Precise algorithms to compute surface correlation functions of two-phase heterogeneous media and their applications

Area of Science:

• Materials Science
• Statistical Physics
• Applied Mathematics

Background:

• Quantitative characterization of random heterogeneous media is vital for determining effective physical properties.
• Surface correlation functions (Fss, Fsv) offer critical interfacial information for estimating transport properties, complementing traditional two-point correlations.
• Current technical challenges in sampling surface correlation functions limit their widespread application.

Purpose of the Study:

• To develop computationally efficient algorithms for surface correlation functions.
• To reduce the complexity of microstructure characterization without sacrificing accuracy.
• To enable precise determination of complex multiphase microstructures.

Main Methods:

• Derivation of small-r behaviors of surface correlation functions linked to mean curvature.
• Development of algorithms to extract interfacial information from a d-dimensional system cut by an infinitely long line.
• Testing algorithms on two-phase media in continuous and discrete spaces, including the overlapping spheres model.

Main Results:

• Excellent agreement between numerical and exact results for the overlapping spheres benchmark model.
• Successful computation of surface correlation functions and local surface-area variances for various microstructures.
• Demonstration of the power of surface correlation functions in characterizing complex multiphase systems.

Conclusions:

• The developed algorithms significantly reduce computational complexity for surface correlation function analysis.
• Precise determination of surface correlation functions offers a powerful tool for characterizing diverse complex microstructures.
• This work facilitates improved estimation of transport properties in heterogeneous materials.