The adiabatic propagation of light beams through twisted nematic liquid crystals is used for the modulation of linear polarization of polychromatic light and, in particular, for the formation of polarization singularities. Rewritable photoalignment of a nematic liquid crystal allows on-demand, spatially addressed modulation of its orientational pattern, and hence the polarization of the propagating light beam. This opto-optical control does not involve dynamic phase modulation of the probe light, making this approach suitable for polarization patterning of spectrally broadband, linearly polarized light beams.

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 laboratory-referenced 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 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.

We experimentally demonstrate that the spin state (up or down) of circularly polarized light can be reliably encoded as a polar structural state (up or down) in chiral liquid crystals, with high selectivity. This enables a spin-driven, nonvolatile binary liquid crystal memory, which can be optically written and electrically erased on demand. The underlying mechanism involves an orientational buckling instability, whose direction depends on whether the handedness of light matches or opposes that of the chiral medium. This optical poling effect arises from a chiral light-matter interaction during the propagation of light through the twisted anisotropic medium.

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 experimental study has been carried out using advanced computer vision methods in order to visualize the moment of excitation and further propagation of a non stationary isotropic domain in a hybrid aligned nematic (HAN) microsized volume under the effect of a laser beam focused on a bounding liquid crystal surface. It has been shown that, when the laser power exceeds a certain threshold value, in bulk of the HAN microvolume, an isotropic circular domain is formed. We also observed a structure of alternating concentric rings around the isotropic circular region, which increases with distance from the center of the isotropic domain. The formation of a sequence of rings in a polarizing microscopic image indicates the formation of a complex topology of the director field in the HAN cell under study. The following evolution of the texture can be represented by two modes. Firstly, the “fast” heating mode, which is responsible for the formation and explosive expansion of an isotropic zone in bulk of the HAN microvolume with characteristic time τ1 due to a laser spot heating on the upper indium tin oxide (ITO) layer. Secondly, the “slow” heating mode, when an isotropic zone and concentric rings slowly expand with characteristic time τ2 mainly due to the finite thermoconductivity of ITO layer. When the laser power significantly exceeds the threshold value, damped oscillations of the isotropic domain are observed. We also introduced the metrics that allows quantitatively estimate the behavior of texture observed. The results obtained form an experimental basis for further investigation of thermomechanical force appearing in the LC system with coupled gradients of temperature and director fields.

The elementary steps in the rotation of several second-generation molecular motors are analyzed by finding the minimum energy path between the metastable and stable states and evaluating the transition rate within harmonic transition state theory based on energetics obtained from density functional theory. Comparison with published experimental data shows remarkably good agreement and demonstrates the predictive capability of this approach. While previous measurements by Feringa and co-workers have shown that a replacement of the hydrogen atom at the stereogenic center by a fluorine atom can slow down the rate-limiting thermal helix inversion (THI) step by raising the energy of the transition state, even to the extent that the backreaction in the ground state becomes preferred in some cases, we find that a replacement of a CH3 group by CF3 at the same site accelerates the THI by elevating the energy of the metastable state without affecting the transition state significantly. Since these two fluorine substitutions have an opposite effect on the rate of the THI, the combination of both can provide ways to fine-tune the rotational speed of molecular motors.

A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's climate, ecosystems, and the economy. These systems exhibit high-dimensional, non-linear dynamics, making their modelling, classification, and prediction particularly challenging. Advances in information technology have enabled data-driven approaches to studying such systems. However, the sheer volume and complexity of spatio-temporal data often hinder traditional methods like dimensionality reduction, phase-space reconstruction, and attractor characterisation. This paper introduces a geometric framework for analysing spatio-temporal data from complex systems, grounded in the theory of vector fields over discrete measure spaces. We propose a two-parameter family of metrics suitable for data analysis and machine learning applications. The framework supports time-dependent images, image gradients, and real- or vector-valued functions defined on graphs and simplicial complexes. We validate our approach using data from numerical simulations of biological and physical systems on flat and curved domains. Our results show that the proposed metrics, combined with multidimensional scaling, effectively address key analytical challenges. They enable dimensionality reduction, mode decomposition, phase-space reconstruction, and attractor characterisation. Our findings offer a robust pathway for understanding complex dynamical systems, especially in contexts where traditional modelling is impractical but abundant experimental data are available.

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.

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.

Chiral nematic liquid crystals are capable of hosting a variety of non-trivial orientational configurations, such as skyrmions and hopfions; however, their on-demand generation still remains a challenging task. In this study, we investigate the generation and subsequent relaxation of predefined topological structures in frustrated chiral nematic films using a low-power light beam. The light beam, absorbed in the bulk of a dye-doped liquid crystal, induces the formation of an isotropic region. The motion of this isotropic region, followed by the isotropic-tonematic phase transition, results in the excitation of orientational structures. In particular, we demonstrate the creation and characterization of topological solitons, open-ended cholesteric finger fragments, and cholesteric finger loops. The specific type of cholesteric finger formed is determined by the speed and trajectory of the light beam, as well as the presence of colloidal inclusions, which act as nucleation sites for particular orientational configurations. Following numerical simulations of the director field, we identify one of the finger loops as a hopfion that gradually relaxes into a toron. The presented approach offers an efficient way for the spatially controlled generation of predetermined extended orientational patterns and metastable topological solitons in chiral nematic films.

