Ryan H. Allaire September 2014 Graduate Assistant Work Phone:

Transcription

1 Ryan H. Allaire September 2014 Graduate Assistant Work Phone: The Graduate School Montclair State University Montclair, NJ U.S.A. EDUCATION M.S. Pure and Applied Mathematics Montclair State University May 2015* Montclair, NJ B.A. Mathematical Sciences Rutgers University May 2012 New Brunswick, NJ A.S. Mathematical Sciences Mercer County Cmty College May 2010 West Windsor, NJ PROFESSIONAL EXPERIENCE Graduate Assistant Montclair State University The Graduate School September 2013 Present Mathematics Tutor November 2011 August 2013 Rutgers, the State University of NJ Rutgers Learning Center Mathematics Grader September 2011 December 2011 Rutgers, the State University of NJ Department of Mathematical Sciences PUBLICATIONS Allaire, R. H., Vaidya, A., Nita, B., Nolan, P., Guerron, P. (2014). On the Equilibrium Configurations of Flexible Fibers in a Flow. International Journal of Nonlinear Mechanics. Manuscript Accepted for publication. *Expected Date of Graduation

2 TEACHING EXPERIENCE Focus Groups Coordinated: Basic Skills Math MATH 071 F13, F14, Intermediate Algebra MATH 100 F13, S14, F14 Development of Math MATH 103 S14, F14 MEMBERSHIPS Society of Industrial and Applied Mathematics (SIAM) Canadian Society for the History and Philosophy of Mathematics (CSHPM) Alpha Epsilon Lambda National Graduate Honor Society COMPUTER SKILLS Experienced in COMSOL Multphysics Experienced in MATLAB Experienced in MAPLE Proficient in Latex Experience with Beamer Experience with Excel, Word, PowerPoint Experience with MathType RESEARCH INTERESTS Partial Differential Equations, Ordinary Differential Equations, Dynamical Systems, Fluid Dynamics, Fluid-Structure Interaction. Complex Fluids Research: Used Comsol Multiphysics to create a 3 dimensional model of a ball and fiber in a fluid flow with fluid-structure interaction. In this model I coupled both Navier-Stokes Equations and Linear elasticity. Analyzed the effects of meshing on the domain. Analyzed the effect on the size of the ball. Analyzed the bending effects for different lengths of fibers and varying speeds Analyzed the difference between drag and lift for varying fiber lengths and fluid speeds.

3 GRADUATE COURSEWORK: Partial Differential Equations Applied Industrial Mathematics Numerical Analysis Mathematical Computing-MATLAB based Real Variables 1 & 2 Complex Variables Linear Algebra Abstract Algebra Fluid-Structure Interaction OTHER RELEVANT COURSEWORK: PROJECTS: Quantum Mechanics Applied Mathematics-Nonlinear Dynamical Systems & Traffic Flow Cryptography Signal & Image Processing using Discrete Fourier & Wavelet Transforms On the 3-Dimensional Fluid-Structure Interaction of Flexible Fibers in a Flow In this Master s Thesis, I am currently expanding upon the recent publication to the International Journal of Nonlinear Mechanics. Comsol Multiphysics is being used to further investigate the 3-dimensional effects of fluid flow past a fiber attached to a sphere in a flow tank. The analysis being done includes but is not limited to: bending angles, drag and lift forces, Vogel exponents, mesh studies, wall studies, the effect of fiber length, the effect of the solid on the vortices in the third dimension, and numerical analysis of the finite element method used to solve these equations. Numerical work is then being compared to experimental data being gathered in the Complex Fluids Laboratory Analysis of Poisson s Equation on Domains with Sharp Corners using FEM In this project, we used the finite element method to solve various forms of Poisson s Equation on L-shaped domains. Specifically, we analyzed the stability of the solutions as a function of the interior angle of the domain. The partial differential equations toolbox in Matlab was used to assist in the calculations. The project resulted in a poster presentation given to the class.

4 2. On an Overbooking Strategy for Airlines In this project we create a stochastic strategy for airlines by using the binomial distribution to find the probability that a passenger would show up for his/her flight. 3. On the Reconstruction of signals post noise reduction In this project we are given specific signals with noise. Using a matched filter we filtered out the noise and attempted to reconstruct the original signal. The error in the signal reconstruction was analyzed and the amplitudes were analyzed using the sound feature in Matlab. 4. Modeling the Vogel Exponents of Drag Force for a Fiber in Fluid Flow In this project we analyzed fluid structure interaction of a ball with flexible fiber attached in a laminar flow. In coupling Navier-Stokes Equations and equations of linear elasticity, we we re able to model the force of drag on the fiber and find the Vogel exponent; that is, find the power at which F d v α. We compared results to those of published papers in fluid dynamics The Blasius Function The Blasius equation, an equation governing certain boundary layers in fluid flow, was analyzed numerically and analytically. A Taylor Series representation was using the approximate the solution of the equation. Matlab was used to numerically run this simulation Digital Signals and Computer Graphics In this project sounds are quantized into 2-bits and 4-bits and compared. Additionally, linear transformations, such as translations and rotation, are performed on various objects. 2. Convolution and Discrete Fourier Transform The methods of circular convolution and Fourier transforms are applied to signals. Specifically, sounds (such as phone dials) are analyzed in great detail, contrasting the different approaches to accuracy and efficiency. 3. Haar Wavelet Transform The Haar Wavelet Transform was used to compress data. The data was then decomposed and filtered in reconstruction. This process was used to compress noisy signals.

5 4. Implementation of Wavelet Transforms The CDF and Daub4 wavelet transforms were used to decompose signals into its details. With each component of the detail we were able to filter the noise and remove wavelet details to reconstruct the original signal. 5. Image Wavelet Analysis In this project wavelets were used to analyze 2d signals (images). We used the transforms to convert to grey-scale, decompose pictures into detail and nondetail, pass through high-pass and low-pass filters, and make a blurry image look clear The Digits of Learning Digits Constructed a model using differential equations that describes how long it takes for an individual to memorize a set of numbers. 2. Modeling Population Variances Analyzed exponential and logistic equations that modeled the growth of yeast cells over time with differential equations. 3. Forces of Nature: Modeling the Effects of Gravity & Air Resistance Analyzed Newton s laws of motion and how adding air resistance changes the fundamental solution of the differential equations governing motion of an object in the air. 4. The Mathematics of Love In this project we quantified love by creating a Romeo & Juliet scale and created a dynamical system that describes the amount of love that one party feels for the other at any given time, t.