# User:Athompson

From REU@MU

## 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 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