow over the Riga plate. The Cattaneo–Christov heat and mass flux were used to examine the behaviour of heat and mass relaxation time. …

Leveraging Subject Matter Expertise To Optimize Machine Learning Techniques For Air And Space Applications, Philip Y. Cho

Theses and Dissertations

We develop new machine learning and statistical methods that are tailored for Air and Space applications through the incorporation of subject matter expertise. In particular, we focus on three separate research thrusts that each represents a different type of subject matter knowledge, modeling approach, and application. In our first thrust, we incorporate knowledge of natural phenomena to design a neural network algorithm for localizing point defects in transmission electron microscopy (TEM) images of crystalline materials. In our second research thrust, we use Bayesian feature selection and regression to analyze the relationship between fighter pilot attributes and flight mishap rates. We …

Computing Rational Powers Of Monomial Ideals, Pratik Dongre, Benjamin Drabkin, Josiah Lim, Ethan Partida, Ethan Roy, Dylan Ruff, Alexandra Seceleanu, Tingting Tang

Department of Mathematics: Faculty Publications

This paper concerns fractional powers of monomial ideals. Rational powers of a monomial ideal generalize the integral closure operation as well as recover the family of symbolic powers. They also highlight many interesting connections to the theory of convex polytopes. We provide multiple algorithms for computing the rational powers of a monomial ideal. We also introduce a mild generalization allowing real powers of monomial ideals. An important result is that given any monomial ideal I, the function taking a real number to the corresponding real power of I is a step function which is left continuous and has rational …

Stochastic Modeling Of Flows In Membrane Pore Networks, Binan Gu

Dissertations

Membrane filters provide immediate solutions to many urgent problems such as water purification, and effective remedies to pressing environmental concerns such as waste and air treatment. The ubiquity of applications gives rise to a significant amount of research in membrane material selection and structural design to optimize filter efficiency. As physical experiments tend to be costly, numerical simulation and analysis of fluid flow, foulant transport and geometric evolution due to foulant deposition in complex geometries become particularly relevant. In this dissertation, several mathematical modeling and analytical aspects of the industrial membrane filtration process are investigated. A first-principles mathematical model for …

Maker Math: Exploring Mathematics Through Digitally Fabricated Tools With K–12 In-Service Teachers, Jason R. Harron, Yi Jin, Amy F. Hillen, Lindsey Mason, Lauren Siegel

Faculty Open Access Publishing Fund Collection

This paper reports on nine elementary, middle, and high school in-service teachers who participated in a series of workshops aimed at exploring the wonder, joy, and beauty of mathematics through the creation and application of digitally fabricated tools (i.e., laser-cut and 3D printed). Using the Technological Pedagogical and Content Knowledge (TPACK) framework to investigate technological, pedagogical, contextual, and content knowledge, researchers applied qualitative methods to uncover the affordances and constraints of teaching and learning math concepts with digitally fabricated tools and examined how the workshops supported broadening participation in mathematics by focusing on the connections between mathematical inquiry, nature, and …

Duality For Asymptotic Invariants Of Graded Families, Michael Dipasquale, Thái Thành Nguyễn, Alexandra Seceleanu

Department of Mathematics: Faculty Publications

The starting point of this paper is a duality for sequences of natural numbers which, under mild hypotheses, interchanges subadditive and superadditive sequences and inverts their asymptotic growth constants.

We are motivated to explore this sequence duality since it arises naturally in at least two important algebraic-geometric contexts. The first context is Macaulay- Matlis duality, where the sequence of initial degrees of the family of symbolic powers of a radical ideal is dual to the sequence of Castelnuovo-Mumford regularity values of a quotient by ideals generated by powers of linear forms. This philosophy is drawn from an influential paper of …

The Art Of Landslides: How Stochastic Mass Wasting Shapes Topography And Influences Landscape Dynamics, Benjamin Campforts, Charles Shobe, Irina Overeem, Gregory Tucker

Faculty & Staff Scholarship

Bedrock landslides shape topography and mobilize large volumes of sediment. Yet, interactions between landslide-produced sediment and fluvial systems that together govern large-scale landscape evolution are not well understood. To explain morphological patterns observed in steep, landslide-prone terrain, we explicitly model stochastic landsliding and associated sediment dynamics. The model accounts for several common landscape features such as slope frequency distributions, which include values in excess of regional stability limits, quasi-planar hillslopes decorated with straight, closely spaced channel-like features, and accumulation of sediment in valley networks rather than on hillslopes. Stochastic landsliding strongly affects the magnitude and timing of sediment supply to …

Vertex-Magic Graphs, Karissa Massud

Honors Program Theses and Projects

In this paper, we will study magic labelings. Magic labelings were first introduced by Sedláček in 1963 [3]. At this time, the labels on the graph were only assigned to the edges. In 1970, Kotzig and Rosa defined what are now known as edge-magic total labelings, where both the vertices and the edges of the graph are labeled. Following this in 1999, MacDougall, Miller, Slamin, and Wallis introduced the idea of vertex-magic total labelings. There are many different types of magic labelings. In this paper will focus on vertex-magictotal labelings.

