Numerical Analysis and Computation Commons^™

Acceleration Methods For Nonlinear Solvers And Application To Fluid Flow Simulations, Duygu Vargun

All Dissertations

This thesis studies nonlinear iterative solvers for the simulation of Newtonian and non-Newtonian fluid models with two different approaches: Anderson acceleration (AA), an extrapolation technique that accelerates the convergence rate and improves the robustness of fixed-point iterations schemes, and continuous data assimilation (CDA) which drives the approximate solution towards coarse data measurements or observables by adding a penalty term.

We analyze the properties of nonlinear solvers to apply the AA technique. We consider the Picard iteration for the Bingham equation which models the motion of viscoplastic materials, and the classical iterated penalty Picard and Arrow-Hurwicz iterations for the incompressible Navier–Stokes …

Extending The Spectral Difference Method With Divergence Cleaning (Sddc) To The Hall Mhd Equations, Russell J. Hankey, Kuangxu Chen, Chunlei Liang

Northeast Journal of Complex Systems (NEJCS)

The Hall Magnetohydrodynamic (MHD) equations are an extension of the standard MHD equations that include the “Hall” term from the general Ohm’s law. The Hall term decouples ion and electron motion physically on the ion inertial length scales. Implementing the Hall MHD equations in a numerical solver allows more physical simulations for plasma dynamics on length scales less than the ion inertial scale length but greater than the electron inertial length. The present effort is an important step towards producing physically correct results to important problems, such as the Geospace Environmental Modeling (GEM) Magnetic Reconnection problem. The solver that is …

Numerical Analysis Of A Combustion Model For Layered Media Via Mathematical Homogenization, Jessica M. Riggs, Ana Maria Soane

Mathematica Militaris

We propose to investigate a mathematical model
for combustion in a rod made of periodically alternating thin
layers of two combustible materials such as those occurring in
gun propellants. We apply the homogenization theory to resolve
the fast oscillations of the model’s coefficients across adjacent
layers, and set up numerical simulations to better understand
the reactions occurring in such media.

Hydrodynamic And Physicochemical Interactions Between An Active Janus Particle And An Inactive Particle, Jessica S. Rosenberg

Dissertations, Theses, and Capstone Projects

Active matter is an area of soft matter science in which units consume energy and turn it into autonomous motion. Groups of these units – whether flocks of birds, bacterial colonies, or even collections of synthetically-made active particles – may exhibit complex behavior on large scales. While the large-scale picture is of great importance, so is the microscopic scale. Studying the individual particles that make up active matter will allow us to understand how they move, and whether and under what circumstances their activity can be controlled.

Here we delve into the world of active matter by studying colloidal-sized (100 …

(R1951) Numerical Solution For A Class Of Nonlinear Emden-Fowler Equations By Exponential Collocation Method, Mohammad Aslefallah, Saeid Abbasbandy, Şuayip Yüzbaşi

Applications and Applied Mathematics: An International Journal (AAM)

In this research, exponential approximation is used to solve a class of nonlinear Emden-Fowler equations. This method is based on the matrix forms of exponential functions and their derivatives using collocation points. To demonstrate the usefulness of the method, we apply it to some different problems. The numerical approximate solutions are compared with available (existing) exact (analytical) solutions to show the accuracy of the proposed method. The method has been checked with several examples to show its validity and reliability. The reported examples illustrate that the method is reasonably efficient and accurate.

(R1987) Hermite Wavelets Method For System Of Linear Differential Equations, Inderdeep Singh, Manbir Kaur

Applications and Applied Mathematics: An International Journal (AAM)

In this research paper, we present an accurate technique for solving the system of linear differential equations. Such equations often arise as a result of modeling in many systems and applications of engineering and science. The proposed scheme is based on Hermite wavelets basis functions and operational matrices of integration. The demonstrated scheme is simple as it converts the problem into algebraic matrix equation. To validate the applicability and efficacy of the developed scheme, some illustrative examples are also considered. The results so obtained with the help of the present proposed numerical technique by using Hermite wavelets are observed to …

Homotopy Analysis Method Using Jumarie’S Approach For Multi-Dimensional Nonlinear Schrödinger Equations, Naveed Imran, Raja Mehmood Khan

International Journal of Emerging Multidisciplinaries: Mathematics

In this paper, we suggest a fractional functional for the Homotopy Analysis Method (HAM) to solve the nonlinear fractional order partial differential equations with fractional order initial conditions by using the modified Riemann–Liouville fractional derivative proposed by G. Jumarie. Graphs have been plotted for different values of α , which clearly reflect the reliability of proposed scheme

