Applied Mathematics Commons^™

Mhd Boundary Layer Slip Flow Over A Flat Plate With Soret And Dufour Effects, B. Shashidar Reddy, K. Saritha

Applications and Applied Mathematics: An International Journal (AAM)

The present paper studies the effects of Soret and Dufour on MHD boundary layer slip flow over a flat plate. The governing partial differential equations are converted to a set of nonlinear ordinary differential equations by using similarity transformations. Then, these equations are solved numerically by implicit Finite Difference Scheme. The numerical solutions for Velocity, Temperature and Concentration profiles for the related essential physical parameters are visualized through graphs and discussed. Results show that the velocity rises whereas the temperature and concentration reduces with the respective slip parameters. The increase in Soret number or decrease in Dufour number reduces the …

Brownian Motion And Thermophoresis Effects On Casson Nanofluid Over A Chemically Reacting Stretching Sheet With Inclined Magnetic Field, D. Gopal, N. Kishan

Applications and Applied Mathematics: An International Journal (AAM)

The contemporary study explores the impact of thermophoresis and Brownian motion on two-dimensional magnetohydrodynamic boundary layer flow of Casson nanofluid over a chemically reacting stretching sheet. To control the heat and mass transport phenomena we also included the thermophoresis diffusion coefficient, Brownian motion parameter, and thermal radiation. The regular physical governing systems of partial differential equations are transmogrifying into ordinary differential equations. The transmogrifying governing equations are checked numerically by using Runge-Kutta-Fehlberg method. The numerical solutions for heterogeneous governing parameters such as Schmidt number, Joule heating parameter, and permeability parameter, chemical reaction parameters on velocity, temperature, and concentration profiles were …

Joule Heat Parameter Effects On Unsteady Mhd Flow Over A Stretching Sheet With Viscous Dissipation And Heat Source, Srinivas Maripala, Kishan Naikoti

Applications and Applied Mathematics: An International Journal (AAM)

In the present investigation, we studied the effects of heat source and Joule heating parameter on unsteady magneto-hydro-dynamic and heat transfer of a fluid flow over a radiating stretching sheet. The governing partial differential equations of nonlinear with boundary conditions are solved numerically by implicit finite difference method with Gauss Seidel iteration scheme. The obtained numerical solutions of velocity and temperature profiles are discussed and represented graphically. The effects of various parameters on the velocity and temperature profiles are shown graphically and numerical values of physical quantities such as the skin friction coefficient and the local Nusselt number are presented …

Optimal Homotopy Asymptotic Solution For Thermal Radiation And Chemical Reaction Effects On Electrical Mhd Jeffrey Fluid Flow Over A Stretching Sheet Through Porous Media With Heat Source, Gossaye Aliy, Naikoti Kishan

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the problem of thermal radiation and chemical reaction effects on electrical MHD Jeffrey fluid flow over a stretching surface through a porous medium with the heat source is presented. We obtained the approximate analytical solution of the nonlinear differential equations governing the problem using the Optimal Homotopy Asymptotic Method (OHAM). Comparison of results has been made with the numerical solutions from the literature, and a very good agreement has been observed. Subsequently, effects of governing parameters of the velocity, temperature and concentration profiles are presented graphically and discussed.

Mhd Boundary Layer Flow Of Darcy-Forchheimer Mixed Convection In A Nanofluid Saturated Porous Media With Viscous Dissipation, S. Jagadha, P. Amrutha

Applications and Applied Mathematics: An International Journal (AAM)

The steady laminar viscous incompressible nanofluid flow of mixed convection and mass transfer about an isothermal vertical flat plate embedded in Darcy porous medium in the presence of magnetic field and viscous dissipation is analyzed. The governing partial differential equations are converted into ordinary differential equations by similarity transformations. The coupled nonlinear ordinary differential equations are linearized by Quasi-linearization technique. The linear ordinary differential equations are solved by using implicit finite difference scheme with the help of C-programming. Numerical calculations are carried out for different values of dimensionless parameter such as magnetic field, mixed convection parameter, inertia parameter, buoyancy ratio …

From Big Science To “Deep Science”, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

The Standard Model of particle physics has accomplished a great deal including the discovery of Higgs boson in 2012. However, since the supersymmetric extension of the Standard Model has not been successful so far, some physicists are asking what alternative deeper theory could be beyond the Standard Model? This article discusses the relationship between mathematics and physical reality and explores the ways to go from Big Science to “Deep Science”.