Topological orientation structures in chiral nematic liquid crystals, such as torons, exhibit promising optical properties and are of increasing interest for applications in photonic devices. However, despite this attention, their polarization and phase dynamics during formation remain insufficiently explored. In this work, we investigate the dynamic optical response of a toron generated by focused femtosecond infrared laser pulses. A custom-designed polarization holographic microscope is employed to simultaneously record four polarization-resolved interferograms in a single exposure. This enables the real-time reconstruction of the Jones matrix, providing a complete description of the local polarization transformation introduced by the formation of the topological structure. The study demonstrates that torons can facilitate spin-orbit coupling of light in a manner analogous to q-plates, highlighting their potential for advanced vector beam shaping and topological photonics applications.

We experimentally report on nonvolatile and rewritable binary optical memory where the photon spin state controls the polarity of optically recorded localized orientational distortions in liquid crystals, which behave as elastic quasiparticles having long-term storage capabilities. The memory effect is made possible by the chiral nature of the liquid crystal mesophase, while the supramolecular polarity of the recorded 'spinbits' results from the chiral light-matter interaction involving spin-angular momentum transfer from light to matter.

On the basis of the selective reactions of hydrazines with trialkylsilyl-substituted cross-conjugated enynones (pent-1-en-4-yn-3-ones) as fundamental building blocks, this work presents the developed common methodology for the synthesis of polysubstituted luminescent derivatives of acetylenic pyrazolines, pyrazoles, and combined polyheterocycles containing structural fragments from pyrazolines, isoxazoles, thiophenes, thiazoles, benzo[d]thiazoles, and benzo[d]imidazoles. In reactions with hydrazine and its monosubstituted aromatic and heteroaromatic derivatives, the mentioned pent-1-en-4-yn-3-ones, containing Me3Si, Et3Si, and t-BuMe2Si groups at the triple bond, give 3-(trialkylsilyl)ethynylpyrazolines. Following stages of desilylation and 1,3-dipolar cycloaddition with nitrile oxides, the 3-(trialkylsilyl)ethynylpyrazolines provide the formation of combined polyheterocyclic derivatives. Thus, a one-pot synthetic route to pyrazoline-containing isoxazoles from cross-conjugated enynones, arylhydrazines, and α-chlorobenzaldoximes has been developed. Some aspects of cyclocondensation mechanism and luminescent properties of synthesized azoles derivatives were examined.

Liquid crystal materials, with their unique properties and diverse applications, have long captured the attention of researchers and industries alike. From liquid crystal displays and electro-optical devices to advanced sensors and emerging technologies, the study and application of liquid crystals continue to be of paramount importance in the fields of materials science, chemistry and physics. With the ever-increasing complexity and diversity of liquid crystal materials, researchers face new challenges in understanding their behaviors, properties, and potential applications. On the other hand, machine learning, a rapidly evolving interdisciplinary field at the intersection of computer science and data analysis, has already become a powerful tool for unraveling implicit correlations and predicting new properties of a wide variety of physical and chemical systems and structures. Here we aim to consider how machine learning methods are suitable for solving fundamental problems in the field of liquid crystals and what are the advantages of this artificial intelligence based approach. A comprehensive review of machine learning perspectives for the analysis and prediction of macroscopic and molecular properties of liquid crystals.

Microparticles exhibit light-driven trapping, oscillation, rotation, and complex motions in free-surface liquid crystal films due to Marangoni convection and related director deformations.

A complex system is formed by entities that, through their interactions and dependencies, give rise to a unified whole with properties and behaviour distinct from those of its constituent parts. Examples of complex systems include the human brain, living cells, organisms, soft matter materials, the Earth's global climate, ecosystems and the economy. A large number of entities and dependencies produce high dimensional non-linear dynamics, which make the modelling, classification and prediction of complex systems dynamics a major challenge. Advances in modern information technology have made possible a successful use of data-driven approaches to the study of dynamical systems. However, in the particular case of complex systems there are still important open questions to address such as large and complex data sets analysis, dimensionality reduction, phase space reconstruction and global attractor classification. In this paper we introduce the theory of vector fields over discrete measure spaces to analyse data structurally complex, such as images, image gradients, and real and vector valued functions over simplicial complexes. We apply our framework to the analysis of data obtained from numerical solutions of equations commonly used in biology and physics to model a variety of complex systems. We show that our geometric framework, together with multidimensional scaling, an unsupervised learning method, can be successfully used in the analysis of large data sets for dimensionality reduction, mode decomposition and global attractor characterisation of complex systems dynamics. These results pave the way towards the characterisation and understanding of a number of complex dynamical systems.

Structural disorder can improve the optical properties of metasurfaces, whether it is emerging from some large-scale fabrication methods or explicitly designed and built lithographically. For example, correlated disorder, induced by a minimum inter-nanostructure distance or by hyperuniformity properties, is particularly beneficial for light extraction. Inspired by topology, we introduce numerical descriptors to provide quantitative measures of disorder with universal properties, suitable to treat both uncorrelated and correlated disorder at all length scales. The accuracy of these topological descriptors is illustrated both theoretically and experimentally by using them to design plasmonic metasurfaces with controlled disorder that we then correlate to the strength of their surface lattice resonances. These descriptors are an example of topological tools that can be used for the fast and accurate design of disordered structures or as aid in improving their fabrication methods.

The formation of long-range networks of nanoparticles in liquid crystals is controlled and reconfigured by applied voltage and temperature. We use topological data analysis to provide quantitative dimensional and structural description of such complex assemblies.

This review discusses three types of soft matter and liquid molecular materials, namely hydrogels, liquid crystals and gas bubbles in liquids, which are explored with an emergent machine learning approach.