Update 7/27

  • Ran simulation with lambda=5 for longer time, to get to steady state:

  • Numerical integration technique for isothermal Parker wind - starting from differential equation in terms of u and r, parameterize in terms of s, so that

We can calculate the Jacobian for this dynamical system, and evaluate it at the critical point:

This gives the linear approximation to the system near the critical point; calculating the eigenvalues and eigenvectors, travel a small distance along the eigenvector with positive eigenvalue (corresponding to tangent to the stable manifold of the original system) and use numerical integrator of choice outward from the critical point.

  • Also started determining B fields for planet and star - looking for sigma of both to be 0.1 initially (based on Jonathan's example parameter space).

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