Numerical Analysis and Computation Commons^™

A Simple Linear Time Algorithm For Computing A 1-Median On Cactus Graphs, Kien T. Nguyen, Pham V. Chien, Ly H. Hai, Huynh D. Quoc

Applications and Applied Mathematics: An International Journal (AAM)

We address the problem of finding a 1-median on a cactus graph. The problem has already been solved in linear time by the algorithms of Burkard and Krarup (1998), and Lan and Wang (2000). These algorithms are complicated and need efforts. Hence, we develop in this paper a simpler algorithm. First, we construct a condition for a cycle that contains a 1-median or for a vertex that is indeed a 1-median of the cactus. Based on this condition, we localize the search for deriving a 1-median on the underlying cactus. Complexity analysis shows that the approach runs in linear time.

Numerical Solution Of Fractional Integro-Differential Equations With Nonlocal Conditions, M. Jani, D. Bhatta, S. Javadi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we present a numerical method for solving fractional integro-differential equations with nonlocal boundary conditions using Bernstein polynomials. Some theoretical considerations regarding fractional order derivatives of Bernstein polynomials are discussed. The error analysis is carried out and supported with some numerical examples. It is shown that the method is simple and accurate for the given problem.

Numerical Study Of Soliton Solutions Of Kdv, Boussinesq, And Kaup-Kuperschmidt Equations Based On Jacobi Polynomials, Khadijeh Sadri, Hamideh Ebrahimi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a numerical method is developed to approximate the soliton solutions of some nonlinear wave equations in terms of the Jacobi polynomials. Wave are very important phenomena in dispersion, dissipation, diffusion, reaction, and convection. Using the wave variable converts these nonlinear equations to the nonlinear ODE equations. Then, the operational Collocation method based on Jacobi polynomials as bases is applied to approximate the solution of ODE equation resulted. In addition, the intervals of the solution will be extended using an rational exponential approximation (REA). The KdV, Boussinesq, and Kaup–Kuperschmidt equations are studied as the test examples. Finally, numerical …

Finite Difference Schemes For Variable Order Time-Fractional First Initial Boundary Value Problems, Gunvant A. Birajdar, M. M. Rashidi

Applications and Applied Mathematics: An International Journal (AAM)

The aim of the study is to obtain the numerical solution of first initial boundary value problem (IBVP) for semi-linear variable order fractional diffusion equation by using different finite difference schemes. We developed the three finite difference schemes namely explicit difference scheme, implicit difference scheme and Crank-Nicolson difference scheme, respectively for variable order type semi-linear diffusion equation. For this scheme the stability as well as convergence are studied via Fourier method. At the end, solution of some numerical examples are discussed and represented graphically using Matlab.

Revisiting Assert Use In Github Projects, Pavneet Singh Kochhar, David Lo

Research Collection School Of Computing and Information Systems

Assertions are often used to test the assumptions that developers have about a program. An assertion contains a boolean expression which developers believe to be true at a particular program point. It throws an error if the expression is not satisfied, which helps developers to detect and correct bugs. Since assertions make developer assumptions explicit, assertions are also believed to improve under-standability of code. Recently, Casalnuovo et al. analyse C and C++ programs to understand the relationship between assertion usage and defect occurrence. Their results show that asserts have a small effect on reducing the density of bugs and developers …

High Performance Computation Of Cardiac Models In Real-Time Using Webgl, Abouzar Kaboudian, Flavio H. Fenton

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Large Reaction-Diffusion Model For Cell Polarization In Yeast, Marissa Renardy

Biology and Medicine Through Mathematics Conference

No abstract provided.

Evolution Of Influenza H3n2: A Random Walk In High Dimensions, James R. Moore

Biology and Medicine Through Mathematics Conference

No abstract provided.

Building And Validating A Model For Investigating The Dynamics Of Isolated Water Molecules, Grant Cates

Senior Theses

Understanding how water molecules behave in isolation is vital to understand many fundamental processes in nature. To that end, scientists have begun studying crystals in which single water molecules become trapped in regularly occurring cavities in the crystal structure. As part of that investigation, numerical models used to investigate the dynamics of isolated water molecules are sought to help bolster our fundamental understanding of how these systems behave. To that end, the efficacy of three computational methods—the Euler Method, the Euler-Aspel Method and the Beeman Method—is compared using a newly defined parameter, called the predictive stability coefficient ρ. This …

Electrodynamical Modeling For Light Transport Simulation, Michael G. Saunders

Undergraduate Honors Theses

Modernity in the computer graphics community is characterized by a burgeoning interest in physically based rendering techniques. That is to say that mathematical reasoning from first principles is widely preferred to ad hoc, approximate reasoning in blind pursuit of photorealism. Thereby, the purpose of our research is to investigate the efficacy of explicit electrodynamical modeling by means of the generalized Jones vector given by Azzam [1] and the generalized Jones matrix given by Ortega-Quijano & Arce-Diego [2] in the context of stochastic light transport simulation for computer graphics. To augment the status quo path tracing framework with such a modeling …

Efficient Denoising And Sharpening Of Color Images Through Numerical Solution Of Nonlinear Diffusion Equations, Linh T. Duong

Honors Theses

The purpose of this project is to enhance color images through denoising and sharpening, two important branches of image processing, by mathematically modeling the images. Modifications are made to two existing nonlinear diffusion image processing models to adapt them to color images. This is done by treating the red, green, and blue (RGB) channels of color images independently, contrary to the conventional idea that the channels should not be treated independently. A new numerical method is needed to solve our models for high resolution images since current methods are impractical. To produce an efficient method, the solution is represented as …

Application Of Symplectic Integration On A Dynamical System, William Frazier

Electronic Theses and Dissertations

Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and one of the key components of a MD simulation is the numerical estimation of the solutions to a system of nonlinear differential equations. Such systems are very sensitive to discretization and round-off error, and correspondingly, standard techniques such as Runge-Kutta methods can lead to poor results. However, MD systems are conservative, which means that we can use Hamiltonian mechanics and symplectic transformations (also known as canonical transformations) in analyzing and approximating solutions. This is standard in MD applications, leading to numerical techniques known as symplectic …

Time Lags Associated With Effects Of Oceanic Conditions On Seabird Breeding In The Salish Sea Region Of The Northern California Current System, Rashida S. Smith, Lynelle M. Weldon, James L. Hayward, Shandelle M. Henson

Faculty Publications

No abstract provided.

