Partial Differential Equations Commons^™

Inverse Boundary Value Problems For Polyharmonic Operators With Non-Smooth Coefficients, Landon Gauthier

Theses and Dissertations--Mathematics

We consider inverse boundary problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity required to establish uniqueness. The proof relies on an averaging technique introduced by Haberman and Tataru for the study of an inverse boundary value problem for a second order operator.

(R1491) Numerical Solution Of The Time-Space Fractional Diffusion Equation With Caputo Derivative In Time By A-Polynomial Method, Saeid Abbasbandy, Jalal Hajishafieiha

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a novel type of polynomial is defined which is equipped with an auxiliary parameter a. These polynomials are a combination of the Chebyshev polynomials of the second kind. The approximate solution of each equation is assumed as the sum of these polynomials and then, with the help of the collocation points, the unknown coefficients of each polynomial, as well as auxiliary parameter, is obtained optimally. Now, by placing the optimal value of a in polynomials, the polynomials are obtained without auxiliary parameter, which is the restarted step of the present method. The time discretization is performed …

(R1480) Heat Transfer In Peristaltic Motion Of Rabinowitsch Fluid In A Channel With Permeable Wall, Mahadev M. Channakote, Dilipkumar V. Kalse

Applications and Applied Mathematics: An International Journal (AAM)

This paper is intended to investigate the effect of heat transfer on the peristaltic flow of Rabinowitsch fluid in a channel lined with a porous material. The Navier -Stokes equation governs the channel's flow, and Darcy's law describes the permeable boundary. The Rabinowitsch fluid model's governing equations are solved by utilizing approximations of the long-wavelength and small number of Reynolds. The expressions for axial velocity, temperature distribution, pressure gradient, friction force, stream function are obtained. The influence on velocity, pressure gradient, friction force, and temperature on pumping action of different physical parameters is explored via graphs.

(R1496) Impact Of Electronic States Of Conical Shape Of Indium Arsenide/Gallium Arsenide Semiconductor Quantum Dots, Md. Fayz-Al-Asad, Md. Al-Rumman, Md. Nur Alam, Salma Parvin, Cemil Tunç

Applications and Applied Mathematics: An International Journal (AAM)

Semiconductor quantum dots (QDs) have unique atom-like properties. In this work, the electronic states of quantum dot grown on a GaAs substrate has been studied. The analytical expressions of electron wave function for cone-like quantum dot on the semiconductor surface has been obtained and the governing eigen value equation has been solved, thereby obtaining the dependence of ground state energy on radius and height of the cone-shaped -dots. In addition, the energy of eigenvalues is computed for various length and thickness of the wetting layer (WL). We discovered that the eigen functions and energies are nearly associated with the GaAs …

(R1494) Approximate Solutions Of The Telegraph Equation, Ilija Jegdić

Applications and Applied Mathematics: An International Journal (AAM)

In this paper the initial boundary value problems for the linear telegraph equation in one and two space dimensions are considered. To find approximate solutions, a recently proposed optimization-free approach that utilizes artificial neural networks with one hidden layer is used, in which the connecting weights from the input layer to the hidden layer are chosen randomly and the weights from the hidden layer to the output layer are found by solving a system of linear equations. One of the advantages of this method, in comparison to the usual discretization methods for the two-dimensional linear telegraph equation, is that this …

Survivals Of Two Cooperating Species Of Animals, Joon Hyuk Kang

Faculty Publications

The purpose of this paper is to give conditions for the existence and uniqueness of positive solution to a rather general type of elliptic system of the Dirichlet problem on a bounded domain Ω" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">Ω in Rn" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: …

Ecological Dynamics On Large Metapopulation Graphs, Daniel Cooney

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Modelling And Simulation Using An Efficient Pinns Algorithm To Understand Spread Of Infection In Enclosed Spaces, Long Nguyen, Arkaprovo Ghosal, Rudra Nagalia, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Multi-Valued Solutions For The Equation Of Motion, Darcy-Jordan Model, As A Cauchy Problem: A Shocking Event, Chandler Shimp

Master's Theses

Shocks are physical phenomenon that occur quite often around us. In this thesis we examine the occurrence of shocks in finite amplitude acoustic waves from a numerical perspective. These waves, or jump discontinuities, yield ill-behaved solutions when solved numerically. This study takes on the challenge of finding both single- and multi-valued solutions.

The previously unsolved problem in this study is the representation of the Equation of Motion (EoM) in the form of the Darcy-Jordan model (DJM) and expressed as a dimensionless IVP Cauchy problem. Prior attempts to solve have resulted only in implicit solutions or explicit solutions with certain initial …

Non-Circular Hydraulic Jumps Due To Inclined Jets, Ahmed Mohamed Abdelaziz

Electronic Thesis and Dissertation Repository

When a laminar inclined circular jet impinges on a horizontal surface, it forms a non-circular hydraulic jump governed by a non-axisymmetric flow. In this thesis, we use the boundary-layer and thin-film approaches in the three dimensions to theoretically analyse such flow and the hydraulic jumps produced in such cases. We particularly explore the interplay among inertia, gravity, and the effective inclination angle on the non-axisymmetric flow.