Comparison Principle For Stochastic Heat Equation On Rd, Le Chen, Jingyu Huang

Mathematical Sciences Faculty Research

We establish the strong comparison principle and strict positivity of solutions to the following nonlinear stochastic heat equation on Rd (∂∂t−12Δ)u(t,x)=ρ(u(t,x))M˙(t,x), for measure-valued initial data, where M˙ is a spatially homogeneous Gaussian noise that is white in time and ρ is Lipschitz continuous. ... (See full text for complete abstract)

Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects, Justin Dunmyre, Nicholas Fortune, Tianna Bogart, Chris Rasmussen, Karen Keene

CODEE Journal

The environmental phenomenon of climate change is of critical importance to today's science and global communities. Differential equations give a powerful lens onto this phenomenon, and so we should commit to discussing the mathematics of this environmental issue in differential equations courses. Doing so highlights the power of linking differential equations to environmental and social justice causes, and also brings important science to the forefront in the mathematics classroom. In this paper, we provide an extended problem, appropriate for a first course in differential equations, that uses bifurcation analysis to study climate change. Specifically, through studying hysteresis, this problem highlights …

Sir Models: Differential Equations That Support The Common Good, Lorelei Koss

CODEE Journal

This article surveys how SIR models have been extended beyond investigations of biologically infectious diseases to other topics that contribute to social inequality and environmental concerns. We present models that have been used to study sustainable agriculture, drug and alcohol use, the spread of violent ideologies on the internet, criminal activity, and health issues such as bulimia and obesity.

Active Control Of A Forced Mindlin-Type Beam, Kenan Yildirim

Applications and Applied Mathematics: An International Journal (AAM)

In this study, optimal dynamic response control of a forced Mindlin-type beam is studied. The beam under consideration, which consists of central host layer and two piezoelectric patch actuators bonded on perfectly to both sides of the beam. It is assumed that the beam is subject to the forcing function, initially at rest and undeformed. Hence, a forced Mindlin-type beam is considered for active vibration control. For this aim, well-posedness and controllability of the system are presented. Performance index functional to be minimized by using minimum level of control voltage consists of a weighted quadratic functions of displacement and velocity …

Parametric Models For Signature Prediction And Feature Extraction, Julie Ann Jackson

Faculty Publications

This paper compares and contrasts numerical electromagnetic (EM) prediction methods and parametric scattering models for radar signature prediction and feature extraction.

Spectral Discretization Errors In Filtered Subspace Iteration, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall

Mathematics and Statistics Faculty Publications and Presentations

We consider filtered subspace iteration for approximating a cluster of eigenvalues (and its associated eigenspace) of a (possibly unbounded) selfadjoint operator in a Hilbert space. The algorithm is motivated by a quadrature approximation of an operator-valued contour integral of the resolvent. Resolvents on infinite dimensional spaces are discretized in computable finite-dimensional spaces before the algorithm is applied. This study focuses on how such discretizations result in errors in the eigenspace approximations computed by the algorithm. The computed eigenspace is then used to obtain approximations of the eigenvalue cluster. Bounds for the Hausdorff distance between the computed and exact eigenvalue clusters …

Hermite Wavelet Approach To Estimate Solution For Bratu´S Problem, Bushra Issa Khashem

Emirates Journal for Engineering Research

In this paper, the construction of hermit wavelets function and their operational matrix of integration is presented. The matrix together with the collection method are then utilized to transform the differential equations to a system of algebraic equation. Avery high level of accuracy explicitly reflected by the proposed examples.

