Numerical Analysis and Computation Commons^™

Mathematical Modeling Of Nonlinear Problem Biological Population In Not Divergent Form With Absorption, And Variable Density, Maftuha Sayfullayeva

Acta of Turin Polytechnic University in Tashkent

В работе установлены критические и двойные критические случаи, обусловленные представлением двойного нелинейного параболического уравнения с переменной плотностью с поглощением в "радиально-симметричной" форме.Такое представление исходного уравнения дало возможность легко построить решения типа Зельдовоч-Баренбатт-Паттл для критических случаев в виде функций сравнения.

Cover Song Identification - A Novel Stem-Based Approach To Improve Song-To-Song Similarity Measurements, Lavonnia Newman, Dhyan Shah, Chandler Vaughn, Faizan Javed

SMU Data Science Review

Music is incorporated into our daily lives whether intentional or unintentional. It evokes responses and behavior so much so there is an entire study dedicated to the psychology of music. Music creates the mood for dancing, exercising, creative thought or even relaxation. It is a powerful tool that can be used in various venues and through advertisements to influence and guide human reactions. Music is also often "borrowed" in the industry today. The practices of sampling and remixing music in the digital age have made cover song identification an active area of research. While most of this research is focused …

Numerical Computations Of Vortex Formation Length In Flow Past An Elliptical Cylinder, Matthew Karlson, Bogdan Nita, Ashwin Vaidya

Department of Mathematics Facuty Scholarship and Creative Works

We examine two dimensional properties of vortex shedding past elliptical cylinders through numerical simulations. Specifically, we investigate the vortex formation length in the Reynolds number regime 10 to 100 for elliptical bodies of aspect ratio in the range 0.4 to 1.4. Our computations reveal that in the steady flow regime, the change in the vortex length follows a linear profile with respect to the Reynolds number, while in the unsteady regime, the time averaged vortex length decreases in an exponential manner with increasing Reynolds number. The transition in profile is used to identify the critical Reynolds number which marks the …

Matrix Low Rank Approximation At Sublinear Cost, Qi Luan

Dissertations, Theses, and Capstone Projects

A matrix algorithm runs at sublinear cost if the number of arithmetic operations involved is far fewer than the number of entries of the input matrix. Such algorithms are especially crucial for applications in the field of Big Data, where input matrices are so immense that one can only store a fraction of the entire matrix in memory of modern machines. Typically, such matrices admit Low Rank Approximation (LRA) that can be stored and processed at sublinear cost. Can we compute LRA at sublinear cost? Our counter example presented in Appendix C shows that no sublinear cost algorithm can compute …

Binary Neutron Star Mergers: Testing Ejecta Models For High Mass-Ratios, Allen Murray

The Journal of Purdue Undergraduate Research

Neutron stars are extremely dense stellar corpses which sometimes exist in orbiting pairs known as binary neutron star (BNS) systems. The mass ratio (q) of a BNS system is defined as the mass of the heavier neutron star divided by the mass of the lighter neutron star. Over time the neutron stars will inspiral toward one another and produce a merger event. Although rare, these events can be rich sources of observational data due to their many electromagnetic emissions as well as the gravitational waves they produce. The ability to extract physical information from such observations relies heavily on numerical …

Advection-Reaction-Diffusion Model Of Drug Concentration In A Lymph Node, Ting Yan

Mathematics Theses and Dissertations

It is recognized that there exist reservoirs of HIV located outside the bloodstream, and that these reservoirs hinder the efficacy of antiretroviral medication regimens in combating the virus. The prevailing theories regarding these reservoirs point to the lymphatic system. In this work, we discuss a novel computational model of viral dynamics in the lymph node, to allow numerical studies of viral “reservoirs” causing reinfection. Our model consists of a system of advection-reaction-diffusion partial differential equations (PDEs), where the diffusion coefficients vary between species (virus, drugs, lymphocytes) and include discontinuous jumps to capture differing properties of internal lymph node structures. We …

