QDS Microphysics Lab

Kernel: K(t,r) = σ² · exp(-|t|/τ_c) · exp(-r² / (2 λ_c²)).
Explore how the finite correlation time τ_c and coherence length λ_c shape temporal and spatial correlations.

1. Kernel parameters

σ² (variance)

τ_c (correlation time, units of t)

λ_c (coherence length, units of r)

For intuition: the temporal curve is shown for t = 0 → 5 τ_c, and the spatial curve for r = 0 → 4 λ_c.

2. Probe a point dimensionless K and K/σ²

|t| (same units as τ_c)

r (same units as λ_c)

σ²:— K(t,r):— K/σ²:— exp(-|t|/τ_c):— exp(-r²/(2 λ_c²)):—

3. Correlation shapes

Top: temporal correlation K(t,0)/σ² vs t (0 → 5 τ_c).
Bottom: spatial correlation K(0,r)/σ² vs r (0 → 4 λ_c).