Parameter Extraction

Extract κ and Σ

Input your experimental time-averaged Legendre coefficients Bl ± σl. The tool minimises χ² to find the best-fit bending rigidity κ and effective surface tension Σ, with full error estimates from the covariance matrix.

Experimental Data — Bl ± σl
Enter time-averaged Legendre coefficients. Each row: mode l, mean Bl, standard error σl. Values are typically in range 10⁻⁵ – 10⁻³.
l
Bl (exp mean)
σl (std error)
Load Example Dataset
Fit Settings
Extracted Parameters
Load data and click "Run χ² Minimisation" to extract parameters.
χ²(s) — Surface Tension Scan
Minimum of \(\chi^2(s)\) gives optimal \(\Sigma\), then \(\kappa=k_B T/j\).
Fit: Bl Theory vs Experiment
Circles = experimental Bl ± σl · Dashed = theoretical B̄l(κ, Σ)