Optimal energy arrangements of 4 points on periodic rectangular grids
Published on:
9 November 2023
Primary Category:
Classical Analysis and ODEs
Paper Authors:
Nathaniel Tenpas
Bullets
Key Details
Shows a class of 4-point configurations that minimize periodic energy functions
Configurations are parallelograms arranged on rectangular periodic grids
Results provide evidence for a conjecture about the optimality of the hexagonal lattice
Connects periodic energy problems to the sphere packing problem
Uses linear programming bounds to prove optimality
Explore the topics in this paper
AI generated summary
Optimal energy arrangements of 4 points on periodic rectangular grids
This paper constructs periodic point configurations that minimize energy for a class of functions. It shows these 4-point configurations, arranged in a parallelogram shape, are optimal among all 4-point configurations with the same rectangular periodicity. The configurations yield insights into energy minimization and provide evidence towards a conjecture about the hexagonal lattice's optimality.
Answers from this paper
You might also like
Optimizing periodic point configurations on the plane
Convergence of periodic approximations for quasicrystal models
Maximizing polygon edge length sums
Ordered and disordered point patterns across dimensions
Mathematical method for searching crystal structure prototypes
Computing stable structures of molecules
Comments
No comments yet, be the first to start the conversation...
Sign up to comment on this paper