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Articles 1  30 of 1035
FullText Articles in Numerical Analysis and Computation
A High Order Finite Difference Method To Solve The Steady State NavierStokes Equations, Nihal J. Siriwardana, Saroj P. Pradhan
A High Order Finite Difference Method To Solve The Steady State NavierStokes Equations, Nihal J. Siriwardana, Saroj P. Pradhan
Applications and Applied Mathematics: An International Journal (AAM)
In this article, we develop a fourth order finite difference method to solve the system of steady state NavierStokes equations and apply it to the benchmark problem known as the square cavity flow problem. The numerical results of 𝑢velocity components and 𝑣velocity components obtained at the center of the cavity are compared with the results obtained by the method developed by Greenspan and Casulli to solve the time dependent system of NavierStokes equations. The method described in this article is easy to implement and it has been shown to be more efficient and stable than the method by Greenspan and ...
Hybrid Algorithm For Singularly Perturbed Delay Parabolic Partial Differential Equations, Imiru T. Daba, Gemechis F. Duressa
Hybrid Algorithm For Singularly Perturbed Delay Parabolic Partial Differential Equations, Imiru T. Daba, Gemechis F. Duressa
Applications and Applied Mathematics: An International Journal (AAM)
This study aims at constructing a numerical scheme for solving singularly perturbed parabolic delay differential equations. Taylor’s series expansion is applied to approximate the shift term. The obtained result is approximated by using the implicit Euler method in the temporal discretization on a uniform step size with the hybrid numerical scheme consisting of the midpoint upwind method in the outer layer region and the cubic spline method in the inner layer region on a piecewise uniform Shishkin mesh in the spatial discretization. The constructed scheme is an ε−uniformly convergent accuracy of order one. Some test examples are considered ...
ThermalDiffusion And DiffusionThermo Effects On Heat And Mass Transfer In Chemically Reacting Mhd Casson Nanofluid With Viscous Dissipation, Timothy L. Oyekunle, Mojeed T. Akolade, Samson A. Agunbiade
ThermalDiffusion And DiffusionThermo Effects On Heat And Mass Transfer In Chemically Reacting Mhd Casson Nanofluid With Viscous Dissipation, Timothy L. Oyekunle, Mojeed T. Akolade, Samson A. Agunbiade
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we examined the combined effects of dissipation and chemical reaction in Casson nanofluid motion through a vertical porous plate subjected to the magnetic field effect placed perpendicular to the flow channel. The physical problem is modeled using partial differential equations (PDEs). These sets of PDEs, with suitable similarity transformations, are simplified into ordinary differential equations (ODEs). Collocation technique with legendary basis function is utilized in solving the transformed equations. The numerical analysis on velocity, concentration, and temperature are plotted and tabled for different flow parameters. Our findings show that by raising the Casson parameter close to infinity ...
Two Temperature DualPhaseLag Fractional Thermal Investigation Of Heat Flow Inside A Uniform Rod, Vinayak Kulkarni, Gaurav Mittal
Two Temperature DualPhaseLag Fractional Thermal Investigation Of Heat Flow Inside A Uniform Rod, Vinayak Kulkarni, Gaurav Mittal
Applications and Applied Mathematics: An International Journal (AAM)
A nonclassical, coupled, fractionally ordered, dualphaselag (DPL) heat conduction model has been presented in the framework of the twotemperature theory in the bounded Cartesian domain. Due to the application of twotemperature theory, the governing heat conduction equation is wellposed and satisfying the required stability criterion prescribed for a DPL model. The mathematical formulation has been applied to a uniform rod of finite length with traction free ends considered in a perfectly thermoelastic homogeneous isotropic medium. The initial end of the rod has been exposed to the convective heat flux and energy dissipated by convection into the surrounding medium through the ...
Generation And Statistical Properties For LindleyPolynomial Distribution, Dariush Ghorbanzadeh
Generation And Statistical Properties For LindleyPolynomial Distribution, Dariush Ghorbanzadeh
Applications and Applied Mathematics: An International Journal (AAM)
For the modeling of the wind speed, we propose a family of distributions in polynomial form generating the Lindley distribution. We call this distribution LindleyPolynomial distribution. The estimation of parameters using the maximum product spacing estimation method. A real data set has been considered to illustrate the practical utility of the paper.
