Numerical Integration Through Concavity Analysis, 2021 Embry-Riddle Aeronautical University

#### Numerical Integration Through Concavity Analysis, Daniel J. Pietz

*Rose-Hulman Undergraduate Mathematics Journal*

We introduce a relationship between the concavity of a C2 func- tion and the area bounded by its graph and secant line. We utilize this relationship to develop a method of numerical integration. We then bound the error of the approximation, and compare to known methods, finding an improvement in error bound over methods of comparable computational complexity.

Neither “Post-War” Nor Post-Pregnancy Paranoia: How America’S War On Drugs Continues To Perpetuate Disparate Incarceration Outcomes For Pregnant, Substance-Involved Offenders, 2021 Pitzer College

#### Neither “Post-War” Nor Post-Pregnancy Paranoia: How America’S War On Drugs Continues To Perpetuate Disparate Incarceration Outcomes For Pregnant, Substance-Involved Offenders, Becca S. Zimmerman

*Pitzer Senior Theses*

This thesis investigates the unique interactions between pregnancy, substance involvement, and race as they relate to the War on Drugs and the hyper-incarceration of women. Using ordinary least square regression analyses and data from the Bureau of Justice Statistics’ 2016 Survey of Prison Inmates, I examine if (and how) pregnancy status, drug use, race, and their interactions influence two length of incarceration outcomes: sentence length and amount of time spent in jail between arrest and imprisonment. The results collectively indicate that pregnancy decreases length of incarceration outcomes for those offenders who are *not *substance-involved but not evenhandedly -- benefitting white pregnant ...

Design Project: Smart Headband, 2021 The University of Akron

#### Design Project: Smart Headband, John Michel, Jack Durkin, Noah Lewis

*Williams Honors College, Honors Research Projects*

Concussion in sports is a prevalent medical issue. It can be difficult for medical professionals to diagnose concussions. With the fast pace nature of many sports, and the damaging effects of concussions, it is important that any concussion risks are assessed immediately. There is a growing trend of wearable technology that collects data such as steps and provides the wearer with in-depth information regarding their performance. The Smart Headband project created a wearable that can record impact data and provide the wearer with a detailed analysis on their risk of sustaining a concussion. The Smart Headband uses accelerometers and gyroscopes ...

Fractals, Fractional Derivatives, And Newton-Like Methods, 2021 Claremont Colleges

#### Fractals, Fractional Derivatives, And Newton-Like Methods, Eleanor Byrnes

*HMC Senior Theses*

Inspired by the fractals generated by the discretizations of the Continuous Newton Method and the notion of a fractional derivative, we ask what it would mean if such a fractional derivative were to replace the derivatives in Newton's Method. This work, largely experimental in nature, examines these new iterative methods by generating their Julia sets, computing their fractal dimension, and in certain tractable cases examining the behaviors using tools from dynamical systems.

Multigrid For The Nonlinear Power Flow Equations, 2020 Southern Methodist University

#### Multigrid For The Nonlinear Power Flow Equations, Enrique Pereira Batista

*Mathematics Theses and Dissertations*

The continuously changing structure of power systems and the inclusion of renewable

energy sources are leading to changes in the dynamics of modern power grid,

which have brought renewed attention to the solution of the AC power flow equations.

In particular, development of fast and robust solvers for the power flow problem

continues to be actively investigated. A novel multigrid technique for coarse-graining

dynamic power grid models has been developed recently. This technique uses an

algebraic multigrid (AMG) coarsening strategy applied to the weighted

graph Laplacian that arises from the power network's topology for the construction

of coarse-grain approximations ...

Uncertainty Quantification Of Nonreflecting Boundary Schemes, 2020 Southern Methodist University

#### Uncertainty Quantification Of Nonreflecting Boundary Schemes, Brian Citty

*Mathematics Theses and Dissertations*

Numerical methods have been developed to solve partial differential equations involving the far-field radiation of waves. In addition, there has been recent interest in uncertainty quantification- a burgeoning field involving solving PDEs where random variables are used to model uncertainty in the data. In this thesis we will apply uncertainty quantification methodology to the 1D and 2D wave equation with nonreflecting boundary. We first derive a boundary condition for the 1D wave equation assuming several models of the random wave speed. Later we use our result to compare to an asymptotic SDE approach, and finally we repeat our analysis for ...

The Revised Nim For Solving The Non-Linear System Variant Boussinesq Equations And Comparison With Nim, 2020 University of Mosul, Mosul

#### The Revised Nim For Solving The Non-Linear System Variant Boussinesq Equations And Comparison With Nim, Oday Ahmed Jasim

*Karbala International Journal of Modern Science*

This research aims to guide researchers to use a new method, and it is the Revised New Iterative Method (RNIM) to solve partial differential equation systems and apply them to solve problems in various disciplines such as chemistry, physics, engineering and medicine. In this paper, the numerical solutions of the nonlinear Variable Boussinesq Equation System (VBE) were obtained using a new modified iterative method (RNIM); this was planned by (Bhaleker and Datterder-Gejj). A numerical solution to the Variable Boussinesq Equation System (VBE) was also found using a widely known method, a new iterative method (NIM). By comparing the numerical solutions ...

