User:Athompson

Amy Thompson

Undergraduate in Applied Mathematics at the University of New Mexico

Research Project

Work with Dr. Elaine Spiller to learn about data assimilation, fluid dynamic models, filtering methods and flow behavior from a dynamical systems perspective. Specifically, implement and evaluate numerical methods to solve differential equations modeling fluid flows and implement filtering methods to explore function space sampling.

Objectives

Infer velocity fields from trajectory data.

• 1D simulation
• 2D simulation
• Apply simulation to data from Dr. Ani Hsieh's Lab.

Weekly Plan

Week 1

• Orientation
• Meet with Mentor to discuss project goals
• Read material pertaining to project: thesis, probability, pde's
• LaTeX tutorials
• Attend Good Research Practices talk
• Develop Goals/Weekly Plan

Week 2

• Read material pertaining to project: probability, pde's
• Attend LaTeX orientation and Good Citation Practices presentation
• Python introduction
• LaTeX practice
• Learn more about Markov Chain Monte Carlo (MCMC) Method
• Meet with Mentor to discuss project direction
• Read MCMC lecture notes
• Begin applying Fourier Series to practice functions

Week 3

• Explore Fourier Series Composition of example bi-modal univariate distribution
• Meet with Mentor to discuss project direction
• Continue reading information about MCMC
• Attend Good Presentations, Good Technical Writing Talk
• Perform Metropolis-Hastings (MH) sampling of a bi-modal univariate distribution
• Attend 15 minute example presentation by Dr. Kim Factor
• Find a simple multivariate distribution on which to perform MH sampling

Week 4

• Research Gibbs Sampling
• Take NSF demographic survey
• Perform Metropolis-Hastings within Gibbs Sampling on simple multivariate distributions
• Transfer project coding from Matlab to Python
• Practice LaTeX
• Begin thinking about mini presentation

Week 5

• Learn how to create presentation in LaTeX
• Watch preparatory video for Responsible Conduct of Research Training
• Create presentation in LaTex
• Meet with Mentor to discuss presentation
• Attend Responsible Conduct of Research Training
• Update/Amend presentation
• Mini Presentation
• Meet with Mentor to discuss 1D simulation

Week 6

• Find appropriate 1D simulation function
• Research bibliographies in LaTeX
• Attend "What Makes a Good Poster" Talk
• Write code based on algorithms in Thesis for 1D simulation
• Meet with Mentor to discuss difficulties in coding 1D simulation
• Holiday
• Continue problem-solving code issues for 1D simulation
• Review Fourier Transform as used in Matlab

Week 7

• Review aspects of coding to continue debugging for 1D simulation
• Debug code for 1D simulation
• Attend working lunch and talk about graduate school
• Continue debugging code for 1D simulation
• Meet with Adam, graduate student, to work on Fourier Transform in Matlab
• Correct/Modify prior draw function
• Learn how to use bibTeX within LaTeX

Week 8

• Meet with Mentor to discuss coding for 1D simulation
• Check that originally chosen 1D function integrates appropriately
• Attend working lunch
• Meet with Mentor to go over code for 1D simulation
• Create code to test 1D simulation
• Complete 1D simulation

Week 9

• Begin working on poster
• Meet with Mentor to discuss rough draft of poster
• Redraft poster according to suggestions/ideas from Mentor
• Submit poster
• Begin work on final paper
• Meet with Mentor to discuss 2D simulation
• Attend working lunch
• Begin working on final presentation
• Start work on 2D simulation
• Continue work on final paper

Week 10

• Continue work on final presentation
• Continue work on final paper
• Continue work on 2D simulation
• Attend Poster Session
• Meet with Mentor to discuss final presentation and code for 2D simulation
• Continue work on final paper
• Revise final presentation
• Continue work on 2D simulation
• Give final presentation
• Submit final paper