Transitions between phyllotactic lattice states in curved geometries

Area of Science:

• Physics
• Materials Science
• Mathematical Biology

Background:

• Phyllotaxis, the study of organ arrangement in plants, has long fascinated scientists.
• Recent interest extends to physical systems, particularly in cylindrical geometries.

Purpose of the Study:

• To investigate phyllotactic state transitions in soft vortex matter within a conical frustum geometry.
• To analyze defect structures during these transitions and explore methods for their elimination.

Main Methods:

• Confined soft vortex matter to a conical frustum.
• Analyzed ground states and defect structures at transitions.
• Introduced density gradients to create single-state configurations.

Main Results:

• Ground states in conical frustums align with previous cylindrical confinement findings.
• Identified defect structures at transitions between phyllotactic states.
• Density gradients effectively eliminated defects within a limited parameter range.

Conclusions:

• The conical frustum system exhibits phyllotactic behaviors consistent with cylindrical models.
• Defect elimination via density gradients is feasible but parameter-limited.
• A horn surface is proposed as a more effective geometry for maintaining defect-free states over a wider parameter range.