The boundary-layer height is found to show an azimuthal dependence at strong gravity level only; however, the thin film thickness as well as the hydraulic jump profile showed a strong non-axisymmetric behaviour at all …

Symphas: A Modular Api For Phase-Field Modeling Using Compile-Time Symbolic Algebra, Steven A. Silber

Electronic Thesis and Dissertation Repository

The phase-field method is a common approach to qualitative analysis of phase transitions. It allows visualizing the time evolution of a phase transition, providing valuable insight into the underlying microstructure and the dynamical processes that take place. Although the approach is applied in a diverse range of fields, from metal-forming to cardiac modelling, there are a limited number of software tools available that allow simulating any phase-field problem and that are highly accessible. To address this, a new open source API and software package called SymPhas is developed for simulating phase-field and phase-field crystal in 1-, 2- and 3-dimensions. Phase-field …

Eigenvalue Problems On Atypical Domains - The Finite Element Method, Toufiic Ayoub

Undergraduate Student Research Internships Conference

Why do we care about eigenvalues and eigenvectors? What's the big deal? For many people enrolled in entry level linear algebra courses, these concepts seem like far fetched abstractions that become pointless exercises in computation. But in reality, these fundamental ideas are vital to how we live our lives every single day. But how?

Application Of Stochastic Control To Portfolio Optimization And Energy Finance, Junhe Chen

Electronic Thesis and Dissertation Repository

In this thesis, we study two continuous-time optimal control problems. The first describes competition in the energy market and the second aims at robust portfolio decisions for commodity markets. Both problems are approached via solutions of Hamilton-Jacobi-Bellman (HJB) and HJB-Isaacs (HJBI) equations.

In the energy market problem, our target is to maximize profits from trading crude oil by determining optimal crude oil production. We determine the optimal crude oil production rate by constructing a differential game between two types of players: a single finite-reserve producer and multiple infinite-reserve producers. We extend the deterministic unbounded-production model and stochastic monopolistic game to …

Finite Element Approximation Of Solutions Of The Equations Of Electroporoelasticity, Yu Hu

Mathematics Theses and Dissertations

In this thesis we consider the solution of the equations of electroporoelasticity, which are a combination of Maxwell's equations and the poroelasticity equations. Included is a description of suitable initial and boundary conditions, weak formulation of the equations, and the error estimate for a general numerical method.

On A Stochastic Model Of Epidemics, Rachel Prather

Master's Theses

This thesis examines a stochastic model of epidemics initially proposed and studied by Norman T.J. Bailey [1]. We discuss some issues with Bailey's stochastic model and argue that it may not be a viable theoretical platform for a more general epidemic model. A possible alternative approach to the solution of Bailey's stochastic model and stochastic modeling is proposed as well. Regrettably, any further study on those proposals will have to be discussed elsewhere due to a time constraint.

The Exact Factorization Equations For One- And Two-Level Systems, Bart Rosenzweig

Theses and Dissertations

Exact Factorization is a framework for studying quantum many-body problems. This decomposes the wavefunctions of such systems into conditional and marginal components. We derive corresponding evolution equations for molecular systems whose conditional electronic subsystems are described by one or two Born-Oppenheimer levels and develop a program for their mathematical study.

Smooth Global Approximation For Continuous Data Assimilation, Kenneth R. Brown

Theses and Dissertations

This thesis develops the finite element method, constructs local approximation operators, and bounds their error. Global approximation operators are then constructed with a partition of unity. Finally, an application of these operators to data assimilation of the two-dimensional Navier-Stokes equations is presented, showing convergence of an algorithm in all Sobolev topologies.

Qualitative Analysis Of A Modified Leslie-Gower Predator-Prey Model With Weak Allee Effect Ii, Manoj K. Singh, B. S. Bhadauria

Applications and Applied Mathematics: An International Journal (AAM)

The article aims to study a modified Leslie-Gower predator-prey model with Allee effect II, affecting the functional response with the assumption that the extent to which the environment provides protection to both predator and prey is the same. The model has been studied analytically as well as numerically, including stability and bifurcation analysis. Compared with the predator-prey model without Allee effect, it is found that the weak Allee effect II can bring rich and complicated dynamics, such as the model undergoes to a series of bifurcations (Homoclinic, Hopf, Saddle-node and Bogdanov-Takens). The existence of Hopf bifurcation has been shown for …

A High Order Finite Difference Method To Solve The Steady State Navier-Stokes 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 Navier-Stokes equations and apply it to the benchmark problem known as the square cavity flow problem. The numerical results of 𝑢-velocity components and 𝑣-velocity 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 Navier-Stokes 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

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 to testify …