Changes between Version 3 and Version 4 of u/erica/radpredictionsink

Timestamp:

04/05/16 14:42:27 (9 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/radpredictionsink

@@ -25 +25 @@
 [[Image(ic.png, 35%)]]
 
-Prediction: By 24 days, expect the diffusion wave to hit the boundary. Depending on the energy injection rate compared to the diffusion rate, the shape of the curve might be different. For instance, if energy injection rate (Er) >> diffusion rate (Dr), might expect the gaussian to be increasing in height as well as width. If Er = Dr, might expect the profile to be flat, as it grows in width. If Er << Dr, expect a gaussian that grows in width over time, but not height. 
+'''Prediction''': By 24 days, expect the diffusion wave to hit the boundary. Depending on the energy injection rate compared to the diffusion rate, the shape of the curve might be different. For instance, if energy injection rate (Er) >> diffusion rate (Dr), might expect the gaussian to be increasing in height as well as width. If Er = Dr, might expect the profile to be flat, as it grows in width. If Er << Dr, expect a gaussian that grows in width over time, but not height. 
 
-Check: Make time curves of Erad(x), and check that the wave hits the boundary by t=24 days.
+'''
+Check''': Make time curves of Erad(x), and check that the wave hits the boundary by t=24 days.
 
 
-Prediction: The total thermal energy (and thus the total energy) should increase like t^2^. This is because, 
+'''Prediction''': The total thermal energy (and thus the total energy) should increase like t^2^. This is because, 
 
 [[latex($\frac{\partial e}{\partial t} = -\kappa_P \rho (4 \pi B - cE)$)]], where
@@ -42 +43 @@
 This holds as long as 4 pi B << the energy injected each time step. That way we can effectively ignore changes to thermal energy induced by increasing B(T).
 
-Check: Make curve of e_total(t), E_total(t).
+'''
+Check''': Make curve of e_total(t), E_total(t).
 
-Prediction: The total radiative energy should increase as:
+'''Prediction''': The total radiative energy should increase as:
 
 [[latex($\frac{dE_{rad}}{dt} = L$)]]
@@ -50 +52 @@
 [[latex($E_{rad}= Lt$)]]
 
-Check: Make curve of Erad_total(t).
+'''Check''': Make curve of Erad_total(t).
+
+'''Prediction''': The thermal energy, e, of a zone immediately adjacent to the kernel should increase linearly. This is because, the difference between the energy injected into the grid, E*, and 4piB, is some height X (where X = L*dt-B). So, right next to kernel, expect the coupling time to go like:
+
+[[latex($\int de=\kappa_P \rho X \int dt$)]]
+
+Or, 
+
+[[latex($\triangle e=\kappa_P \rho (L*dt-B) \triangle t$)]]
+
+*This assumes the energy injection rate is << diffusion rate, so that we know the difference in height between Erad and B*.
+
+'''Check''': Make a time query of a cell near the kernel.
+
+