Analyzing Network Topology For Ddos Mitigation Using The Abelian Sandpile Model, Bhavana Panchumarthi, Monroe Ame Stephenson

altREU Projects

A Distributed Denial of Service (DDoS) is a cyber attack, which is capable of triggering a cascading failure in the victim network. While DDoS attacks come in different forms, their general goal is to make a network's service unavailable to its users. A common, but risky, countermeasure is to blackhole or null route the source, or the attacked destination. When a server becomes a blackhole, or referred to as the sink in the paper, the data that is assigned to it "disappears" or gets deleted. Our research shows how mathematical modeling can propose an alternative blackholing strategy that could improve …

Numerical Approximations Of Phase Field Equations With Physics Informed Neural Networks, Colby Wight

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Designing numerical algorithms for solving partial differential equations (PDEs) is one of the major research branches in applied and computational mathematics. Recently there has been some seminal work on solving PDEs using the deep neural networks. In particular, the Physics Informed Neural Network (PINN) has been shown to be effective in solving some classical partial differential equations. However, we find that this method is not sufficient in solving all types of equations and falls short in solving phase-field equations. In this thesis, we propose various techniques that add to the power of these networks. Mainly, we propose to embrace the …

Exploring Food Deserts And Environmental Impacts On Health In Chicago And Oregon, Sivasomasundari Arunarasu, Paulina Grzybowicz

altREU Projects

Food deserts are defined as, “an impoverished area where residents lack access to healthy foods”. This lack of access can be due to a combination of socioeconomic, geographic, and food-related variables, and has been proven to impact the health of residents in the area. In this project, several statistical and machine learning techniques are used to model the impact of food desserts and various other factors on health outcomes, including diabetes and obesity rates, in both the different neighborhoods in the City of Chicago and the various counties in the state of Oregon. The models are then used to determine …

Combating Covid On College Campuses: The Impact Of Structural Changes On Viral Transmissions, Jared Knofczynski, Aria Killebrew Bruehl, Ben Warner, Ryne Shelton

altREU Projects

One of the most significant issues in the COVID-19 pandemic is the reopening of schools while minimizing the transmission of coronavirus. Opportunities for evaluating the effectiveness of policies that might be utilized at such institutions are limited, as the necessary empirical data has not been gathered yet. Agent-based modeling, where various entities within an environment are simulated as agents, offers an opportunity to examine the effectiveness of various policies in a way that drastically minimizes the health and economic risks involved. Agent-based modeling is common within biology, ecology and other fields; and has seen some use within the coronavirus literature. …

An Adaptive Approach To Gibbs’ Phenomenon, Jannatul Ferdous Chhoa

Master's Theses

Gibbs’ Phenomenon, an unusual behavior of functions with sharp jumps, is encountered while applying the Fourier Transform on them. The resulting reconstructions have high frequency oscillations near the jumps making the reconstructions far from being accurate. To get rid of the unwanted oscillations, we used the Lanczos sigma factor to adjust the Fourier series and we came across three cases. Out of the three, two of them failed to give us the right reconstructions because either it was removing the oscillations partially but not entirely or it was completely removing them but smoothing out the jumps a little too much. …

Examining The Accumulation Statistics Of Index1 Saddle Points On The Potential Energy Surface And Imposing Early Termination On A Rejection Scheme For Off Lattice Kinetic Monte Carlo, Jonathan W. Hicks

Doctoral Dissertations

In the calculation of time evolution of an atomic system where a chemical reaction and/or diffusion occurs, off-lattice kinetic Monte Carlo methods can be used to overcome timescale and lattice based limitations from other methods such as Molecular Dynamics and kinetic Monte Carlo procedures. Off-lattice kinetic Monte Carlo methods rely on a harmonic approximation to Transition State Theory, in which the rate of the rare transitions from one energy minimum to a neighboring minimum require surmounting a minimum energy barrier on the Potential Energy Surface, which is found at an index-1 saddle point commonly referred to as a transition state. …

