On this page I have my unpublished work.  
This includes my current research, school projects, and work reports.

Current Research

• Integrating the Nonlinear Scrodinger Equation using compute capability of NVIDIA GPU cards with CUDA
• A Modulus-Squared-Dirchilet boundary condition for time-dependant complex PDEs
• A 2-Step High-Order Compact Scheme for the Nonlinear Schrodinger Equation
• Structure and Dynamics of Three-Dimensional Vortex Rings in the Nonlinear Schrodinger Equation
  

Ph.D. Dissertation Proposal

Study of Vortex Ring Dynamics in the Nonlinear Schrödinger Equation utilizing GPU-Accelerated High-Order Compact Numerical Integrators
Download: Proposal (PDF)  Presentation (PPTX - 63MB) (PDF)



Ph.D. Qualifying Exam

Existence and Azimuthal Modulational Stability of Vortices in the Cubic-Quintic Nonlinear Schrödinger Equation
(Please note Figure 6 is in error - see publication 2 on this site for correction)
Download: Report (PDF)  Presentation (PPTX) (PDF)



School Projects

San Diego State University and Claremont Graduate University
 
Using AJAX to Develop a Web Interface to Run CO2 Sequestration Simulations on Remote Servers
Final Project #2 for
Computational Science 670:  Problems in Computational Science
Download: Report (PDF) Presentation (PPT) (PDF)

Simulating the Nonlinear Schrödinger Equation using CUDA with MATLAB
Final Project #1 for
Computational Science 670:  Problems in Computational Science
Download: Report (PDF) Presentation (PPT) (PDF) See www.nlsemagic.com for codes.

Numerical Computation of Geodesics on Combined Piecewise-Smooth Surfaces
Final Project for
Math 393:  Math Clinic Boeing
Download: Report (PDF) Presentation (PPT) (PDF)

A MATLAB GUI Program for Integrating Finite Difference Schemes for the 3D NLSE and Visualizing Results
Final Project for
Math 498:  Independent Research
Download: Report (PDF)

Eliminating Ghost Factors in Truncated Gauss-Sum Factorization
Final project for
Math 473:  Seminar on Discrete and Combinatorial Alogrithms
Download: Paper (PDF) Presentation (PPTX) (PDF)

Phase Separation and Dynamics of Two-component Bose-Einstein Condensates
Final project for
Math 281:  Dynamical Systems
Download: Report (PDF) Presentation (PPT) (PDF)

Image Enhancement of Extreme Ultra-Violet Solar Images
Final project for
Math 336:  Digital Image Processing 
Download: Report (PDF) Presentation (PPT) (PDF) Digital Portfolio (URL)

Parallelization of the Classic Gram-Schmidt QR-Factorization
Final project for
Math 543:  Numerical Matrix Analysis
Download: Presentation (PPTX) (PDF)

Finding Steady State Vortex Solutions to the 2D NLSE Using Optimization Algorithms
Final project for
Math 693a: Advanced Numerical Analysis I: Numerical Optimization
Download: (PPTX) (PDF)

Chaotic Stellar Dynamos
Final project for
Math 638: Continuous Nonlinear Dynamics and Chaos
Download: Report (PDF) Presentation (PPT) (PDF)

Tsunami
Final project for
Math 636: Mathematical Modeling
Download: Report (PDF) Presentation (PPT) (PDF)

PDE’s in Curvilinear Coordinates
Final project for
Math 693b:  Advanced Numerical Analysis II: PDE’s
Download: Presentation (PPT) (PDF)

Mimetic Operators
Final project for
Math 542:  Numerical Differential Equations
Download: Report (PDF) Presentation (PPT) (PDF)

Hopping Patterns on Burner Animation
Final visualization for
CS 689: Scientific Visualization
Download: Three-Bumps (MOV) Five-Ten-Bumps (MOV)

Visualization Critique and Revision of “The Mysterious Origins of Solar Flares”
Final Project for
CS 689: Scientific Visualization
Download: Presentation (PPT) (PDF)


University of California Santa Barbara

Stellar Disruptions of Super Massive Black Holes
Joint Final Project for
Physics 198: Directed Reading and
Writing 109ST: Writing for Science and Technology
Download: Paper (PDF) Presentation (PPT) (PDF)


Washington High School

Cosmic Gamma Ray Bursts
Final paper for
English 12A
Download: Paper (PDF)

Black Holes
Final paper for
Honors Physics
Download: Paper (PDF)


Work Reports

San Diego State University Research Foundation

Implementing CUDA-based GPU Acceleration to Hybrid WENO-Spectral Code
This is a report of the work that I did for Professor Gustaaf Jacobs
of the Aerospace Engineering Department at SDSU during the summer of 2010. 
Download: Report (PDF)


Los Alamos National Laboratory

Visualization and Analysis of Numerical Simulation Data
This is a report of the work that I did while at both LANL
and UCSB for the X-2 Division at LANL. 
Download: Report (PDF)