A qualitative look at the model

o The crystal type:

u' = - dE(u,dp) / du

  • Square or round crystals depending on pressure gradient

o The displacement:

mx'' + c x' + k u ( 1 - u x ) x = mg sin(angle)

  • Equilibrium displacement is angular dependent

    ( 1 - u x ) x = (mg/ku) sin(angle)

  • With small initial displacement and velocity
    • The equation is nearly linear
    • Snow will not fracture

  • For large initial velocity or displacement
    • The equation is strongly nonlinear.
    • Snow will fracture for all crystal types
    • Fracture easier for rounds

o Fracture is predicted for
  • Large displacement or large slope angles
  • Large initial velocities

o Where do large initial velocities come from?

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