Inferring The Distribution Of Selective Effects From A Time Inhomogeneous Model, Amei Amei, Shilei Zhour

Mathematical Sciences Faculty Research

We have developed a Poisson random field model for estimating the distribution of selective effects of newly arisen nonsynonymous mutations that could be observed as polymorphism or divergence in samples of two related species under the assumption that the two species populations are not at mutation-selection-drift equilibrium. The model is applied to 91Drosophila genes by comparing levels of polymorphism in an African population of D. melanogaster with divergence to a reference strain of D. simulans. Based on the difference of gene expression level between testes and ovaries, the 91 genes were classified as 33 male-biased, 28 female-biased, and 30 sex-unbiased …

A Variable Nonlinear Splitting Algorithm For Reaction Diffusion Systems With Self- And Cross-Diffusion, Matthew Beauregard, Joshua L. Padgett

Faculty Publications

Self- and cross-diffusion are important nonlinear spatial derivative terms that are included into biological models of predator-prey interactions. Self-diffusion models overcrowding effects, while cross-diffusion incorporates the response of one species in light of the concentration of another. In this paper, a novel nonlinear operator splitting method is presented that directly incorporates both self- and cross-diffusion into a computational efficient design. The numerical analysis guarantees the accuracy and demonstrates appropriate criteria for stability. Numerical experiments display its efficiency and accuracy

Latent Space Models For Temporal Networks, Jasper Alt

Systems Science Friday Noon Seminar Series

In many contexts we may expect the structure of networks to be derived from some kind of abstract distance between actors. We refer to this phenomenon as homophily: like nodes connect to like. For example, people with similar beliefs may be more likely to form social relations.

We formalize this notion by positioning the nodes in a latent space representing the possible values of the homophilous attributes. Realistically, we should expect latent attributes like beliefs to change over time in some nontrivial way, and the structures of temporal networks to evolve accordingly. We introduce a model of latent space dynamics …

Identifying Important Parameters In The Inflammatory Process With A Mathematical Model Of Immune Cell Influx And Macrophage Polarization, Marcella Torres, Jing Wang, Paul J. Yannie, Shobha Ghosh, Rebecca A. Segal, Angela M. Reynolds

Mathematics and Applied Mathematics Publications

In an inflammatory setting, macrophages can be polarized to an inflammatory M1 phenotype or to an anti-inflammatory M2 phenotype, as well as existing on a spectrum between these two extremes. Dysfunction of this phenotypic switch can result in a population imbalance that leads to chronic wounds or disease due to unresolved inflammation. Therapeutic interventions that target macrophages have therefore been proposed and implemented in diseases that feature chronic inflammation such as diabetes mellitus and atherosclerosis. We have developed a model for the sequential influx of immune cells in the peritoneal cavity in response to a bacterial stimulus that includes macrophage …

Universal Quantum Computation, Junya Kasahara

Theses, Dissertations and Capstones

We study quantum computers and their impact on computability. First, we summarize the history of computer science. Only a few articles have determined the direction of computer science and industry despite the fact that many works have been dedicated to the present success. We choose articles by A. M. Turing and D. Deutsch, because A. M. Turing proposed the basic architecture of modern computers while D. Deutsch proposed an architecture for the next generation of computers called quantum computers. Second, we study the architecture of modern computers using Turing machines. The Turing machine has the basic design of modern computers …

Estimation Of Multivariate Asset Models With Jumps, Angela Loregian, Laura Ballotta, Gianluca Gianluca Fusai, Marcos Fabricio Perez

Business Faculty Publications

We propose a consistent and computationally efficient two-step methodology for the estimation of multidimensional non-Gaussian asset models built using Levy processes. The proposed framework allows for dependence between assets and different tail behaviors and jump structures for each asset. Our procedure can be applied to portfolios with a large number of assets as it is immune to estimation dimensionality problems. Simulations show good finite sample properties and significant efficiency gains. This method is especially relevant for risk management purposes such as, for example, the computation of portfolio Value at Risk and intra-horizon Value at Risk, as we show in detail …

Stair Climbing Hand Truck, James Mcpherson

All Undergraduate Projects

Abstract

Getting a heavy object up a flight of stairs usually requires a team of two or more people. Even with a team of people, the task is often still difficult, dangerous, and possibly insurmountable by one person. This problem is especially prevalent in for those who are moving into apartment complexes. Most apartment complexes have many buildings with two or more floors of living quarters, and elevators are often missing. This project sought to offer a solution to this problem. The solution in question; a motorized hand-truck with 2, trigonal planar pinwheels in place of the stock wheels. The …