Vortices Nucleation By Inherent Fluctuations In Nematic Liquid Crystal Cells

Multistable systems are characterized by exhibiting domain coexistence, where each domain accounts for the different states. In the case of these systems are described by vectorial fields, domains are connected through topological defects. Vortices are one of the most frequent and studied topological defect points. Optical vortices are equally relevant for their fundamental features as beams with topological features and their applications in image processing, telecommunications, optical tweezers, and quantum information. The interaction of light beams with matter vortices in liquid crystal cells is a natural source of optical vortices. The rhythms that govern the emergence of matter vortexes due to fluctuations are not established. Here we investigate the nucleation mechanisms of the matter vortices in liquid crystal cells and establish statistical laws that govern them. Based on a stochastic amplitude equation, the law for the number of nucleated vortices as a function of anisotropy, voltage, and noise level intensity is set. Experimental observations in a nematic liquid crystal cell with homeotropic anchoring and a negative anisotropic dielectric constant under the influence of a transversal electric field show a fair agreement with the theoretical findings.

Detection of Hidden Oscillations in Systems Without Equilibrium

Chaotic systems with hidden attractors have been widely studied in recent decades. In this field, systems without equilibrium are of special interest. Since multistable systems can alternate between several hidden attractors, it is difficult to detect their hidden oscillations using known analytical techniques. In this study, we propose to apply recurrence analysis methods as a possible solution to this problem. We consider the new quantity measure, called relative specific volume, which correlates with changes of the attractor. We choose the improved Sprott A system as an example of the multiscroll attractor to verify the proposed approach. We compare the new recurrence measure with other traditional quantitative methods for chaotic systems investigation. It is shown that the relative specific volume possesses the best correlation with the change of attractors among all considered metrics. The proposed approach can be used to study hidden oscillations in experimental data as well.

Multistable Systems with Hidden and Self-Excited Scroll Attractors Generated via Piecewise Linear Systems

In this work, we present an approach to design a multistable system with one-directional (1D), two-directional (2D), and three-directional (3D) hidden multiscroll attractor by defining a vector field on ℝ3 with an even number of equilibria. The design of multistable systems with hidden attractors remains a challenging task. Current design approaches are not as flexible as those that focus on self-excited attractors. To facilitate a design of hidden multiscroll attractors, we propose an approach that is based on the existence of self-excited double-scroll attractors and switching surfaces whose relationship with the local manifolds associated to the equilibria lead to the appearance of the hidden attractor. The multistable systems produced by the approach could be explored for potential applications in cryptography, since the number of attractors can be increased by design in multiple directions while preserving the hidden attractor allowing a bigger key space.