Research Project Ideas
eTeaching Portfolio
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Orbital Analysis
Introductory:
Algebra required for basic orbital study, Physics concepts can be introduced in course of the project.
Intermediate:
Pre-calculus is needed for deeper data analysis. Previous exposure to Physics not required but recommended.
Advanced:
Calculus and Physics are definite pre-requisites. Programming knowledge would greatly help.
About the Notebook
Created by me to access, download and analyze data from current and past space missions directly from JPL/NASA. All mission data is publicly available for research but access is not simple; this notebook streamlines the process and provides a ready-made platform for any related study on a mission of interest. The Notebook can be used purely as a visualization tool for orbital dynamics or as a complete numerical analysis suite for it.
Objective
Related projects can help introduce students to Physics not yet at their grasp through direct manipulation of real-world data. The possibility of working with real data from current and past missions is pretty incredible and can really motivate a student. Moreover, if a student has no familiarity with programming, the project itself can become a perfect tool for learning. Students not only benefit from learning the basics of python but also become comfortable with JPL/NASA tools used in research today.
Project Ideas
Introductory: Compare and contrast Perseverance 2020 mission data to older long-range missions like Juno and Cassini. What are new missions doing differently and why?
Intermediate: Gain insight into tidal forces by studying the trajectory of comet Shoemaker–Levy 9 post-collison with Jupiter.
Advanced: By doing a careful study of gravity-assisted missions like Cassini, prepare a launch schedule for an upcoming mission to the outer planets.
The Ising Model
Introductory:
Basic algebra is all that is needed to gain deep numeric insight for a student.
Although programming is not required it will definitely be developed here.
Intermediate:
Pre-calculus and some statistics are needed to give proper analysis to data produced. There should be some previous exposure to programming.
Advanced:
Calculus and Physics are needed to really understand the nuances of the theory. Computationally the experienced student will thrive.
About the Notebook
The Ising Model is one of the staple problems in Thermodynamics. Exact solutions beyond two dimensions have eluded us but their numerical study have helped develop fields as far away as Neuroscience. I created this Notebook to treat the one dimensional case numerically and provide rich graphical output. Code is written in two languages: python and julia, the latter being a relatively new language that is becoming the choice for STEM.
Objective
Related projects can help introduce students to a wide range of topics. Mathematically it is all about randomness and chance, physically the game is minimization of energy and computationally we must do it all in the shortest time possible. Projects from introductory to advanced can come from any of these fields of study.
Project Ideas
Introductory (Mathematics): Compare and contrast the results when randomness is selected through different methods. Introduces students to probability densities and random numbers.
Intermediate (Computing): Expand the current 1D code to 2D/3D and benchmark using both python and julia. Find optimizations in the code and document the process.
Advanced (Physics): Turn the model into a Potts Model which is a generalization of the Ising Model. There is current research which can become a base for a student to start their own exploration.
Questions? Please do ask! Email me: 📫