He-II fountain effect and zero viscosity

Purpose

Run GPE with a thermomechanical pressure gradient across a narrow channel to reproduce the superfluid fountain effect in He-II.

What it proves

The height rise $\Delta h$ is linear in chemical-potential difference $\Delta\mu$ with $R^{2} = 1.000$ and zero viscous loss, confirming coherent mass flow of the condensate.

Relation to current theory

He-II is the textbook realisation of Landau two-fluid theory. SVT re-derives it from the *same* GPE it uses for the vacuum — providing a laboratory benchmark that the solver is not over-fit to cosmology.

Plots

Scalar metrics

Healing length ξ0.7071

Sound speed c_s1

Chemical potential μ1

Max v deviation0.00000422

Max E_kin deviation0.00111

N_target208

stdout tail

     Δh/ΔT = (ρ_s/ρ)(S/g) = 14.5  m/K
     ΔT = 10 mK  →  Δh = 0.15 m = 14.5 cm
     ΔT = 1 mK   →  Δh = 1.45 cm

  Zero viscosity (v = const)     : PASS   (|δv/v₀| = 4.2e-06)
  Energy conservation            : PASS   (|δE/E₀| = 1.1e-03)
  Fountain Δh grows with Δμ      : PASS
  Δh ∝ Δμ linearity (R²)         : PASS   (slope = 1.831, R² = 1.000000)

  SVT Prediction: He-II fountain effect and zero viscosity
    emerge naturally from GPE superflow in the vacuum superfluid
  Matches data:   YES — Validated
=================================================================

/home/kruiserx/code/SVT2.0/sim_09_helium_fountain.py:223: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
  plt.show()
/home/kruiserx/code/SVT2.0/sim_09_helium_fountain.py:182: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
  plt.show()
/home/kruiserx/code/SVT2.0/sim_09_helium_fountain.py:285: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
  plt.show()