11. Solving the data-flow equations starts with initializing all in-states and out-states to the empty set. 12. For this it uses Feynman diagrams, renormalisation flow equations , and other methods from mathematical physics. 13. However, the flow equation determines a vector field on that theory space which can be investigated. 14. It is the theory space and the RG flow equations that determine possible UV fixed points. 15. Solving the data flow equations starts with initializing all in-states and out-states to the empty set. 16. The transient state form of this flow equation , known commonly as Richards equation writes in 1-D: 17. The generalized flow equation provides the analytical foundation for reservoir engineering that exists to this day. 18. The unsteady flow equation solver was adapted from Dr . Robert L . Barkau s UNET package. 19. This yields a set of data-flow equations : 20. However, in general the Ricci flow equations lead to singularities of the metric after a finite time.
