From Order to Chimeras: Unraveling Dynamic Patterns in Active Fluids with Nonlinear Growth

Summary

The study explores pattern formation in an active fluid system with two chemical species regulating active stress, where one species has nonlinear logistic growth. The system exhibits various dynamical regimes, including oscillatory and stationary instabilities, and chimera states.

Highlights

• Increasing the Péclet number leads to the loss of stability of the homogeneous steady state.
• Asymmetry in the chemical species affects the emergent dynamical phases.
• Nonlinear logistic growth aids the stability of the homogeneous steady state.
• Chimera states emerge at moderately high Péclet numbers.
• The system exhibits merging-emerging solitonic structures in the space-time evolution of concentrations.
• The regime of oscillatory instability is most conducive to chimera states.
• Nonlinear growth enhances the probability of observing chimera states.

Key Insights

• The interplay between advection and diffusion, as captured by the Péclet number, significantly influences the stability of the homogeneous steady state and the emergence of complex patterns.
• The asymmetry parameter β has a crucial role in determining the type of dynamical phases that can exist in the system, with β > 1 allowing for oscillatory instability.
• The incorporation of nonlinear logistic growth in one of the chemical species has a stabilizing effect on the homogeneous steady state, contrary to what might be expected from the introduction of nonlinearity.
• Chimera states, characterized by the coexistence of different dynamical patterns, are a hallmark of the system's complexity and are most likely to be observed at moderately high Péclet numbers and within the regime of oscillatory instability.
• The observation of merging-emerging solitonic structures in the space-time evolution of concentrations adds another layer of complexity to the system's behavior, indicating a rich variety of spatiotemporal patterns.
• The study's findings on the conditions conducive to chimera states and the role of nonlinear growth in enhancing their probability could guide experimental searches for these intriguing patterns in active fluid systems.
• The exploration of pattern formation in this active fluid system contributes to a deeper understanding of the intricate dynamics that can arise from the interplay of chemical and mechanical effects in biological and chemical systems.

Mindmap

Citation

Das, J., Chaudhuri, A., & Sinha, S. (2024). From Order to Chimeras: Unraveling Dynamic Patterns in Active Fluids with Nonlinear Growth (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.14729