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    Area of Science:

    • Nonlinear physics
    • Complex systems
    • Liquid crystal optics

    Background:

    • Dissipative self-organization drives complex behaviors in macroscopic systems with energy flow.
    • Nematic liquid crystals are versatile media for studying pattern formation and nonlinear dynamics.

    Purpose of the Study:

    • To investigate pattern formation and transitions to complex dynamics in a 1D and 2D nematic liquid crystal system.
    • To differentiate between spatiotemporal chaos and amplitude turbulence using advanced analytical techniques.

    Main Methods:

    • Utilized a nematic liquid crystal layer with a spatially modulated input beam and optical feedback.
    • Employed spatiotemporal diagrams and Fourier transforms for analysis.
    • Calculated the largest Lyapunov exponent to characterize system dynamics.

    Main Results:

    • Observed a transition from stationary patterns to spatiotemporal chaotic textures.
    • Successfully distinguished between spatiotemporal chaos and amplitude turbulence, concepts often conflated.
    • Quantified system dynamics using the largest Lyapunov exponent.

    Conclusions:

    • The nematic liquid crystal system provides a controllable platform for studying dissipative pattern formation.
    • The applied methods offer a clear distinction between different types of complex spatiotemporal dynamics.
    • This research clarifies the nature of spatiotemporal chaos versus amplitude turbulence in optical systems.