Angular Auto-Correlation

Visualise ξ(γ)

The equatorial angular auto-correlation function ξ(γ) encodes how membrane shape fluctuations at angle φ are correlated with those at φ+γ. Select modes, set membrane parameters, and observe how each mode contributes.

Mode Selection
l = 0,1 are trivial (volume change, translation). Physical fluctuations start at l ≥ 2.
Membrane Parameters
40
10
Display
Experimental Presets
ξ(γ) — Angular Auto-Correlation Function
\(\gamma \in [0,2\pi]\) rad · \(\xi(\gamma)=\sum_{l\ge2} b_l P_l(\cos\gamma)\)
Mode Amplitude Contributions
\[ b_l = \frac{2l+1}{4\pi}\,\frac{k_B T}{\kappa(l-1)(l+2)\left[l(l+1)+\Sigma\right]} \]
Mode l αl / κ ⟨|ulm|²⟩ · κ bl % of ξ(0)