Shear Driven Micro-Fluidic Pump For Cardiovascular Applications, Nihad E. Daidzic

Aviation Department Publications

A valveless shear-driven micro-fluidic pump design (SDMFP) for hemodynamic applications is presented in this work. One of the possible medical and biomedical applications is in-vivo hemodynamic (human blood circulation) support/assist. One or more SDMFPs can be inserted/implanted into vascular lumens in a form of a stent/duct in series and/or in parallel (bypass duct) to support blood circulation in-vivo. A comprehensive review of various micro-pump designs up to about mid 2000’s is given in [1,2]. Many of micropump designs considered are not suitable for in-vivo or even in-vitro medical/biomedical applications.

Operating principles, design, and SDMFP features are given in [3]. A …

A Coupled Localized Rbf Meshless/Drbem Formulation For Accurate Modeling Of Incompressible Fluid Flows, Leonardo Bueno, Eduardo Divo, Alain J. Kassab

Publications

Velocity-pressure coupling schemes for the solution of incompressible fluid flow problems in Computational Fluid Dynamics (CFD) rely on the formulation of Poisson-like equations through projection methods. The solution of these Poisson-like equations represent the pressure correction and the velocity correction to ensure proper satisfaction of the conservation of mass equation at each step of a time-marching scheme or at each level of an iteration process. Inaccurate solutions of these Poisson-like equations result in meaningless instantaneous or intermediate approximations that do not represent the proper time-accurate behavior of the flow. The fact that these equations must be solved to convergence at …

An Rbf Interpolation Blending Scheme For Effective Shock-Capturing, M. Harris, Eduardo Divo, Alain J. Kassab

Publications

In recent years significant focus has been given to the study of Radial basis functions (RBF), especially in their use on solving partial differential equations (PDE). RBF have an impressive capability of inter- polating scattered data, even when this data presents localized discontinuities. However, for infinitely smooth RBF such as the Multiquadrics, inverse Multiquadrics, and Gaussian, the shape parameter must be chosen properly to obtain accurate approximations while avoiding ill-conditioning of the interpolating matrices. The optimum shape parameter can vary significantly depending on the field, particularly in locations of steep gradients, shocks, or discontinuities. Typically, the shape parameter is chosen …

Haar Wavelet Solution Of Poisson’S Equation And Their Block Structures, The British University In Egypt, Ain Shams University

Basic Science Engineering

The structure of the algebraic system which results from the use of Haar wavelet when solving Poisson’s equation is studied. Haar wavelet technique is used to solve Poisson’s equation on a unit square domain. The form of collocation points are used at the mid points of the subintervals i.e at the odd multiple of the sub interval length labeling. It is proved that the coefficient matrix has symmetric block structure. Comparison with the tridagonal block structure obtained by the finite difference with the natural ordering is introduced. The numerical results have illustrated the superiority of the use of Haar wavelet …

Computational Algorithms For Improved Representation Of The Model Error Covariance In Weak-Constraint 4d-Var, Jeremy A. Shaw

Dissertations and Theses

Four-dimensional variational data assimilation (4D-Var) provides an estimate to the state of a dynamical system through the minimization of a cost functional that measures the distance to a prior state (background) estimate and observations over a time window. The analysis fit to each information input component is determined by the specification of the error covariance matrices in the data assimilation system (DAS). Weak-constraint 4D-Var (w4D-Var) provides a theoretical framework to account for modeling errors in the analysis scheme. In addition to the specification of the background error covariance matrix, the w4D-Var formulation requires information on the model error statistics and …

Application Of An Rbf Blending Interpolation Method To Problems With Shocks, Michael Harris, Eduardo Divo, Alain J. Kassab

Publications

Radial basis functions (RBF) have become an area of research in recent years, especially in the use of solving partial differential equations (PDE). Radial basis functions have an impressive capability in interpolating scattered data, even for data with discontinuities. Although, for infinitely smooth radial basis functions such as the multi-quadrics and inverse multi-quadrics, the shape parameter must be chosen properly to obtain accurate approximations while avoiding ill-conditioning of the interpolating matrices. The optimum shape parameter can vary depending on the field, such as in locations of sharp gradients or shocks. Typically, the shape parameter is chosen to maintain a high …

On The Three Dimensional Interaction Between Flexible Fibers And Fluid Flow, Bogdan Nita, Ryan Allaire

Department of Mathematics Faculty Scholarship and Creative Works

In this paper we discuss the deformation of a flexible fiber clamped to a spherical body and immersed in a flow of fluid moving with a speed ranging between 0 and 50 cm/s by means of three dimensional numerical simulation developed in COMSOL . The effects of flow speed and initial configuration angle of the fiber relative to the flow are analyzed. A rigorous analysis of the numerical procedure is performed and our code is benchmarked against well established cases. The flow velocity and pressure are used to compute drag forces upon the fiber. Of particular interest is the behavior …