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This study reveals how diffusive waves transition from collective to agent-based propagation. Wave speed depends critically on system dimensionality, challenging continuum theory assumptions in certain configurations.

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Area of Science:

  • Physics
  • Biology
  • Complex Systems

Background:

  • Diffusive waves are observed in diverse fields like population genetics and cell signaling.
  • These waves are often propagated by discrete agents, such as individual cells.

Purpose of the Study:

  • To characterize the transition between continuum and agent-based diffusive wave propagation.
  • To investigate the influence of system dimensionality and disorder on this transition.

Main Methods:

  • Theoretical analysis of diffusive wave propagation.
  • Modeling of agent-based wave dynamics.
  • Comparison with continuum theory predictions.

Main Results:

  • The transition between collective and agent-based propagation is highly dependent on system dimensionality.
  • Disordered systems exhibit dynamics similar to lattice systems.
  • Continuum approximations can be inaccurate in specific dimensionalities, violating intuition about source packing.

Conclusions:

  • System dimensionality is a critical factor governing diffusive wave propagation dynamics.
  • Agent-based modeling is essential for understanding wave behavior where continuum theory fails.
  • Findings challenge common assumptions about how discrete sources influence wave propagation.