Variable Compact Multi-Point Upscaling Schemes For Anisotropic Diffusion Problems In Three-Dimensions, James Quinlan

Dissertations

Simulation is a useful tool to mitigate risk and uncertainty in subsurface flow models that contain geometrically complex features and in which the permeability field is highly heterogeneous. However, due to the level of detail in the underlying geocellular description, an upscaling procedure is needed to generate a coarsened model that is computationally feasible to perform simulations. These procedures require additional attention when coefficients in the system exhibit full-tensor anisotropy due to heterogeneity or not aligned with the computational grid. In this thesis, we generalize a multi-point finite volume scheme in several ways and benchmark it against the industry-standard routines. …

Hybrid Symbolic-Numeric Computing In Linear And Polynomial Algebra, Leili Rafiee Sevyeri

Electronic Thesis and Dissertation Repository

In this thesis, we introduce hybrid symbolic-numeric methods for solving problems in linear and polynomial algebra. We mainly address the approximate GCD problem for polynomials, and problems related to parametric and polynomial matrices. For symbolic methods, our main concern is their complexity and for the numerical methods we are more concerned about their stability. The thesis consists of 5 articles which are presented in the following order:

Chapter 1, deals with the fundamental notions of conditioning and backward error. Although our results are not novel, this chapter is a novel explication of conditioning and backward error that underpins the rest …

Dynamics Of Discontinuities In Elastic Solids, Arkadi Berezovski, Mihhail Berezovski

Publications

The paper is devoted to evolving discontinuities in elastic solids. A discontinuity is represented as a singular set of material points. Evolution of a discontinuity is driven by the configurational force acting at such a set. The main attention is paid to the determination of the velocity of a propagating discontinuity. Martensitic phase transition fronts and brittle cracks are considered as representative examples.

Optimal Allocation Of Two Resources In Annual Plants, David Mcmorris

Department of Mathematics: Dissertations, Theses, and Student Research

The fitness of an annual plant can be thought of as how much fruit is produced by the end of its growing season. Under the assumption that annual plants grow to maximize fitness, we can use techniques from optimal control theory to understand this process. We introduce two models for resource allocation in annual plants which extend classical work by Iwasa and Roughgarden to a case where both carbohydrates and mineral nutrients are allocated to shoots, roots, and fruits in annual plants. In each case, we use optimal control theory to determine the optimal resource allocation strategy for the plant …

Desarrollo De Una Aplicación Móvil Para La Resolución De Problemas De Optimización Del Cálculo Diferencial, Julián David Arévalo Garcia, Camilo Sebastian Guerrero Briceño

Ingeniería en Automatización

El presente trabajo consiste en el desarrollo de una aplicación móvil que facilite la comprensión de un problema de optimización en los estudiantes de cálculo diferencial, y a su vez de soporte al proyecto de investigación “Aprendiendo a solucionar problemas de optimización del cálculo diferencial a través de tecnología móvil”. Este trabajo es efectuado por los autores como auxiliares del proyecto de investigación. Las actividades que se tendrán en cuenta en el desarrollo incluyen un levantamiento de requerimientos en bases de datos sobre las aplicaciones móviles existentes en el mercado y un análisis en el aprendizaje de las matemáticas, en …

Multigrid Methods For Elliptic Optimal Control Problems, Sijing Liu

LSU Doctoral Dissertations

In this dissertation we study multigrid methods for linear-quadratic elliptic distributed optimal control problems.