A Guide To Uncertainty And Global Sensitivity Analysis In Lumped-Parameter Models Of The Cardiovascular System, Raheem Gul, Aamir Shahzad, Syed Muhammad Jawwad Riaz

International Journal of Emerging Multidisciplinaries: Mathematics

In this paper, a general 5-steps framework of uncertainty analysis (UA) and sensitivity analysis (SA) in lumped parameter models of the cardiovascular system (partial or complete) is presented. In order to conduct proper UA and SA, a high number of model simulations is required. Therefore, lumped parameter (0D) models of the cardiovascular system (CVS) are suitable for UA and SA as compared to high or multi-dimensional models (3D,2D,1D). As an example, a linear elastic lumped-parameter model of arm arteries is considered and a 5-steps framework is applied to quantify the impact of input parameters on output variables. The framework uses …

Fem Simulations To Analyze Flow And Thermal Characteristics Of Carreau Non-Newtonian Fluid In A Square Cavity, Sardar Muhammad Bilal, Noor Zeb Khan, Rimsha Nisar

International Journal of Emerging Multidisciplinaries: Mathematics

Heat transfer aspects induced by natural convection in enclosures have promising utilizations and essence from theoretical as well as practical prospective like in, nuclear and chemical reactors, electronic devices, cooling, polymeric processes, solar power collection and so forth. After viewing aforementioned extensive practical importance present communicatn is addressed to explain the flow attributes of Non-Newtonian Carreau fluid model in a square cavity. For non-elastic Carreau fluid model expressing the stress and strain relations at infinite and zero stress magnitude. Mathematical formulation of problem is conceded by obliging conservation laws of momentum and energy. A square enclosure with unit dimension is …

Radiation Effects On Boundary Layer Flow And Heat Transfer Of The Power Law Fluid Over A Stretching Cylinder With Convective Boundary Conditions, Azeem Shahzad, Areeba Zafar, Shakil Shaiq, Tahir Naseem

International Journal of Emerging Multidisciplinaries: Mathematics

In this work, a power law fluid model is used to examine the boundary layer flow and heat transfer characteristics over an unsteady horizontal stretching cylinder under the influence of convective boundary conditions. It is presumed that partial slip conditions exist and that the thermal conductivity of the nanofluid is a function of temperature at the boundary. Through similarity transformation, the coupled partial differential equations are converted into ordinary differential equations (ODEs), which are then resolved in MATLAB with BVP4C. By contrasting the computed findings with the published results, the validity of the results is proven. The effects of different …

Effect Of Cattaneo-Christov Model Over A Vertical Stretching Cylinder Using Sio2 Nanofluid, Zaffer Elahi, Maimoona Siddiqua, Azeem Shahzad

International Journal of Emerging Multidisciplinaries: Mathematics

This paper represents the heat transfer of SiO2 nano uid over a vertical stretching cylinder. By using, suitable transformations, the governing partial differential equations are changed into non-linear ordinary differential equations, which are then solved by the numerical solver namely BVP4C. The scrutinized results both in the form of graphical and numerically have been developed from the scheme BVP4C. By using pictorial graphs, the physical parameter that appear in temperature profile are discussed. Further, the rate of shear-stress and heat transfer at the surface have been computed and tabulated in Tables 3-4.

Covid-19 In Casinos: Analysis Of Covid-19 Contamination And Spread With Economic Impact Assessment, Anastasia (Stasi) D. Baran, Jason D. Fiege

International Conference on Gambling & Risk Taking

Abstract:

The COVID-19 pandemic caused tremendous disruption for casinos, with the virus causing various lengths of shutdowns, capacity restrictions, and social distancing strategies such as machine removals or section closures. Although most of the world has now eased off these measures, it is important to review lessons learned to understand, and better prepare for similar circumstances in the future. We present Monte Carlo slot floor simulation software customized to simulate players spreading COVID-19 on the slot floor. We simulate the amount of touch surface contamination; the number of potential surface contact exposure events per day, and a proximity exposures statistic …

Stochastic Gradient Descent Method For A Parameter Identification Problem In Elasticity Imaging, Basca Jadamba

Biology and Medicine Through Mathematics Conference

No abstract provided.

