Tetiana Orlova

The method based on umbilics that expose line-like organization of complex director fields is used to introduce umbilic surfaces as a numerically robust probe of three-dimensional (3D) topological solitons in frustrated cholesteric liquid crystals. We present a coordinate-free analytical formulation of the umbilic-line approach that ensures reliable detection of umbilics on discrete simulation grids and thus avoids the problems caused by instabilities and sensitivity to coordinate choices. By using our method we introduce the laboratoryreferenced phase field giving a natural tool for intuitive surface colorization. In addition, we employ this field to define the two fundamental integer invariants of umbilic loops: the transverse index (the strength) and the longitudinal winding (the profile twist). These invariants directly link the umbilic geometry to the topological characteristics of textures, thus enabling soliton identification and a comparison of solitons by topological content. We apply the technique to the three canonical solitons obtained by the free-energy minimization: the toron and the looped cholesteric fingers of the first and second types with the Hopf indices equal to zero and unity, respectively. It is found that the umbilic-surface representation clearly exposes defect structures, discriminates between visually similar but topologically distinct textures and provides a tool for quantifying and visualizing 3D solitons from director field data.

Understanding the behavior and evolution of a dynamical many-body system by analyzing patterns in their experimentally captured images is a promising method relevant for a variety of living and nonliving self-assembled systems. The arrays of moving liquid crystal skyrmions studied here are a representative example of hierarchically organized materials that exhibit complex spatiotemporal dynamics driven by multiscale processes. Joint geometric and topological data analysis (TDA) offers a powerful framework for investigating such systems by capturing the underlying structure of the data at multiple scales. In the TDA approach, we introduce the Ψ function, a robust numerical topological descriptor related to both the spatiotemporal changes in the size and shape of individual topological solitons and the emergence of regions with their different spatial organization. The geometric method based on the analysis of vector fields generated from images of skyrmion ensembles offers insights into the nonlinear physical mechanisms of the system's response to external stimuli and provides a basis for comparison with theoretical predictions. The methodology presented here is very general and can provide a characterization of system behavior both at the level of individual pattern-forming agents and as a whole, allowing one to relate the results of image data analysis to processes occurring in a physical, chemical, or biological system in the real world.

This study advances fundamental knowledge about the regular dynamic behavior of supramolecular self‐assembled structures formed and remotely controlled by light in chiral nematic liquid crystals. The main focus of this study is on revolving chiral patterns induced by ultraviolet light in frustrated films of photoactive chiral nematics. While the size of the localized pattern and its rotation frequency are determined by the power of the recording light beam, the uniformity and regularity of the rotation depend on the ratio of the localized pattern size to the light spot diameter. When this ratio reaches about eight, the rotation of the supramolecular pattern becomes nonuniform or even interrupted. This is explained by light‐induced processes at both the molecular and supramolecular levels, causing the director field distortions of the revolving structure. Adjusting the diameter of the light spot efficiently restores the regular revolving behavior. Understanding the relationship between the light beam parameters, the characteristics of a supramolecular chiral pattern, and its behavioral features opens up prospects for the use of localized liquid crystal structures as dynamic elastic transporters of micro‐ and nanoscale objects for light‐controllable soft micromechanical systems.

A simple and efficient approach to spatially addressed polychromatic modulation of light polarization using a photopatterned nematic liquid crystal film is proposed and investigated. In particular, we demonstrate linear polarization structuring of the broadband probe beam, including the formation of polarization singularities under the adiabatic propagation of linearly polarized light, which is achieved through in situ, rewritable photoalignment of nematic liquid crystal by a pump beam. This opto-optical control of polarization does not involve dynamic phase modulation and enables spatially resolved polarization patterning of broadband linearly polarized light in real time.

The increasing complexity in designing nanostructured materials for electronics, biomedicine, and energy applications requires advanced computational methods to enhance research efficiency and minimize experimental costs. This study proposes an innovative agent-based retrieval-augmented generation (RAG) system integrated with large language models (LLMs) to automate the extraction and analysis of scientific information from extensive literature databases, specifically targeting nanostructured materials developed via two-photon polymerization (2PP). In addition to extracting and analyzing scientific data, our approach emphasizes understanding how these nanostructured materials interact with cells, which is crucial for controlling their application in biomedicine. The developed platform demonstrates robust semantic accuracy (cosine similarity: 0.82) and high overall task precision (0.81), significantly reducing the likelihood of misinformation by incorporating dynamic query refinement mechanisms. The intuitive, user-friendly interface facilitates quick access to relevant scientific data, thereby improving researchers' productivity and enabling more accurate experimental planning. Although the system exhibits certain limitations regarding domain-specific terminology coverage, further fine-tuning and specialized training are anticipated to enhance its performance and reliability for advanced scientific applications.

By using a polarization-resolved common-path diffraction phase microscope coupled with a spin-to-orbit converter, we experimentally study two-dimensional in-plane distributions of amplitude and phase of light transmitted through a spherulite formed in a frustrated cholesteric liquid crystal cell. These distributions measured at different orientations of the output linear polarizer (analyzer) are used to obtain the orbital angular momentum (OAM) spectra characterizing the OAM content of the beam. The experimental data are found to be in good agreement with the theoretical results describing both the distributions and the OAM spectra based on an analytically designed model of toron-like localized liquid crystal structures. We show that the OAM spectrum can be controlled by changing the analyzer azimuth angle so that the dominant mode evolves between the limiting cases of the vortex mode with l=−2 and the vortex-free mode with l=0.

Understanding the behavior and evolution of a dynamical many-body system by analyzing patterns in their experimentally captured images is a promising method relevant for a variety of living and non-living self-assembled systems. The arrays of moving liquid crystal skyrmions studied here are a representative example of hierarchically organized materials that exhibit complex spatiotemporal dynamics driven by multiscale processes. Joint geometric and topological data analysis (TDA) offers a powerful framework for investigating such systems by capturing the underlying structure of the data at multiple scales. In the TDA approach, we introduce the $Ψ$-function, a robust numerical topological descriptor related to both the spatiotemporal changes in the size and shape of individual topological solitons and the emergence of regions with their different spatial organization. The geometric method based on the analysis of vector fields generated from images of skyrmion ensembles offers insights into the nonlinear physical mechanisms of the system's response to external stimuli and provides a basis for comparison with theoretical predictions. The methodology presented here is very general and can provide a characterization of system behavior both at the level of individual pattern-forming agents and as a whole, allowing one to relate the results of image data analysis to processes occurring in a physical, chemical, or biological system in the real world.