Christopher J. Kimmer, Ph.D.
IU Southeast Informatics
iSci
the informatics of scientific computing
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Conclusions
Higher resolution numerical studies of the limiting process involved in the anisotropic Landau-Ginzburg functional have revealed no new surprises about the structure and topology of the interface, and it is indeed tempting to speculate that the topology of the limit structure is dominated by the two important Fourier modes. The highest resolution results reveal that the critical surface is faceted, and this interesting result clearly begs for still higher-resolution numerical work. The limitations currently imposed by available computer memory call for further Landau-Ginzburg studies to be used with an alternate computational approach such as cluster-based or parallel processing in order to ease reliance on data structures too large to be efficiently used on available one-processor computers.
The stability of the topology of the interface as t decreases allows the Voronoi construction to be an excellent tool for desribing the structure of the surface and quickly using this construction to represent the structure in parallel space. This cell complex also provides a natural starting point for refinements that can model the 5D surface ever more accurately as a cell complex in six dimensions. Most important for future work, the accuracy of the Voronoi construction coupled with the impractical memory needs of the real space method indicate that a most effective way to continue to study this surface is by using the Voronoi construction as a starting point to model the surface directly as a set of 5-simplices approximating the continuous surface.
Next: An Ensemble of Quasiperiodic Up: Quasiperiodic Minimal Surfaces Previous: The Physical Space Structure