A superior descriptor of random textures and its predictive capacity

Area of Science:

• Multidisciplinary science
• Materials science
• Physics

Background:

• Two-phase random textures are prevalent across diverse scientific fields, including materials science, ecology, biology, and astrophysics.
• Understanding the spatial structure of these textures presents significant theoretical challenges, particularly in extracting higher-order information from measurable functions.

Purpose of the Study:

• To identify a two-point function capable of reflecting nontrivial higher-order structural information in random textures.
• To introduce and validate the two-point cluster function C(2)(r) as a superior descriptor for texture analysis.

Main Methods:

• Utilized inverse reconstruction techniques to probe the information content of various two-point functions.
• Examined the widest class of two-point functions to date.
• Focused on the sensitivity of the two-point cluster function C(2)(r) to topological connectedness.

Main Results:

• Demonstrated that the two-point cluster function C(2)(r) is a superior descriptor compared to other two-point functions.
• Successfully reconstructed textures from materials science, cosmology, and granular media using C(2)(r).
• Showed C(2)(r) is sensitive to topological connectedness information.

Conclusions:

• The two-point cluster function C(2)(r) provides a robust method for characterizing complex random textures.
• This approach offers a theoretical pathway for predicting the bulk physical properties of random textures.
• The findings have significant implications for understanding atomic and molecular systems.