Exciton Domain Transport Simulation

This is a new feautre and is not yet finished. I am writing the equations as I implment them in the solver. [sec:electrical]

\[\frac{dN_{S}}{dt}=\frac{1}{4}R_{free}+\frac{1}{4}\kappa_{TT} N_{T}^{2}-\\ \\ (\kappa_{S}+\kappa_{ISC})N_{s}\\ \\ -(\frac{7}{4}\kappa_{SS} N_{S} -\kappa_{ST} N_{T})N_{S}\]

\[\frac{dN_{t}}{dt}=\frac{3}{4}R_{free}+\kappa_{ISC} N_{S} + \frac{3}{4}\kappa_{SS} N_{S}^2\]

\[\frac{dN_{SD}}{dt}=\frac{\kappa_{FRET}}{N_{DOP}} (N_{DOP}-N_{SD}-N_{TD})N_{s}\\ \\ +\frac{1}{4}\kappa_{TTD}N_{TD}^{2} \\ -(\frac{7}{4}\kappa_{SSD} N_{SD}+\kappa_{STD}N_{TD}) N_{SD}\]