For optimal control problems constrained by general second order elliptic partial differential equations, we design and analyze a $P_1$ finite element method based on a saddle point formulation. We construct a $W$-cycle algorithm for the discrete problem and show that it is uniformly convergent in the energy norm for convex domains. Moreover, the contraction number decays at the optimal rate of $m^{-1}$, where $m$ is the number of smoothing steps. We also prove that the convergence is robust with respect to a regularization parameter. The robust …

Basins Of Convergence In The Collinear Restricted Four-Body Problem With A Repulsive Manev Potential, Euaggelos E. Zotos, Md Sanam Suraj, Rajiv Aggarwal, Charanpreet Kaur

Applications and Applied Mathematics: An International Journal (AAM)

The Newton-Raphson basins of convergence, related to the equilibrium points, in the collinear restricted four-body problem with repulsive Manev potential are numerically investigated. We monitor the parametric evolution of the position as well as of the stability of the equilibrium points, as a function of the parameter e. The multivariate Newton-Raphson optimal method is used for revealing the basins of convergence, by classifying dense grids of initial conditions in several types of two-dimensional planes. We perform a systematic and thorough analysis in an attempt to understand how the parameter e affects the geometry as well as the basin entropy …

Mathematical Modeling For Studying The Sustainability Of Plants Subject To The Stress Of Two Distinct Herbivores, B. Chen-Charpentier, M. C.A. Leite, O. Gaoue, F. B. Agusto

Applications and Applied Mathematics: An International Journal (AAM)

Viability of plants, especially endangered species, are usually affected by multiple stressors, including insects, herbivores, environmental factors and other plant species. We present new mathematical models, based on systems of ordinary differential equations, of two distinct herbivore species feeding (two stressors) on the same plant species. The new feature is the explicit functional form modeling the simultaneous feedback interactions (synergistic or additive or antagonistic) between the three species in the ecosystem. The goal is to investigate whether the coexistence of the plant and both herbivore species is possible (a sustainable system) and under which conditions sustainability is feasible. Our theoretical …

Dynamic Optimal Control For Multi-Chemotherapy Treatment Of Dual Listeriosis Infection In Human And Animal Population, B. Echeng Bassey

Applications and Applied Mathematics: An International Journal (AAM)

Following the rising cases of high hospitalization versa-vise incessant fatality rates and the close affinity of listeriosis with HIV/AIDS infection, which often emanates from food-borne pathogens associated with listeria monocytogenes infection, this present paper seek and formulated as penultimate model, an 8-Dimensional classical mathematical Equations which directly accounted for the biological interplay of dual listeriosis virions with dual set of population (human and animals). The model was studied under multiple chemotherapies (trimethoprim-sulphamethoxazole with a combination of penicillin or ampicillin and/or gentamicin). Using ODE’s, the positivity and boundedness of system solutions was investigated with model presented as an optimal control problem. …

Exploring The Convergence Properties Of A New Modified Newton-Raphson Root Method, Euaggelo E. Zotos, Wei Chen

Applications and Applied Mathematics: An International Journal (AAM)

We examine the convergence properties of a modified Newton-Raphson root method, by using a simple complex polynomial equation, as a test example. In particular, we numerically investigate how a parameter, entering the iterative scheme, affects the efficiency and the speed of the method. Color-coded polynomiographs are deployed for presenting the regions of convergence, as well as the fractality degree of the complex plane. We demonstrate that the behavior of the modified Newton-Raphson method is correlated with the numerical value of the parameter 1. Additionally, there are cases for which the method works flawlessly, while in some other cases we encounter …

A Study Of The Design Of Adaptive Camber Winglets, Justin J. Rosescu

Master's Theses

A numerical study was conducted to determine the effect of changing the camber of a winglet on the efficiency of a wing in two distinct flight conditions. Camber was altered via a simple plain flap deflection in the winglet, which produced a constant camber change over the winglet span. Hinge points were located at 20%, 50% and 80% of the chord and the trailing edge was deflected between -5° and +5°. Analysis was performed using a combination of three-dimensional vortex lattice method and two-dimensional panel method to obtain aerodynamic forces for the entire wing, based on different winglet camber configurations. …

A New Class Of Discontinuous Galerkin Methods For Wave Equations In Second-Order Form, Lu Zhang