Computational Design Of Nonlinear StressStrain Of Isotropic Materials, Askhad M.Polatov, Akhmat M. Ikramov, Daniyarbek Razmukhamedov
Computational Design Of Nonlinear StressStrain Of Isotropic Materials, Askhad M.Polatov, Akhmat M. Ikramov, Daniyarbek Razmukhamedov
Chemical Technology, Control and Management
The article deals with the problems of numerical modeling of nonlinear physical processes of the stressstrain state of structural elements. An elastoplastic medium of a homogeneous solid material is investigated. The results of computational experiments on the study of the process of physically nonlinear deformation of isotropic elements of threedimensional structures with a system of one and doubleperiodic spherical cavities under uniaxial compression are presented. The influence and mutual influence of stress concentrators in the form of spherical cavities, vertically located two cavities and a horizontally located system of two cavities on the deformation of the structure are investigated. Numerical ...
HighOrder Flexible Multirate Integrators For Multiphysics Applications, Rujeko Chinomona
HighOrder Flexible Multirate Integrators For Multiphysics Applications, Rujeko Chinomona
Mathematics Theses and Dissertations
Traditionally, time integration methods within multiphysics simulations have been chosen to cater to the most restrictive dynamics, sometimes at a great computational cost. Multirate integrators accurately and efficiently solve systems of ordinary differential equations that exhibit different time scales using two or more time steps. In this thesis, we explore three classes of time integrators that can be classified as onestep multistage multirate methods for which the slow dynamics are evolved using a traditional one step scheme and the fast dynamics are solved through a sequence of modified initial value problems. Practically, the fast dynamics are subcycled using a small ...
Morgan Voyce Approach For Solution Bratu Problems, Bushra Eesa Kashiem
Morgan Voyce Approach For Solution Bratu Problems, Bushra Eesa Kashiem
Emirates Journal for Engineering Research
Bratu equations are substantial in electrostatic and plasma problem. The aim of this paper is design a morganvoyce approach for solving bratu problem. We present a morganvoyce polynomial along with significant properties; the effectiveness of the proposed algorithm is demonstrated by considering three numerical examples.
Lexicographic Sensitivity Functions For Nonsmooth Models In Mathematical Biology, Matthew D. Ackley
Lexicographic Sensitivity Functions For Nonsmooth Models In Mathematical Biology, Matthew D. Ackley
Electronic Theses and Dissertations
Systems of ordinary differential equations (ODEs) may be used to model a wide variety of realworld phenomena in biology and engineering. Classical sensitivity theory is wellestablished and concerns itself with quantifying the responsiveness of such models to changes in parameter values. By performing a sensitivity analysis, a variety of insights can be gained into a model (and hence, the realworld system that it represents); in particular, the information gained can uncover a system's most important aspects, for use in design, control or optimization of the system. However, while the results of such analysis are desirable, the approach that classical ...
A ComponentWise Approach To Smooth Extension Embedding Methods, Vivian Montiforte
A ComponentWise Approach To Smooth Extension Embedding Methods, Vivian Montiforte
Dissertations
Krylov Subspace Spectral (KSS) Methods have demonstrated to be highly scalable methods for PDEs. However, a current limitation of these methods is the requirement of a rectangular or boxshaped domain. Smooth Extension Embedding Methods (SEEM) use fictitious domain methods to extend a general domain to a simple, rectangular or boxshaped domain. This dissertation describes how these methods can be combined to extend the applicability of KSS methods, while also providing a componentwise approach for solving the systems of equations produced with SEEM.
Efficient Denoising Of High Resolution Color Digital Images Utilizing Krylov Subspace Spectral Methods, Eva Lynn Greenman
Efficient Denoising Of High Resolution Color Digital Images Utilizing Krylov Subspace Spectral Methods, Eva Lynn Greenman
Dissertations
The solution to a parabolic nonlinear diffusion equation using a Krylov Subspace Spectral method is applied to high resolution color digital images with parallel processing for efficient denoising. The evolution of digital image technology, processing power, and numerical methods must evolve to increase efficiency in order to meet current usage requirements. Much work has been done to perfect the edge detector in PeronaMalik equation variants, while minimizing the effects of artifacts. It is demonstrated that this implementation of a regularized partial differential equation model controls backward diffusion, achieves strong denoising, and minimizes blurring and other ancillary effects. By adaptively tuning ...
