Faraday Instability
Forcing
Drive freq ω_d:
1.0
Drive amplitude a:
0.3
Fluid / Damping
Damping γ:
0.05
Surface tension σ:
0.5
Pattern mode:
Stripes
Hexagonal
Squares
Chaotic
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Apply Perturbation
Status
Time
0
Amplitude
—
Unstable?
—
Mathieu eq:
ẍ + [δ + ε cos(t)]x = 0
Instability when:
δ ≈ n²/4
for integer n
Faraday wavelength:
λ_F ≈ 2λ/2 = λ_d
Pattern selection: hexagons (low forcing), stripes (high forcing)
Surface Height Field
Mathieu Stability Diagram
Top View — Pattern
Mode Amplitude vs Time