Contents

Creating a Network

Creating a Network

We can now assemble them together in this ChemicalNetwork. This object helps us do all the neccessary computations to arrive at the symbolic rhs and jacobian functions, which ultimately eases us of the process of deriving them by hand.

In our example with only two reactions, that consisted of \(\rm H, H^+, e^-\). Note that in the below they represent the number density \((\rm cm^{-3})\) of different species.

\[ \mathrm{ H^+ + e^- \rightarrow H} \]
\[ \mathrm{ H + e^- \rightarrow H^+ + 2 e^-} \]
\[\begin{split} \begin{align*} \mathrm{ \frac{d H}{dt} = k_{02}(T) \, H^+ \, e^- - k_{01}(T) \, H \, e^- \\ \frac{d H^+}{dt} = - k_{02}(T) \, H^+ \, e^- + k_{01}(T) \, H \, e^- \\ \frac{d e^-}{dt} = - k_{02}(T) \, H^+ \, e^- + k_{01}(T) \, H \, e^- \\ } \end{align*} \end{split}\]

We can do a quick sanity check on the conservation of the species \(H\) and the charge \(e^-\) and the equation above apparently satisfies our conservation law.

\[ \frac{d}{dt} (\rm H + H^+) = 0 \]
\[ \frac{d}{dt} (\rm H^+ -e^-) = 0 \]

Import Libraries and Create the Network

Primordial rates and cooling for the 9-species network are included in the default dengo library in dengo.primordial_rates and dengo.primordial_cooling. The reactions and cooling are added automatically to the reaction_registry, cooling_registry and species_registry with the call to dengo.primordial_rates.setup_primordial. Here we setup the same sample network we demonstrated in the last chapter with k01, k02 and reHII.

import dengo
from dengo.chemical_network import \
 ChemicalNetwork, \
 reaction_registry, \
 cooling_registry, species_registry
import dengo.primordial_rates
import dengo.primordial_cooling

dengo.primordial_rates.setup_primordial()

simpleNetwork = ChemicalNetwork()
simpleNetwork.add_reaction("k01")
simpleNetwork.add_reaction("k02")
simpleNetwork.add_cooling("reHII")
simpleNetwork.init_temperature((1e0, 1e8))

Adding reaction: k01 : 1*H_1 + 1*de => 1*H_2 + 2*de
Adding reaction: k02 : 1*H_2 + 1*de => 1*H_1

simpleNetwork is fed with the reactions and cooling actions. We are now ready to use dengo to build a solver.

previous

Create Cooling Functions

next

Building A ODE solver