Revisiting the tree Constraint

International audienceThis paper revisits the tree constraint introduced in [2] which partitions the nodes of a n-nodes, m-arcs directed graph into a set of node-disjoint anti-arborescences for which only certain nodes can be tree roots. We introduce a new filtering algorithm that enforces generalized arc-consistency in O(n + m) time while the original filtering algorithm reaches O(nm) time. This result allows to tackle larger scale problems involving graph partitioning

Pinch-off of rods by bulk diffusion

The morphology of a rod embedded in a matrix undergoing pinching by interfacial-energy-driven bulk diffusion is determined near the point of pinching. We find a self-similar solution that gives a unique temporal power law and interfacial shape prior to pinching and self-similar solutions after pinching. The theory is compared to experiments that employ in situ four-dimensional X-ray tomographic microscopy for rods of liquid or solid pinching by solute diffusion in the high-diffusivity liquid phase. The excellent agreement between experiment and theory confirms that the interfacial morphology near the singularity is universal both before and after pinching; the shape holds regardless of the material system and initial condition. This also implies that the predictions of the time-dependence of the process can be used to determine the time to pinching for a wide variety of physical systems, and thus provide estimates of the time required for capillarity-driven break-up of microstructures from the detachment of secondary dendrite arms to polymer blends