Application Of Randomness In Finance, Jose Sanchez, Daanial Ahmad, Satyanand Singh
Application Of Randomness In Finance, Jose Sanchez, Daanial Ahmad, Satyanand Singh
Publications and Research
Brownian Motion which is also considered to be a Wiener process and can be thought of as a random walk. In our project we had briefly discussed the fluctuations of financial indices and related it to Brownian Motion and the modeling of Stock prices.
Netsci High: Bringing Agency To Diverse Teens Through The Science Of Connected Systems, Stephen M. Uzzo, Catherine B. Cramer, Hiroki Sayama, Russell Faux
Netsci High: Bringing Agency To Diverse Teens Through The Science Of Connected Systems, Stephen M. Uzzo, Catherine B. Cramer, Hiroki Sayama, Russell Faux
Northeast Journal of Complex Systems (NEJCS)
This paper follows NetSci High, a decadelong initiative to inspire teams of teenage researchers to develop, execute and disseminate original research in network science. The project introduced high school students to the computerbased analysis of networks, and instilled in the participants the habits of mind to deepen inquiry in connected systems and statistics, and to sustain interest in continuing to study and pursue careers in fields involving network analysis. Goals of NetSci High ranged from proximal learning outcomes (e.g., increasing high school student competencies in computing and improving student attitudes toward computing) to highly distal (e.g., preparing students ...
Toward Improving Understanding Of The Structure And Biophysics Of Glycosaminoglycans, Elizabeth K. Whitmore
Toward Improving Understanding Of The Structure And Biophysics Of Glycosaminoglycans, Elizabeth K. Whitmore
Electronic Theses and Dissertations
Glycosaminoglycans (GAGs) are the linear carbohydrate components of proteoglycans (PGs) that mediate PG bioactivities, including signal transduction, tissue morphogenesis, and matrix assembly. To understand GAG function, it is important to understand GAG structure and biophysics at atomic resolution. This is a challenge for existing experimental and computational methods because GAGs are heterogeneous, conformationally complex, and polydisperse, containing up to 200 monosaccharides. Molecular dynamics (MD) simulations come close to overcoming this challenge but are only feasible for short GAG polymers. To address this problem, we developed an algorithm that applies conformations from unbiased allatom explicitsolvent MD simulations of short GAG polymers ...
Modeling Covid19 Infection Rates Using Sir And Arima Models, Janelle Domantay, Ilya Pivavaruk, Victor Taksheyev
Modeling Covid19 Infection Rates Using Sir And Arima Models, Janelle Domantay, Ilya Pivavaruk, Victor Taksheyev
Undergraduate Research Symposium Posters
With the onset of the COVID19 pandemic, it has become of increasing interest to both monitor and predict the growth of its infection rates. In order to analyze the accuracy of epidemiological prediction, we consider two different models for prediction, the Susceptible Infected and Removed (SIR), and Autoregressive Integrated Moving Average (ARIMA) models. Using a dataset of Clark County COVID19 infections, we create various ARIMA and SIR models that attempt to predict the progression of COVID19 infections whilst comparing these predictions to the dataset. We observed that the ARIMA model performed more accurately overall, having a much lower Root Mean ...
Flocc: From AgentBased Models To Interactive Simulations On The Web, Scott Donaldson
Flocc: From AgentBased Models To Interactive Simulations On The Web, Scott Donaldson
Northeast Journal of Complex Systems (NEJCS)
Agentbased modeling (ABM) is a computational technique wherein systems are represented through the actions and interactions of many individual entities (‘agents’) over time. ABM often attempts to elucidate the unpredictable, highlevel behavior of systems through the predictable, lowlevel behavior of actors within the system. There are currently few software or frameworks for ABM that allow modelers to design and build interactive models on the web, for a wide audience as well as a scientifically literate audience wellversed in complexity, models, and simulations. Flocc is a novel framework for agentbased modeling written in JavaScript, the lingua franca programming language of the ...
Emergent Hierarchy Through ConductanceBased Degree Constraints, Christopher Tyler Diggans, Jeremie Fish, Erik M. Bollt
Emergent Hierarchy Through ConductanceBased Degree Constraints, Christopher Tyler Diggans, Jeremie Fish, Erik M. Bollt
Northeast Journal of Complex Systems (NEJCS)
The presence of hierarchy in many realworld networks is not yet fully understood. We observe that complex interaction networks are often coarsegrain models of vast modular networks, where tightly connected subgraphs are agglomerated into nodes for simplicity of representation and computational feasibility. The emergence of hierarchy in such growing complex networks may stem from one particular property of these ignored subgraphs: their graph conductance. Being a quantification of the main bottleneck of flow through the coarsegrain node, this scalar quantity implies a structural limitation and supports the consideration of heterogeneous degree constraints. The internal conductance values of the subgraphs are ...
