UROP Project
Optimal potential energy via gradient descent
Gradient descent, potential energy, optimization
Research Mentor: Aleksandr Reznikov, He/Him/His
Department, College, Affiliation: Mathematics, Arts and Sciences
Contact Email: areznikov@fsu.edu
Research Assistant Supervisor (if different from mentor):
Research Assistant Supervisor Email:
Faculty Collaborators:
Faculty Collaborators Email:
Department, College, Affiliation: Mathematics, Arts and Sciences
Contact Email: areznikov@fsu.edu
Research Assistant Supervisor (if different from mentor):
Research Assistant Supervisor Email:
Faculty Collaborators:
Faculty Collaborators Email:
Looking for Research Assistants: Yes
Number of Research Assistants: 1
Relevant Majors: Mathematics, Physics, Computer Science, Statistics, Engineering
Project Location: On FSU Main Campus
Research Assistant Transportation Required: Remote or In-person: In-person
Approximate Weekly Hours: 7, Flexible schedule (Combination of business and outside of business. TBD between student and research mentor.)
Roundtable Times and Zoom Link:
Not participating in the roundtable
Number of Research Assistants: 1
Relevant Majors: Mathematics, Physics, Computer Science, Statistics, Engineering
Project Location: On FSU Main Campus
Research Assistant Transportation Required: Remote or In-person: In-person
Approximate Weekly Hours: 7, Flexible schedule (Combination of business and outside of business. TBD between student and research mentor.)
Roundtable Times and Zoom Link:
Not participating in the roundtable
Project Description
Put four electrons on the unit sphere and let them repel each other. They will move around until they reach the "ground state": i.e., the state, when their potential energy is minimal. If we were not too unlucky with our original placement, the electrons will end up in the vertices of the regular tetrahedron. In fact, this is a conjecture that is not yet rigorously proved.For the project, I propose to verify it experimentally; i.e., write a code that will place four random points on the sphere and move them, via the gradient descent method, to nearly-optimize the potential energy.
This project has many very interesting extensions; for example, moving to higher dimensions or to shapes other than the sphere (e.g., a donut).
Research Tasks: The most important task is to write a robust code for the gradient descent method for this specific problem. The code should ideally provide the video of points moving and eventually converging to the tetrahedron.
Skills that research assistant(s) may need: Required: strong knowledge of Calculus 1. You should be able to apply chain rule multiple times to a fairly inconvenient function.
Also required some coding skills, preferably in Python, but I do not have a strong opinion here.
Strongly recommended: partial derivatives, Calculus 3
Knowledge of physics is not required but will certainly make the project feel more applicable.