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A painting, like human skin, develops cracks on the surface as it dries and ages. The painting cracks, also known as craquelure, are often considered analogous to human fingerprints; these have been regarded as a unique signature reflective of the painting’s characteristics and are important in art authentication. Intriguingly, studies in other fields, such as geology, have observed the presence of distinctive characteristics in soil desiccation cracks. These cracks exhibit self-similarity, forming patterns that suggest broader geological processes at work. In light of this connection, the primary objective of this study is to investigate whether the painting cracks also exhibit a self-similar nature. By delving into this, we seek to shed light on the underlying properties of the painting cracks. This study also aims to investigate whether the characteristic self-similar trait of the cracks can serve as an identifier in relation to the provenances of the paintings. To this end, this study adopts the methodology originally designed to characterize the phenotypic traits of 3D particle geometries in granular materials research. This study develops a 2D equivalent concept, focusing on the phenotypic traits of the individual islands enclosed by cracks within paintings. The results successfully demonstrate that the phenotypic trait of painting cracks exhibits a self-similar nature, which can reveal characteristics associated with the provenances of paintings. The findings will offer valuable insights into the scientific examination of artworks based on painting cracks. 

This paper introduces a new paradigm that integrates the concepts of particle abrasion and breakage. Both processes can co-occur under loading as soil particles are subjected to friction as well as collisions between particles. Therefore, the significance of this integrating paradigm lies in its ability to address both abrasion and breakage in a single framework. The new paradigm is mapped out in a framework called the particle geometry space. The x-axis corresponds to the surface-area-to-volume ratio (A/V), while the y-axis represents volume (V). This space facilitates a holistic characterization of the four-particle geometry features, that is, shape (β) and size (D) as well as surface area (A) and volume (V). Three distinct paths (abrasion, breakage, and equally occurring abrasion and breakage processes), three limit lines (breakage line, sphere line, and average shape-conserving line), and five different zones are defined in the particle geometry space. Consequently, this approach enables us to systematically relate the extent of co-occurring abrasion and breakage to the particle geometry evolution. 

Particle shape plays a critical role in governing the properties and behavior of granular materials. Despite advances in capturing and analyzing 3D particle shapes, these remain more demanding than 2D shape analysis due to the high computational costs and time-consuming nature of 3D imaging processes. Consequently, there is a growing interest in exploring potential correlations between 3D and 2D shapes, as this approach could potentially enable a reasonable estimation of a 3D shape from a 2D particle image, or at most, a couple of images. In response to this research interest, this study provides a thorough review of previous studies that have attempted to establish a correlation between 3D and 2D shape measures. A key finding from the extensive review is the high correlation between 2D perimeter circularity (cp) and Wadell’s true sphericity (S) defined in 3D, suggesting that a 3D shape can be estimated from the cp value in terms of S. To further substantiate the correlation between cp and S, this study analyzes approximately 400 mineral particle geometries available from an open-access data repository in both 3D and 2D. The analysis reveals a strong linear relationship between S and cp compared with other 2D shape descriptors broadly used in the research community. Furthermore, the limited variance in cp values indicates that cp is insensitive to changes in viewpoint, which indicates that fewer 2D images are needed. This finding offers a promising avenue for cost-effective and reliable 3D shape estimation using 2D particle images. 

This dataset has (i) 3D geometry files of mineral particles from Florida and Virginia and (ii) analyzed 3D particle geometries. A total of 382 particle geometry files are included in this dataset. The Florida particles in this dataset are limestones, while the Virginia particles are freshly crushed granites from a quarry in Richmond, Virginia. The geometry files are obtained by 3D structured light scanning and presented in wavefront .obj format. These files can be viewed using free 3D geometry viewers such as MeshLab, Blender, and Microsoft 3D Viewer, enabling users to zoom in/out and rotate the 3D particles. The 3D particle geometries have been analyzed for shape, size, surface area, and volume. The analysis includes the use of 3D shape indices such as M (= A/V × L/6) and β, in addition to common 3D geometry measures such as surface area (A), volume (V), and size (L or D). The overall geometric properties of each particle group are also analyzed in terms of α and β*; the α informs the geometric variation (i.e., the relation between particle shape and size), and β* informs the average shape angularity of the particles. This dataset will be valuable for investigating the particle geometry-dependent soil behavior, by performing laboratory testing on analog soils after 3D printing the geometry files or using the files for discrete element modeling. Further information can be found in the related work linked above and the data report (see Data_report.pdf) included within the dataset. 

This study evidences that the particle surface-area-to-volume ratio (A/V) and the particle volume (V) have the key information of particle geometry and the ‘signature’ is realized by a power-law relationship between A/V and V in a form of V = (A/V)^α × β. We find that the power value α is influenced by the shape-size relationship while the β* term (β evaluated with a fixed value of α = -3) informs the average particle shape of a granular material regarding the overall angularity. This study also discusses how the particle shape can be retrieved in terms of Wadell’s true sphericity using the A/V and V. This concept is linked to another shape index M that interprets the particle shape as a function of surface area A, volume V, and size L. This paper explains the analytical aspects of geometric ‘signature’ and examines the idea using the example particles to address the DEM modelling-related questions.