Longitudinal Partitioning Waveform Relaxation Methods For The Analysis Of Transmission Line Circuits, 2020 The University of Western Ontario

#### Longitudinal Partitioning Waveform Relaxation Methods For The Analysis Of Transmission Line Circuits, Tarik Menkad

*Electronic Thesis and Dissertation Repository*

Three research projects are presented in this manuscript. Projects one and two describe two waveform relaxation algorithms (WR) with longitudinal partitioning for the time-domain analysis of transmission line circuits. Project three presents theoretical results about the convergence of WR for chains of general circuits.

The first WR algorithm uses a assignment-partition procedure that relies on inserting external series combinations of positive and negative resistances into the circuit to control the speed of convergence of the algorithm. The convergence of the subsequent WR method is examined, and fast convergence is cast as a generic optimization problem in the frequency-domain. An automatic ...

Using Statistical Analysis To Examine Weather Variability In New York City, 2020 CUNY New York City College of Technology

#### Using Statistical Analysis To Examine Weather Variability In New York City, Ryan Chen, Yuhuang Wang, Jiehao Huang

*Publications and Research*

As the overall temperature of Earth continues to warm, atmospheric hazards (e.g. heatwaves, cyclones) may be driving increases in climatological trends. This study examines the daily precipitation and temperature record of the greater New York City region during the 1979-2014 period. Daily station observations from three greater New York City airports: John F. Kennedy (JFK), LaGuardia (LGA) and Newark (EWR), are used in this study. Climatological & statistical analyses are performed for the weather variability of New York City metro area to understand the impacts of climate change.The temperature climatology reveals a distinct seasonal cycle, while the precipitation climatology ...

A Collection Of Fast Algorithms For Scalar And Vector-Valued Data On Irregular Domains: Spherical Harmonic Analysis, Divergence-Free/Curl-Free Radial Basis Functions, And Implicit Surface Reconstruction, 2020 Boise State University

#### A Collection Of Fast Algorithms For Scalar And Vector-Valued Data On Irregular Domains: Spherical Harmonic Analysis, Divergence-Free/Curl-Free Radial Basis Functions, And Implicit Surface Reconstruction, Kathryn Primrose Drake

*Boise State University Theses and Dissertations*

This dissertation addresses problems that arise in a diverse group of fields including cosmology, electromagnetism, and graphic design. While these topics may seem disparate, they share a commonality in their need for fast and accurate algorithms which can handle large datasets collected on irregular domains. An important issue in cosmology is the calculation of the angular power spectrum of the cosmic microwave background (CMB) radiation. CMB photons offer a direct insight into the early stages of the universe's development and give the strongest evidence for the Big Bang theory to date. The Hierarchical Equal Area isoLatitude Pixelation (HEALPix) grid ...

Sum Of Cubes Of The First N Integers, 2020 California State University, San Bernardino

#### Sum Of Cubes Of The First N Integers, Obiamaka L. Agu

*Electronic Theses, Projects, and Dissertations*

In Calculus we learned that Sum^{n}_{k=1} k = [n(n+1)]/2 , that Sum^{n}_{k=1} k^2 = [n(n+1)(2n+1)]/6 , and that Sum^{n}_{k=1} k^{3} = (n(n+1)/2)^{2}. These formulas are useful when solving for the area below quadratic or cubic function over an interval [a, b]. This tedious process, solving for areas under a quadratic or a cubic, served as motivation for the introduction of Riemman integrals. For the overzealous math student, these steps were replaced by a simpler method of evaluating antiderivatives at ...

Asymptotic Analysis Of Radial Point Rupture Solutions For Elliptic Equations, 2020 Illinois State University

#### Asymptotic Analysis Of Radial Point Rupture Solutions For Elliptic Equations, Attou Miloua

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Deep Learning With Physics Informed Neural Networks For The Airborne Spread Of Covid-19 In Enclosed Spaces, 2020 George Mason University

#### Deep Learning With Physics Informed Neural Networks For The Airborne Spread Of Covid-19 In Enclosed Spaces, Udbhav Muthakana, Padmanabhan Seshaiyer, Maziar Raissi, Long Nguyen

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Mathematical Modelling And In Silico Experimentation To Estimate The Quantity Of Covid-19 Infected Individuals In Tijuana, México, 2020 Tijuana Institute of Technology, México

#### Mathematical Modelling And In Silico Experimentation To Estimate The Quantity Of Covid-19 Infected Individuals In Tijuana, México, Karla A. Encinas, Luis N. Coria, Paul A. Valle

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

From Wave Propagation To Spin Dynamics: Mathematical And Computational Aspects, 2020 University of New Mexico

#### From Wave Propagation To Spin Dynamics: Mathematical And Computational Aspects, Oleksii Beznosov

*Mathematics & Statistics ETDs*

In this work we concentrate on two separate topics which pose certain numerical challenges. The first topic is the spin dynamics of electrons in high-energy circular accelerators. We introduce a stochastic differential equation framework to study spin depolarization and spin equilibrium. This framework allows the mathematical study of known equations and new equations modelling the spin distribution of an electron bunch. A spin distribution is governed by a so-called Bloch equation, which is a linear Fokker-Planck type PDE, in general posed in six dimensions. We propose three approaches to approximate solutions, using analytical and modern numerical techniques. We also present ...