Brief Review: Low Frequency Event Charts (G-Charts) In Healthcare, James Espinosa, David Ho, Alan Lucerna, Henry Schuitema

Stratford Campus Research Day

The ability to determine if a change in a system is actually an improvement—or worsening in function—is one of the essential desiderata of quality improvement efforts. There are many ways to look at the issue. A special problem occurs when the event being studied is low frequency by nature. By way of example, patient falls in a given hospital or division of a hospital may occur in a way that is low frequency—yet each event is important. Process engineering has developed an approach to low frequency events. Part of this approach may involve specialized charts that look at the “time-between-events”—as …

Advancements In Fluid Simulation Through Enhanced Conservation Schemes, Sean Ingimarson

All Dissertations

To better understand and solve problems involving the natural phenomenon of fluid and air flows, one must understand the Navier-Stokes equations. Branching several different fields including engineering, chemistry, physics, etc., these are among the most important equations in mathematics. However, these equations do not have analytic solutions save for trivial solutions. Hence researchers have striven to make advancements in varieties of numerical models and simulations. With many variations of numerical models of the Navier-Stokes equations, many lose important physical meaningfulness. In particular, many finite element schemes do not conserve energy, momentum, or angular momentum. In this thesis, we will study …

Head And Neck Tumor Histopathological Image Representation With Pre- Trained Convolutional Neural Network And Vision Transformer, Ranny Rahaningrum Herdiantoputri, Daisuke Komura, Tohru Ikeda, Shumpei Ishikawa

Journal of Dentistry Indonesia

Image representation via machine learning is an approach to quantitatively represent histopathological images of head and neck tumors for future applications of artificial intelligence-assisted pathological diagnosis systems. Objective: This study compares image representations produced by a pre-trained convolutional neural network (VGG16) to those produced by a vision transformer (ViT-L/14) in terms of the classification performance of head and neck tumors. Methods: W hole-slide images of five oral t umor categories (n = 319 cases) were analyzed. Image patches were created from manually annotated regions at 4096, 2048, and 1024 pixels and rescaled to 256 pixels. Image representations were …

The Magnetic Field Of Protostar-Disk-Outflow Systems, Mahmoud Sharkawi

Electronic Thesis and Dissertation Repository

Recent observations of protostellar cores reveal complex magnetic field configurations that are distorted in the innermost disk region. Unlike the prestellar phase, where the magnetic field geometry is simpler with an hourglass configuration, magnetic fields in the protostellar phase are sculpted by the formation of outflows and rapid rotation. This gives rise to a significant azimuthal (or toroidal) component that has not yet been analytically modelled in the literature. Moreover, the onset of outflows, which act as angular momentum transport mechanisms, have received considerable attention in the past few decades. Two mechanisms: 1) the driving by the gradient of a …

Control Of Shear Layers Using Heating Patterns, Shoyon Panday

Electronic Thesis and Dissertation Repository

The presence of spatially modulated flows is universal in nature. Distributed heating and surface roughness are the most common elements to cause non-uniformity in the flows. Spatially distributed heating leads to fundamentally distinct convection, different from the classical Rayleigh-Bénard instability. Interestingly, the onset of convective motion due to horizontal temperature gradients requires no critical conditions – a forced response. At the same time, surface roughness is known to significantly influence flow behaviours and heat transfer characteristics. The current work aims to analyze modulated flows and assess their potential as a mixing technique for low Reynolds number flows. Spanwise modulations (perpendicular …

Analysis Of An Seir Model With Non-Constant Population, Kylar Byrd, Tess Tracy, Sunil Giri, Swarup Ghosh

Student Research

Analysis of an SEIR model with Non-Constant Population
by Kylar Byrd and Tess Tracy, with Dr. Sunil Giri and Dr. Swarup Ghosh.

Mathematical modeling can be useful in helping us to understand disease dynamics. Epidemiological models consist of differential equations with variables and parameters defined to portray these dynamics. We will be presenting the mathematics involved in formulating and analyzing a model for a disease such as influenza. We will first explain a simple SIR model, and then we will introduce our model. We will be looking at an SEIR model that incorporates the use of an exposed class as …

Data-Driven Computational Methods For Quasi-Stationary Distribution And Sensitivity Analysis, Yaping Yuan

Doctoral Dissertations

The goal of the dissertation is to develop the computational methods for quasi-stationary- distributions(QSDs) and the sensitivity analysis of a QSD against the modification of the boundary conditions and against the diffusion approximation.
Many models in various applications are described by Markov chains with absorbing states. For example, any models with mass-action kinetics, such as ecological models, epidemic models, and chemical reaction models, are subject to the population-level randomness called the demographic stochasticity, which may lead to extinction in finite time. There are also many dynamical systems that have interesting short term dynamics but trivial long term dynamics, such as …