Visualizing Nuclear Scission through a Multifield Extension of Topological Analysis

Abstract

Abstract-In nuclear science, density functional theory (DFT) is a powerful tool to model the complex interactions within the atomic nucleus, and is the primary theoretical approach used by physicists seeking a better understanding of fission. However DFT simulations result in complex multivariate datasets in which it is difficult to locate the crucial 'scission' point at which one nucleus fragments into two, and to identify the precursors to scission. The Joint Contour Net (JCN) has recently been proposed as a new data structure for the topological analysis of multivariate scalar fields, analogous to the contour tree for univariate fields. This paper reports the analysis of DFT simulations using the JCN, the first application of the JCN technique to real data. It makes three contributions to visualization: (i) a set of practical methods for visualizing the JCN, (ii) new insight into the detection of nuclear scission, and (iii) an analysis of aesthetic criteria to drive further work on representing the JCN.

Description of induced nuclear fission with Skyrme energy functionals: Static potential energy surfaces and fission fragment properties

“…• As recalled above, a fork at the high-density end of the JCN (red, upper right part of each graph) shows the presence of two distinct features meeting at a critical point, rather than a single peak, i.e. two topologically distinct regions of space [95]. Here, we interpret the first occurrence of such a fork at high density values as the precursor to scission, marking the upper bound q (max) of the interval I q defining scission.…”

“…In fact, we have recently shown that the sudden division of the compound nucleus in two separate fragments at the discontinuity of one-dimensional fission pathways E(q 20 ) is clearly associated with a fork in the JCN [95]. Here, we extend the method to the more difficult problem of detecting features along a continuous fission pathway characterized by the q N constraint.…”

Characterization of microstructures using contour tree connectivity for fluid flow analysis

“…Contour trees are topological abstractions that follow the evolution of level sets as they appear, join, split or disappear by means of graphs. They have mostly been used to simplify volumes and to visualize high dimensional scalar fields [9][10][11][12][13][14].…”

Interactive Visualization for Singular Fibers of Functions f : R3 → R2

“…Visually, Duke et al [11] arranged JCNs aesthetically in 3D space for arbitrary dimension of the range space, and applied it to analyzing real datasets. In our case, however, it is better to keep the connection with the range, and this requires a new layout algorithm (Section 6).…”

“…Thus, like the solution used by Duke et al [11], a heuristic layout is called for, based on a spring layout algorithm, shown in Figure 9. The popular force-directed graph layout algorithm [15] in 2D works fine for the 3D layout of the Reeb space in our experiments, but with a few modifications.…”