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Area of Science:

  • * Biophysics
  • * Theoretical Biology
  • * Control Theory

Background:

  • * Maintaining a flat lamina, like a leaf, during growth is challenging due to the energetic ease of triggering long wavelength fluctuations.
  • * Thin elastic plates are susceptible to shape instabilities.
  • * Biological growth processes often involve complex regulatory mechanisms.

Purpose of the Study:

  • * To investigate the physical mechanisms and control strategies enabling leaf flatness during growth.
  • * To explore the roles of in-plane and out-of-plane growth variations in shape regulation.
  • * To model the effects of local and nonlocal feedback laws on growth stability.

Main Methods:

  • * Combining the physics of thin elastic plates with feedback control theory.
  • * Analyzing both metric (in-plane) and curvature (out-of-plane) growth variations.
  • * Investigating both local and nonlocal feedback control laws.
  • * Developing a linearized feedback theory incorporating spatial nonlocality and temporal delays.

Main Results:

  • * A linearized feedback theory effectively suppresses long wavelength fluctuations crucial for maintaining leaf flatness.
  • * The model accounts for both spatially nonlocal and temporally delayed feedback effects.
  • * The theoretical framework explains observed statistical growth features in tobacco leaves.
  • * Both in-plane and out-of-plane growth variations are critical for shape regulation.

Conclusions:

  • * Feedback control is essential for stabilizing leaf shape during growth, preventing unwanted fluctuations.
  • * Spatially nonlocal and temporally delayed feedback mechanisms are key to regulating leaf flatness.
  • * This work provides a foundational framework for understanding the growth and shape regulation of laminar biological structures.