Numerical Simulations Of Nonlinear Waves And Their Stability: Stokes Waves And Nonlinear Schroedinger Equation, 2020 Doctoral Student, Applied Mathematics

#### Numerical Simulations Of Nonlinear Waves And Their Stability: Stokes Waves And Nonlinear Schroedinger Equation, Anastassiya Semenova

*Mathematics & Statistics ETDs*

The present work offers an investigation of dynamics and stability of nonlinear waves in Hamiltonian systems. The first part of the manuscript discusses the classical problem of water waves on the surface of an ideal fluid in 2D. We demonstrate how to construct the Stokes waves, and how to apply a continuation method to find waves in close vicinity to the limiting Stokes wave. We provide new insight into the stability of the Stokes waves by identifying previously inaccessible branches of instability in the equations of motion for the fluid. We provide numerical evidence that pairs of unstable eigenvalues of ...

Applying The Data: Predictive Analytics In Sport, 2020 University of Washington, Tacoma

#### Applying The Data: Predictive Analytics In Sport, Anthony Teeter, Margo Bergman

*Access*: Interdisciplinary Journal of Student Research and Scholarship*

The history of wagering predictions and their impact on wide reaching disciplines such as statistics and economics dates to at least the 1700’s, if not before. Predicting the outcomes of sports is a multibillion-dollar business that capitalizes on these tools but is in constant development with the addition of big data analytics methods. Sportsline.com, a popular website for fantasy sports leagues, provides odds predictions in multiple sports, produces proprietary computer models of both winning and losing teams, and provides specific point estimates. To test likely candidates for inclusion in these prediction algorithms, the authors developed a computer model ...

A Phase-Field Approach To Diffusion-Driven Fracture, 2020 Louisiana State University and Agricultural and Mechanical College

#### A Phase-Field Approach To Diffusion-Driven Fracture, Friedrich Wilhelm Alexander Dunkel

*LSU Doctoral Dissertations*

In recent years applied mathematicians have used modern analysis to develop variational phase-field models of fracture based on Griffith's theory. These variational phase-field models of fracture have gained popularity due to their ability to predict the crack path and handle crack nucleation and branching.

In this work, we are interested in coupled problems where a diffusion process drives the crack propagation. We extend the variational phase-field model of fracture to account for diffusion-driving fracture and study the convergence of minimizers using gamma-convergence. We will introduce Newton's method for the constrained optimization problem and present an algorithm to solve ...

Numerical Approach To Non-Darcy Mixed Convective Flow Of Non-Newtonian Fluid On A Vertical Surface With Varying Surface Temperature And Heat Source, 2020 Department of Mathematics, College of Engineering and Technology,Bhubaneswar-751029, Odisha, INDIA

#### Numerical Approach To Non-Darcy Mixed Convective Flow Of Non-Newtonian Fluid On A Vertical Surface With Varying Surface Temperature And Heat Source, Ajaya Prasad Baitharu, Sachidananda Sahoo, Gauranga Charan Dash

*Karbala International Journal of Modern Science*

An analysis is performed on non-Darcy mixed convective flow of non-Newtonian fluid past a vertical surface in the presence of volumetric heat source originated by some electromechanical or other devices. Further, the vertical bounding surface is subjected to power law variation of wall temperature, but the numerical solution is obtained for isothermal case. In the present non-Darcy flow model, effects of high flow rate give rise to inertia force. The inertia force in conjunction with volumetric heat source/sink is considered in the present analysis. The Runge-Kutta method of fourth order with shooting technique has been applied to obtain the ...

Heat And Mass Transfer Of Mhd Casson Nanofluid Flow Through A Porous Medium Past A Stretching Sheet With Newtonian Heating And Chemical Reaction, 2020 Veer Surenrda Sai University of Technology, Burla, India

#### Heat And Mass Transfer Of Mhd Casson Nanofluid Flow Through A Porous Medium Past A Stretching Sheet With Newtonian Heating And Chemical Reaction, Lipika Panigrahi, Jayaprakash Panda, Kharabela Swain, Gouranga Charan Dash

*Karbala International Journal of Modern Science*

An analysis is made to investigate the effect of inclined magnetic field on Casson nanofluid over a stretching sheet embedded in a saturated porous matrix in presence of thermal radiation, non-uniform heat source/sink. The heat equation takes care of energy loss due to viscous dissipation and Joulian dissipation. The mass transfer and heat equation become coupled due to thermophoresis and Brownian motion, two important characteristics of nanofluid flow. The convective terms of momentum, heat and mass transfer equations render the equations non-linear. This present flow model is pressure gradient driven and it is eliminated with the help of potential ...