Initialisation

I will list out all relevant general parameters that I have initialised for my galaxy(in normalised form):

1. Resolution of $z$ is $dz = 0.04$
2. Resolution of $t$ is $dt = 0.00079$
3. $\alpha = sin(\pi z)$
4. I solve my equations for $r = 0.4kpc$
5. When working on Task 3, I evaluate $B_{tot}$ at $z=0$
6. I work with Dirichlet Boundary conditions for Task 3
7. My simulations run for $t_{final} = 11.85t_0 = 8.95 Gyr$

For completeness, I will list all scaling parameters again:

$$ \begin{array}{|c | c | c |}\hline \text{Scaling Constant} & \text{ Value } & \text{Unit} \\ \hline R_0 & 10 & kpc \\ \hline h_0 & 0.5 & kpc \\ \hline B_0 & 1e-6 & G \\ \hline \alpha_0 & 2000 & cm s^{-1}\\ \hline \Omega_0 & 100 & km s^{-1} kpc^{-1} \\ \hline S_0 & -50 & km s^{-1} kpc^{-1} \\ \hline \eta_T & 1e26 & cm^2 s^{-1} \\ \hline t_0 = h_0^2/\eta_T & 0.745 & Gyr \\ \hline r_\Omega & 2 & kpc \\ \hline \end{array} $$

Results

I will first present the results, and discuss them later in the discussions section.

Parameter space for oscillatory solutions

I perform simulations for $R_\omega \in[-20, 0]$ and $R_\alpha\in[0,20]$ with step sizes of $0.5.$ According to my simulations, the results for the parameter space of oscillatory and non-oscillatory solutions is given in figure (1).