NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2011, 2 (4), P. 51–60
BIFURCATION CONDITION FOR OPTIMAL SETS
OF THE AVERAGE DISTANCE FUNCTIONAL
X.Y. Lu – Scuola Normale Superiore, Pisa, Italy. PhD student in Mathematics, email@example.com
Consider the quasi-static irreversible evolution of a connected network, which minimizes the average distance functional. We look for conditions forcing a bifurcation, thus changing the topology. We would give here a sufficient conditions. Then we will give an explicit example of sets satisfying the bifurcation condition, and analyze this special case. Proofs given here will be somewhat sketchy, and this work is based on the paper X.Y. Lu. Branching time estimates in quasi static evolution for the average distance functional, Preprint on CVGMT, in which more details can be found.
Keywords: Optimal transport, Euler scheme, minimizing movements, average distance.