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Journals and Conferences
We construct local energy-minimizing bubble clusters in the plane that are not simply-connected. Numerical evidence suggests that these minima are not isolated.
The floppiness of bubble chains and the rigidity with respect to slidings of three-bubble clusters are used to construct numerically degenerate local energy-minimizing bubble clusters in the plane with as many cavities as desired. Experimental demonstrations are also given. © 2009 Elsevier Ltd. All rights reserved. 1. Formulation of the problem and… (More)
We consider the singularly perturbed Allen-Cahn equation on a strictly convex plane domain. We show that when the perturbation parameter tends to zero there are solutions having a transition layer that tends to a straight line segment. This segment can be characterized as the shortest path intersecting the boundary orthogonally at two points.
Land surveying in ancient states is documented not only for Eurasia but also for the Americas, amply attested by two Acolhua-Aztec pictorial manuscripts from the Valley of Mexico. The Codex Vergara and the Códice de Santa María Asunción consist of hundreds of drawings of agricultural fields that uniquely record surface areas as well as perimeter… (More)