Robust Estimation of Position-Dependent Anisotropic Diffusivity Tensors from Stochastic Trajectories

Area of Science:

• Physics
• Materials Science
• Computational Chemistry

Background:

• Confinement significantly alters material properties compared to bulk.
• Characterizing position-dependent and anisotropic properties in confined matter is challenging.
• Existing methods for estimating transport properties like diffusivity are not rigorously generalized for confined systems.

Purpose of the Study:

• To develop novel estimators for anisotropic and position-dependent diffusivity tensors in confined systems.
• To validate the proposed estimators using simulated stochastic trajectories with known diffusivity profiles.
• To provide a more robust and functional approach to diffusivity estimation in confined matter.

Main Methods:

• Development of two filtered covariance estimators.
• Application of estimators to stochastic trajectories with predefined diffusivity profiles.
• Validation against known diffusivity variations spanning orders of magnitude and diverse functional forms.

Main Results:

• The proposed estimators accurately capture spatial variations in diffusivity.
• The kernel-based approach demonstrates robustness to implementation details like localization functions and time discretization.
• Performance significantly surpasses estimators relying solely on local covariance.
• Functional estimates of diffusivity are achievable, moving beyond pointwise data.

Conclusions:

• The novel filtered covariance estimators effectively characterize anisotropic and position-dependent diffusivity in confined materials.
• The kernel-based method offers a robust and versatile tool for analyzing transport properties in complex environments.
• While generally robust, estimators show increased susceptibility to time discretization near hard boundaries, a common issue for covariance-based methods.