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New Framework for Interfacial Statistics: Exact n-Point Correlations of Gaussian Level Sets
Aleksei M Cherkasov1, Kirill M Gerke1,2, Aleksey Khlyupin1,3
1Moscow Institute of Physics and Technology, Center for Computational Physics, Landau School of Physics and Research, 9 Institutskiy per., Dolgoprudny, 141701, Moscow Region, Russia.
Physical Review Letters
|May 29, 2026
Summary
Researchers developed a framework for analyzing Gaussian interfaces, linking bulk field statistics to interface geometry. This aids in reconstructing disordered media and modeling complex material structures.
Area of Science:
- Physics
- Materials Science
- Applied Mathematics
Background:
- Understanding the geometry of interfaces in disordered media is crucial for predicting material properties and transport phenomena.
- Gaussian level-set interfaces are common in various scientific fields, but their statistical analysis remains challenging.
Purpose of the Study:
- To derive exact analytical expressions for higher-order correlations of Gaussian level-set interfaces.
- To establish a direct link between bulk field statistics and interface geometry.
- To enable efficient reconstruction and detailed modeling of disordered media and complex interface structures.
Main Methods:
- Derivation of exact analytical expressions for higher-order correlations.
- Utilizing Gaussian statistics to model level-set interfaces.
- Developing a framework connecting bulk field properties to geometric features.
Main Results:
- Established a direct link between bulk field statistics and interface geometry.
- Developed a framework for efficient reconstruction of disordered media.
- Enabled detailed modeling of Gaussian foams-structured, double-thresholded interfaces with tunable morphology.
- Enabled analysis of memory-enhanced anisotropy in surface structure.
Conclusions:
- The derived framework provides new possibilities for characterizing complex transport phenomena.
- The results facilitate stochastic reconstructions and the design of materials with specific properties.
- The study offers a method for quantifying information in correlation functions and modeling directional processes on irregular boundaries.
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