An approximate graph elicits detonation lattice

Abstract

This study presents a novel algorithm based on graph theory for the precise segmentation and measurement of detonation cells from 3D pressure traces, termed detonation lattices, addressing the limitations of manual and primitive 2D edge detection methods prevalent in the field. Using a segmentation model, the proposed training-free algorithm is designed to accurately extract cellular patterns, a longstanding challenge in detonations research. First, the efficacy of segmentation on generated data is shown with a prediction error 2%. Next, 3D simulation data is used to establish performance of the graph-based workflow. The results of statistics and joint probability densities show oblong cells aligned with the wave propagation axis with 17% deviation, whereas larger dispersion in volume reflects cubic amplification of linear variability. Although the framework is robust, it remains challenging to reliably segment and quantify highly complex cellular patterns. However, the graph-based formulation generalizes across diverse cellular geometries, positioning it as a practical tool for detonation analysis and a strong foundation for future extensions in triple-point collision studies.

Figures (6)

• Figure 1: Relating graph message passing to cellular detonation structure: (a) Directed message-passing graph: node features $h_i$ exchange edge ($e_{ij}$) messages $m_{ij}$, (b) Cellular detonation interpreted as a graph: triple points and collision kernels serve as nodes connected along Mach stems and incident shocks; wave motion induces directional interactions and (c) 2D detonation lattice as a graph, with collisions points as nodes and wave path as edges, illustrating how collisions localize within the network.
• Figure 2: Search in Euclidean space: a root node proposes its top four beam-search candidates; after applying occupancy constraints, only the green-marked (physically consistent) candidates are accepted, while the red-marked is rejected.
• Figure 3: Plot for 3-D generated lattice segmented by the model: (a) $n_x$=60 and (b) $n_x$=480. Red box shows mask fragmentation due to over-segmentation in $n_x$=480 case.
• Figure 4: Plot of geometric features from 25 samples: (a) major-axis length, (b) minor-axis length, each shown as a KDE (normalized) with stick marks indicating individual samples (blue) and an inline boxplot (median = red line, mean = green dashed line, whiskers 5$^{\text{th}}$–95$^{\text{th}}$ percentiles); (c) joint density of volume and aspect ratio (major/minor axis) with overlaid points (normalized density color scale).
• Figure 5: Plot of joint density of volume and aspect ratio (AR) from 25 samples with overlaid points (normalized density color scale): (a) AR$_1$=$L_x$/$L_y$, (b) AR$_2$=$L_x$/$L_z$ and (c) AR$_3$=$L_y$/$L_z$.