Insights into distorted lamellar phases with small-angle scattering and machine learning.

Area of Science:

• Soft Matter Physics
• Materials Science
• Complex Systems

Background:

• Lamellar phases are crucial in soft matter.
• Topological defects in these phases significantly impact mechanical properties.
• Quantitative analysis of defect dynamics is challenging.

Purpose of the Study:

• To present a machine-learning approach for analyzing distorted lamellar phases.
• To quantitatively analyze the structure and dynamics of topological defects.
• To enable investigation of defect influence on material properties.

Main Methods:

• Utilized Kolmogorov-Arnold networks for data analysis.
• Reconstructed phase conformations from small-angle scattering intensities.
• Analyzed wave field phase singularities and temporal evolution of defects.

Main Results:

• Successfully reconstructed distorted lamellar phase conformations.
• Obtained statistics on the spatial distribution of topological defects.
• Derived temporal evolution of defects from time-dependent wave fields.

Conclusions:

• The machine-learning method enables quantitative analysis of lamellar phase structure and dynamics.
• This approach enhances understanding of defect-property relationships in soft matter.
• Opens new avenues for dynamic scattering techniques like neutron spin echo and X-ray photon correlation spectroscopy.