Shape minimization of the dissipated energy in dyadic trees (Q717929)

The goal of this work is to determine the shape of dyadic trees that would minimize the viscous energy of a Newtonian fluid under a volume constraint on the tree. The authors show that for both -- low-flow regime and nonlinear flow regime -- the optimal structure depends on the fluid boundary conditions that are applied at tree root and leaves. Moreover, the numerical simulations in the nonlinear case give precisely the geometry of the bifurcation.