Computational codes for "Emergence of Periodic Potential for Point Defects in a 2D Hexagonal Colloidal Lattice" [ZIP Archive]

This repository contains the Jupyter Notebook codes and data for the manuscript. The codes implement a complete computational pipeline for analyzing Brownian motion of point defects (mono-vacancy, di-vacancy, mono-interstitial, di-interstitial) in a 2D hexagonal colloidal crystal, within the evolution mechanics framework:<b>01_DriftDiffusion_Extraction</b> — extracts the spatially resolved drift vector <b>f</b>(q) and diffusion matrix <b>D</b>(q) from experimental trajectories via conditional moments [Eq. (8)].<b>02_Dmatrix_FourierFitting</b> — fits the position-dependent <b>D</b>(q) with a Fourier series and performs Cholesky decomposition for SDE construction.<b>03_Potential_FourierFitting</b> — reconstructs the stochastic potential φ(q) from <b>f</b>(q) and <b>D</b>(q) via weighted least-squares Fourier fitting [Eqs. (10)–(14)].<b>04_SDE_EulerMaruyama</b> — integrates the reconstructed SDE (dq = <b>f</b>dt + <b>L</b>dW) via Euler–Maruyama to generate simulated trajectories (FIG. 3).<b>04-1_CriticalPoint_Analysis</b> — identifies minima and saddle points of φ(q), calculates energy barriers, and visualizes the potential landscape (FIG. 2, Table IV).<b>06_Rsquared_GoodnessOfFit</b> — computes the weighted coefficient of determination R² for the Fourier expansion fit (Tables I–II).The Codes/ directory contains 7 notebooks (Python 3, requires numpy/pandas/scipy/matplotlib). The Results/ directory contains the experimental trajectory CSV files and all intermediate/final NPZ outputs. See README.md for detailed documentation.