2 papers
physics.comp-ph2026
Computer-Assisted Proofs for Geometric Optimization: From Crystallization to Carbon Nanotubes
Miguel Ayala, Rustum Choksi, Benedikt Wirth
We present a framework based on computer-assisted proofs that turns geometry optimization simulations for atomistic structures into mathematical proofs. Starting from a numerically…
math.DS2026
Computer-Assisted Proofs of Gap Solitons in Bose-Einstein Condensates
Miguel Ayala, Carlos GarcÃa-Azpeitia, Jean-Philippe Lessard
We provide a framework for turning a numerical simulation of a gap soliton in the one-dimensional Gross-Pitaevskii equation into a rigorous mathematical proof of its existence. The…