Mathematics Theses and Dissertations

Discontinuous Galerkin methods are widely used in many practical fields. In this thesis, we focus on a new class of discontinuous Galerkin methods for second-order wave equations. This thesis is constructed by three main parts. In the first part, we study the convergence properties of the energy-based discontinuous Galerkin proposed in [3] for wave equations. We improve the existing suboptimal error estimates to an optimal convergence rate in the energy norm. In the second part, we generalize the energy-based discontinuous Galerkin method proposed in [3] to the advective wave equation and semilinear wave equation in second-order form. Energy-conserving or energy-dissipating …

The Boundary Element Method For Parabolic Equation And Its Implementation In Bem++, Sihao Wang

Mathematics Theses and Dissertations

The goal of this work is to develop a fast method for solving Galerkin discretizations of boundary integral formulations of the heat equation. The main contribution of this work is to devise a new fast algorithm for evaluating the dense matrices of the discretized integral equations.

Similar to the parabolic FMM, this method is based on a subdivision of the matrices into an appropriate hierarchical block structure. However, instead of an expansion of the kernel in both space and time we interpolate kernel in the temporal variables and use of the adaptive cross approximation (ACA) in the spatial variables.

The …

Parallel-In-Time Simulation Of Biofluids, Weifan Liu, Minghao Rostami

Biology and Medicine Through Mathematics Conference

No abstract provided.

On The Properties Of Solutions Of A Cross-Diffusion System With Nonlinear Boundary Flux, Zafar Rakhmonov, Jasur Urunbaev, Bobur Allaberdiyev

Scientific Journal of Samarkand University

In this paper, based on a self-similar analysis and the method of standard equations, the properties of a nonlinear cross-diffusion system coupled via nonlocal boundary conditions are studied. We are investigated the qualitative properties of solutions of a nonlinear system of parabolic equations of cross-diffusion in a medium coupled with nonlinear boundary conditions. It is proved that for certain values of the numerical parameters of the nonlinear cross-diffusion system of parabolic equations coupled via nonlinear boundary conditions, they may not have global solutions in time. Based on a self-similar analysis and the principle of comparing solutions, a critical exponent of …

Sensor Data Analysis In Smart Buildings, Manuel A. Mane Penton

Publications and Research

Data analysis and Machine Learning are destined to evolve the current technology infrastructure by solving technology and economy demands present mainly in developed cities like New York. This research proposes a machine learning (ML) based solution to alleviate one of the main issues that big buildings such as CUNY campuses have, that is the waste of energy resources. The analysis of data coming from the readings of different deployed sensors such as CO2, humidity and temperature can be used to estimate occupancy in a specific room and building in general. The outcome of this research established a relationship between the …

A Method To Reclaim Multifractal Statistics From Saturated Images, Jeremy Juybari

Electronic Theses and Dissertations

The CompuMAINE lab has developed a patented computational cancer detection method utilizing the 2D Wavelet Transform Modulus Maxima (WTMM) method to help predict disrupted, tumor-associated breast tissue from mammography. The lab has a database of mammograms in which some of the image subregions contain artefacts which are excluded from the analysis, image saturation is one such artefact. To maximize statistical power in our clinical analyses, our goal is therefore to minimize the rejection of image subregions containing artefacts. The goal of this particular project is to explore the effects of image saturation on the resulting multifractal statistics from the 2D …

Joint Inversion Of Gpr And Er Data, Diego Domenzain

Boise State University Theses and Dissertations

Imaging the subsurface can shed knowledge on important processes needed in a modern day human's life such as ground-water exploration, water resource monitoring, contaminant and hazard mitigation, geothermal energy exploration and carbon dioxide storage. As computing power expands, it is becoming ever more feasible to increase the physical complexity of Earth's exploration methods, and hence enhance our understanding of the subsurface.

We use non-invasive geophysical active source methods that rely on electromagnetic fields to probe the depths of the Earth. In particular, we use Ground penetrating radar (GPR) and Electrical resistivity (ER). Both methods are sensitive to electrical conductivity while …