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Contents
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 bimodal univariate distribution
 Meet with Mentor to discuss project direction
 Continue reading information about MCMC
 Attend Good Presentations, Good Technical Writing Talk
 Perform MetropolisHastings (MH) sampling of a bimodal 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 MetropolisHastings 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 problemsolving 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