| 77 | The following is for a 1D isothermal sim of the Jeans Instability. |

| 78 | |

| 79 | In !ProblemModuleInit, I read in ambient density and temperature. These are used to uniformly set a corresponding Ambient Object. |

| 80 | |

| 81 | [[latex($READ ~ rho$)]] |

| 82 | |

| 83 | |

| 84 | [[latex($Info \% q(i, :, :, 1) = rho$)]] |

| 85 | |

| 86 | [[latex($Ambient\%density = info \% q(i, :, :, 1) $)]] |

| 87 | |

| 88 | |

| 89 | In ProblemGridInit, I loop over the cells in x (indexed by i) adding the following density perturbation: |

| 90 | |

| 91 | [[latex($info \% q(i, :, :, 1) = info\%q(i, :, :, 1) + 0.1*info\%q(i, :, :, 1)*Cos(kx)*e^0 $)]] |

| 92 | |

| 93 | |

| 94 | I am not 100% sure, but I think if I wanted to place the analytical function in astrobear, I would then add to !ProblemBeforeStep a loop over cells in i that continues to perturb the density function in time t: |

| 95 | |

| 96 | [[latex($info \% q(i, :, :, 1) = info\%q(i, :, :, 1, t=0)*e^{\omega t} $)]] |

| 97 | |

| 98 | Thus we should see the characteristic growth rate of [[latex($\omega$)]]. |

| 99 | |

| 100 | |