Joint PDF transport equation final form

Combining (6.9) and (6.18), and using the fact that the equality must hold for arbitrary choices of Q, leads to the joint velocity, composition PDF transport equation 19 

From this expression, it can be seen that the joint PDF evolves by transport in 

However, in order to use (6.19) to solve for the joint PDF, closures must be supplied for the conditional acceleration and reaction/diffusion terms. For simplicity, we will refer to these terms as the conditional fluxes. 

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