(R1480) Heat Transfer In Peristaltic Motion Of Rabinowitsch Fluid In A Channel With Permeable Wall, 2021 Ramaiah University of Applied Sciences
(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.
Survivals Of Two Cooperating Species Of Animals, 2021 Andrews University
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, 2021 Illinois State University
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, 2021 George Mason University
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, 2021 The University of Southern Mississippi
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, 2021 The University of Western Ontario
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, 2021 The University of Western Ontario
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, 2021 Western University
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, 2021 The University of Western Ontario
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, 2021 Southern Methodist University
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, 2021 The University of Southern Mississippi
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, 2021 CUNY Hunter College
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, 2021 CUNY Hunter College
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, 2021 Babasaheb Bhimrao Ambedkar University
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, 2021 Prairie View A&M University
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, 2021 Wollega University
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 …
An Examination Of Fontan Circulation Using Differential Equation Models And Numerical Methods, 2021 Kutztown University of Pennsylvania
An Examination Of Fontan Circulation Using Differential Equation Models And Numerical Methods, Vanessa Maybruck
Honors Student Research
Certain congenital heart defects can lead to the development of only a single pumping chamber, or ventricle, in the heart instead of the usual two ventricles. Individuals with this defect undergo a corrective, three-part surgery, the third step of which is the Fontan procedure, but as the patients age, their cardiovascular health will likely deteriorate. Using computational fluid dynamics and differential equations, Fontan circulation can be modeled to investigate why the procedure fails and how Fontan failure can be maximally prevented. Borrowing from well-established literature on RC circuits, the differential equation models simulate systemic blood flow in a piecewise, switch-like …
A Component-Wise Approach To Smooth Extension Embedding Methods, 2021 The University of Southern Mississippi
A Component-Wise 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 box-shaped domain. Smooth Extension Embedding Methods (SEEM) use fictitious domain methods to extend a general domain to a simple, rectangular or box-shaped domain. This dissertation describes how these methods can be combined to extend the applicability of KSS methods, while also providing a component-wise approach for solving the systems of equations produced with SEEM.
The Effect Of Initial Conditions On The Weather Research And Forecasting Model, 2021 Stephen F Austin State University
The Effect Of Initial Conditions On The Weather Research And Forecasting Model, Aaron D. Baker
Electronic Theses and Dissertations
Modeling our atmosphere and determining forecasts using numerical methods has been a challenge since the early 20th Century. Most models use a complex dynamical system of equations that prove difficult to solve by hand as they are chaotic by nature. When computer systems became more widely adopted and available, approximating the solution of these equations, numerically, became easier as computational power increased. This advancement in computing has caused numerous weather models to be created and implemented across the world. However a challenge of approximating these solutions accurately still exists as each model have varying set of equations and variables to …
Lecture 08: Partial Eigen Decomposition Of Large Symmetric Matrices Via Thick-Restart Lanczos With Explicit External Deflation And Its Communication-Avoiding Variant, 2021 University of California, Davis
Lecture 08: Partial Eigen Decomposition Of Large Symmetric Matrices Via Thick-Restart Lanczos With Explicit External Deflation And Its Communication-Avoiding Variant, Zhaojun Bai
Mathematical Sciences Spring Lecture Series
There are continual and compelling needs for computing many eigenpairs of very large Hermitian matrix in physical simulations and data analysis. Though the Lanczos method is effective for computing a few eigenvalues, it can be expensive for computing a large number of eigenvalues. To improve the performance of the Lanczos method, in this talk, we will present a combination of explicit external deflation (EED) with an s-step variant of thick-restart Lanczos (s-step TRLan). The s-step Lanczos method can achieve an order of s reduction in data movement while the EED enables to compute eigenpairs in batches along with a number …