Nanoinformatics by Isao Tanaka

Author:Isao Tanaka
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

The top panel shows the evolution of Betti numbers for varying Sc concentration. At each value of Sc concentration threshold “δ”, those voxels having a concentration of δ ± 0.02 were chosen. Consider β0: at a high concentration threshold, beyond 0.5, a very small number of simply connected components are observed. This is because very few voxels have concentration value equal or more than this threshold. As concentration threshold is decreased, more voxels qualify to be included in the group leading to an increase in β0. The value of β0 remains constant for a certain range indicating that these are real features. A plot of the voxels at δ = 0.3 shows that it indeed captures real clusters of Sc. With further decrease of concentration threshold, a decrease in β0 is observed. This is because every voxel outside the Sc clusters has some minimal content of Sc and the inclusion of all exterior voxels results in one single connected component. We also observe a peak in the value of β1 at a low concentration of δ = 0.03. When we plot the isoconcentration surface for those voxels we find that these represent cavities. These voxels with very low Sc concentration sit on the edge of the Sc clusters, and thereby, enclose Sc clusters within themselves. A similar trend is observed with Mg where for low concentration we see Mg Isosurface containing cavities that enclose Sc clusters, whereas for high concentration there are few voxels.

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