The Foundations Of Mathematics: Axiomatic Systems And Incredible Infinities, Catherine Ferris

Honors Program Theses and Projects

Often, people who study mathematics learn theorems to prove results in and about the vast array of branches of mathematics (Algebra, Analysis, Topology, Geometry, Combinatorics, etc.). This helps them move forward in their understanding; but few ever question the basis for these theorems or whether those foundations are sucient or even secure. Theorems come from our foundations of mathematics, Axioms, Logic and Set Theory. In the early20th century, mathematicians set out to formalize the methods, operations and techniques people were assuming. In other words, they were formulating axioms. The most common axiomatic system is known as the Zermelo-Fraenkel axioms with …

The Role Of Surprise In Guessing Games, Justin Carpender

Honors Program Theses and Projects

In this thesis we will study the connection between game structure, surprise, and guessing strategies for these first two versions of a word guessing game. Our analysis will have three levels: one, a basic understanding of language and letter probabilities and the creation of programs that seek to use the structure of a game to efficiently guess words; two, an introduction of mathematical background and Information Theory; three, an analysis of the games and their corresponding guesses via a creative use of the key ideas of Information Theory, particularly, the concepts of surprise and entropy.

Vertex-Magic Total Labeling On G-Sun Graphs, Melissa Mejia

Honors Program Theses and Projects

Graph labeling is an immense area of research in mathematics, specifically graph theory. There are many types of graph labelings such as harmonious, magic, and lucky labelings. This paper will focus on magic labelings. Graph theorists are particularly interested in magic labelings because of a simple problem regarding tree graphs introduced in the 1990’s. The problem is still unsolved after almost thirty years. Researchers have studied magic labelings on other graphs in addition to tree graphs. In this paper we will consider vertex-magic labelings on G-sun graphs. We will give vertex-magic total labelings for ladder sun graphs and complete bipartite …

Data Engineering Techniques And Designs With Music Generating Neural Networks, Noah Solomon

Honors Program Theses and Projects

The generation of music artificially is an interesting concept to many and has received a lot of attention in recent years. The advancement of neural networks has allowed for the creation of models that can seemingly generate music creatively to mimic a specific genre or composer. This project delved deep into the many ways to construct music generating neural networks and compared different model architectures and data engineering techniques. Three main types of models were implemented and the resulting generated music was evaluated with respect to the melody, note agreeableness, and rhythm. These models used the Bach Chorales corpus as …

Spectral Analysis Of Multiscale Cultural Traits On Twitter, Chandler Squires, Nikhil Kunapuli, Yaneer Bar-Yam, Alfredo Morales

Northeast Journal of Complex Systems (NEJCS)

Understanding and mapping the emergence and boundaries of cultural areas is a challenge for social sciences. In this paper, we present a method for analyzing the cultural composition of regions via Twitter hashtags. Cultures can be described as distinct combination of traits which we capture via principal component analysis (PCA). We investigate the top 8 PCA components of an area including France, Spain, and Portugal, in terms of the geographic distribution of their hashtag composition. We also discuss relationships between components and the insights those relationships can provide into the structure of a cultural space. Finally, we compare the spatial …

Solving Partial Differential Equations Using The Finite Difference Method And The Fourier Spectral Method, Jenna Siobhan Parkinson

Undergraduate Student Research Internships Conference

This paper discusses the finite difference method and the Fourier spectral method for solving partial differential equations.

Lecture Note On Delay Differential Equation, Wenfeng Liu

Undergraduate Student Research Internships Conference

Delay differential equation is an important field in applied mathematics since it concerns more situations than the ordinary differential equation. Moreover, it makes the equations more applicable to the object's movement in real life.

My project is the lecture note on the delay differential equation provides a basic introduction to the delay differential equation, its application in real life, improving the ordinary differential equation, the primary method and definition for solving the delay differential equation and the use of the way in the ordinary differential equation to estimate the periodic solution to the delay differential equation.

Simulating And Modelling Adaptive Walks With The Nk Model, Abigail K. Kushnir

Undergraduate Student Research Internships Conference

This presentation outlines results obtained by simulating adaptive walks using the NK model. We were interested in how the mutation bias affects the distribution of fitness effects and how we could use our results to form theoretical equations to model the behaviour of a walk. Necessary biological background is also described.

A Kuramoto Model Approach To Predicting Chaotic Systems With Echo State Networks, Sophie Wu, Jackson Howe

Undergraduate Student Research Internships Conference

An Echo State Network (ESN) with an activation function based on the Kuramoto model (Kuramoto ESN) is implemented, which can successfully predict the logistic map for a non-trivial number of time steps. The reservoir in the prediction stage exhibits binary dynamics when a good prediction is made, but the oscillators in the reservoir display a larger variability in states as the ESN’s prediction becomes worse. Analytical approaches to quantify how the Kuramoto ESN’s dynamics relate to its prediction are explored, as well as how the dynamics of the Kuramoto ESN relate to another widely studied physical model, the Ising model.

Travelling Wave Solutions On A Cylindrical Geometry, Karnav R. Raval

Undergraduate Student Research Internships Conference

Fluid equations are generally quite difficult and computationally-expensive to solve. However, if one is primarily interested in how the surface of the fluid deforms, we can re-formulate the governing equations purely in terms of free surface variables. Reformulating equations in such a way drastically cuts down on computational cost, and may be useful in areas such as modelling blood flow. Here, we study one such free-boundary formulation on a cylindrical geometry.

Mathematical Models Yield Insights Into Cnns: Applications In Natural Image Restoration And Population Genetics, Ryan Cecil

Electronic Theses and Dissertations

Due to a rise in computational power, machine learning (ML) methods have become the state-of-the-art in a variety of fields. Known to be black-box approaches, however, these methods are oftentimes not well understood. In this work, we utilize our understanding of model-based approaches to derive insights into Convolutional Neural Networks (CNNs). In the field of Natural Image Restoration, we focus on the image denoising problem. Recent work have demonstrated the potential of mathematically motivated CNN architectures that learn both `geometric' and nonlinear higher order features and corresponding regularizers. We extend this work by showing that not only can geometric features …