Are Terrorist Networks Just Glorified Criminal Cells?, Elie Alhajjar, Ryan Fameli, Shane Warren
Are Terrorist Networks Just Glorified Criminal Cells?, Elie Alhajjar, Ryan Fameli, Shane Warren
Northeast Journal of Complex Systems (NEJCS)
The notions of organized crime and terrorism have an old and rich history around the globe. Researchers and practitioners have been studying events and phenomena related to these notions for a long time. There are pointers in the literature in which it is misleading to see the unfair comparison between terrorist and criminal networks with the argument that all actors involved in these networks are simply evil individuals. In this paper, we conduct a systematic study of the operational structure of such networks from a network science perspective. We highlight some of the major differences between them and support our ...
Computational Modelling Enables Robust Multidimensional Nanoscopy, Matthew D. Lew
Computational Modelling Enables Robust Multidimensional Nanoscopy, Matthew D. Lew
Electrical & Systems Engineering Publications and Presentations
The following sections are included:

Present State of Computational Modelling in Fluorescence Nanoscopy

Recent Contributions to Computational Modelling in Fluorescence Nanoscopy

Outlook on Computational Modelling in Fluorescence Nanoscopy

Acknowledgments

References
Modeling And Analysis Of Affiliation Networks With Subsumption, Alexey Nikolaev
Modeling And Analysis Of Affiliation Networks With Subsumption, Alexey Nikolaev
Dissertations, Theses, and Capstone Projects
An affiliation (or twomode) network is an abstraction commonly used for representing systems with group interactions. It consists of a set of nodes and a set of their groupings called affiliations. We introduce the notion of affiliation network with subsumption, in which no affiliation can be a subset of another. A network with this property can be modeled by an abstract simplicial complex whose facets are the affiliations of the network.
We introduce a new model for generating affiliation networks with and without subsumption (represented as simplicial complexes and hypergraphs, respectively). In this model, at each iteration, a constant number ...
Numerical Integration Through Concavity Analysis, Daniel J. Pietz
Numerical Integration Through Concavity Analysis, Daniel J. Pietz
RoseHulman 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 “PostWar” Nor PostPregnancy Paranoia: How America’S War On Drugs Continues To Perpetuate Disparate Incarceration Outcomes For Pregnant, SubstanceInvolved Offenders, Becca S. Zimmerman
Neither “PostWar” Nor PostPregnancy Paranoia: How America’S War On Drugs Continues To Perpetuate Disparate Incarceration Outcomes For Pregnant, SubstanceInvolved 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 hyperincarceration 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 substanceinvolved but not evenhandedly  benefitting white pregnant ...
Design Project: Smart Headband, John Michel, Jack Durkin, Noah Lewis
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 indepth 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 NewtonLike Methods, Eleanor Byrnes
Fractals, Fractional Derivatives, And NewtonLike 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, Enrique Pereira Batista
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 coarsegraining
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 coarsegrain approximations ...
Uncertainty Quantification Of Nonreflecting Boundary Schemes, Brian Citty
Uncertainty Quantification Of Nonreflecting Boundary Schemes, Brian Citty
Mathematics Theses and Dissertations
Numerical methods have been developed to solve partial differential equations involving the farfield 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 NonLinear System Variant Boussinesq Equations And Comparison With Nim, Oday Ahmed Jasim
The Revised Nim For Solving The NonLinear 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 DatterderGejj). 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, Tarik Menkad
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 timedomain 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 assignmentpartition 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 frequencydomain. An automatic ...
Using Statistical Analysis To Examine Weather Variability In New York City, Ryan Chen, Yuhuang Wang, Jiehao Huang
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 19792014 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 VectorValued Data On Irregular Domains: Spherical Harmonic Analysis, DivergenceFree/CurlFree Radial Basis Functions, And Implicit Surface Reconstruction, Kathryn Primrose Drake
A Collection Of Fast Algorithms For Scalar And VectorValued Data On Irregular Domains: Spherical Harmonic Analysis, DivergenceFree/CurlFree 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 ...