A Two-Dimensional Kinetic Triangulation with Near-Quadratic Topological Changes

Topological changes in a two-dimensional foam cluster.

Experiments on a small cluster of bubbles in a nominally two-dimensional foam show an instability in which a topological change forces one of the bubbles to be ejected to the outside of the cluster at a point where this is not predicted by a two-dimensional model of a foam. This is interpreted in terms of the energy of the initial and ejected states and of the finite liquid content of the exper...

Two{dimensional Topological Dynamics

A Topological Framework for Advancing Front Triangulation

In this paper we study advancing front methods for surface reconstruction. We propose a topological framework based on handlebody theory to implement such methods in a simple and robust way. As an example of the application of this framework we show an implementation of the Ball-Pivoting Algorithm. Triangulating the Stanford Bunny using the Ball-Pivoting advancing front algorithm.

The immersed boundary method for two-dimensional foam with topological changes

We extend the immersed boundary (IB) method to simulate the dynamics of a 2D dry foam by including the topological changes of the bubble network. In the article [Y. Kim, M.-C. Lai, and C. S. Peskin, J. Comput. Phys. 229:5194-5207, 2010], we implemented an IB method for the foam problem in the two-dimensional case, and tested it by verifying the von Neumann relation which governs the coarsening ...

Multifarious topological quantum phase transitions in two-dimensional topological superconductors

We study the two-dimensional topological superconductors of spinless fermions in a checkerboard-lattice Chern-insulator model. With the short-range p-wave superconducting pairing, multifarious topological quantum phase transitions have been found and several phases with high Chern numbers have been observed. We have established a rich phase diagram for these topological superconducting states. ...