Systems with energy injection and dissipation self-organise by forming patterns of stripes, hexagons, squares, and superlattices at the onset of spatial instabilities. Increasing the disproportion between injection and dissipation of energy generates the emergence of disordered patterns with complex spatiotemporal behaviours. We investigate the turbulent dynamics of labyrinthine patterns far from the primary spatial instabilities in a liquid crystal light valve with optical feedback experiment. The structure functions associated with light intensity allow us to establish that the observed dynamical behaviours are also of intermittent nature.
Spatial branching processes are ubiquitous in nature, yet the mechanisms that drive their growth may vary significantly from one system to another. In soft matter physics, chiral nematic liquid crystals provide a playground to study the emergence of disordered branching patterns in a controlled setting. Via an appropriate forcing, a cholesteric phase may nucleate in a chiral nematic liquid crystal, which self-organizes into an extended branching pattern. It is known that branching events occur when the rounded tips of cholesteric fingers swell, become unstable, and split into two new cholesteric tips. The origin of this interfacial instability and the mechanisms that drive the large-scale spatial organization of these cholesteric patterns remain unclear. In this work, we investigate the spatial and temporal organization of thermally-driven branching patterns in chiral nematic liquid crystal cells experimentally. We describe the observations through a mean-field model and find that chirality is responsible for the creation of fingers, regulates their interactions, and controls the tip-splitting process. Furthermore, we show that the complex dynamics of the cholesteric pattern may be reduced to a small set of interaction rules that drive the large-scale morphological and topological organization. Our theoretical findings have a good agreement with the experimental observations.
Metamaterials have subwavelength periodic structures that manipulate electromagnetic waves. Typically, difficulties are encountered in fabricating this type of materials due to the sophisticated techniques involved in their creation. Bubble domains in chiral nematic liquid crystals present a skyrmion lattice which has periodicity regions along a cell, which allow the observation of unconventional light-matter interaction. However, the interaction dynamics between vortices presents a challenge to ensure the order of the lattice throughout the space it covers. In this work we study the use of liquid crystal microdroplets as potential wells and the clustering of topological defects in them.
Several morphologies are observed in out-of-equilibrium systems. They can be highly symmetric as stripes, hexagons, or squares, and more complicated such as labyrinthine patterns. These shapes arise in different contexts, ranging from chemistry, biology, and physics. Here we study the emergence of chiral labyrinthine patterns near the winding/unwinding transition of a chiral liquid crystal under geometrical frustration. The patterns emerge due to morphological instabilities of cholesteric fingers of type 1. Experimentally, we show that when heating the cholesteric liquid crystal cell at different rates, the winding/unwinding transition is remarkably different. At low rates, chiral fingers appear and exhibit a serpentine instability along their longitudinal direction. At higher rates, after the chiral fingers nucleate, the splitting of their rounded tips and side-branching along their body is observed. Both mechanisms create labyrinthine patterns. Theoretically, based on an amplitude equation inferred by symmetry arguments, we study the morphological instabilities and characterize them by their interface curvature distribution. We discuss the possible velocity-curvature relationship of the finger rounded tips..
Particle-type solutions are generic behaviors in out-of-equilibrium systems. These localized states are characterized by a discrete set of parameters such as position, width, and height. Even these solutions can have topological charges, localized vortices, which enriches the solutions and strengthens their respective stability. These solutions are characterized by exhibiting vorticity surrounded by a homogeneous state without vorticity. Frustrated chiral liquid crystals are a natural habitat for localized vortices, cholesteric bubbles. Here we study the emergence of chiral bubbles in the winding/unwinding transition of a chiral liquid crystal cell with homeotropic anchoring. Experimentally, we show that this winding/unwinding transition is subcritical in nature when one modifies the temperature, which also generates the emergence of spherulites through the contraction of cholesteric labyrinthine patterns. Theoretically, based on an amplitude equation inferred by symmetry arguments, we reveal the emergence of chiral bubbles from a cholesteric labyrinthine patterns.
Cholesteric liquid crystals have attracted the scientific community's attention in the last decades due to the impressive textures displayed in various experiments. In particular, when varying the temperature of a cholesteric liquid crystal sample with homeotropic anchoring, complex textures arise, which resemble labyrinthine patterns built on the connections of the so-called cholesteric fingers.
Near the winding/unwinding transition, we proposed a minimal phenomenological model that accounts for the first-order type transition and the symmetries in the system. At this transition, localized cholesteric fingers suffer a tip-splitting instability and the merging of pointed tips. We discuss the emergence of cholesteric labyrinths using experimental, analytical, and numerical techniques.
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