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Analyzing diffusion-limited processes in a cylinder using pair-correlation functions.

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This study introduces efficient pair-correlation functions (PCFs) to analyze diffusion-limited processes (DLP) in complex spaces. The new method accurately captures spatial patterns, aiding simulations and understanding phenomena like microbial growth.

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Area of Science:

  • Physics
  • Biology
  • Engineering
  • Computational Science

Background:

  • Diffusion-limited processes (DLP) are prevalent across scientific disciplines but challenging to quantify in intricate spatial environments.
  • Existing methods for analyzing spatial patterns in DLP often face computational limitations, hindering large-scale applications.

Purpose of the Study:

  • To develop and validate efficient one-dimensional pair-correlation functions (PCFs) for assessing spatial patterns of DLP within cylindrical domains.
  • To introduce a computationally feasible binning-based approach for PCF calculations, enabling large-scale simulations.
  • To distinguish between intrinsic spatial randomness deviations and sampling variations in PCF analysis.

Main Methods:

  • Development of refined one-dimensional nonperiodic and periodic pair-correlation functions (PCFs).
  • Implementation of an efficient binning-based computational approach for PCF calculation.
  • Utilizing an off-lattice agent-based model to simulate and analyze DLP patterns.
  • Examination of PCF variability and its interpretation in different spatial projections (azimuthal, Cartesian).

Main Results:

  • The refined PCF method significantly reduces computational costs for analyzing DLP.
  • Simulations successfully reproduced self-organized patterns and fractal-like aggregation characteristic of DLP.
  • Periodic PCFs effectively capture spatial correlations in DLP, with specific advantages in certain projections.
  • Nonperiodic PCFs were shown to be preferable under specific conditions.

Conclusions:

  • Pair-correlation functions (PCFs) serve as robust statistical tools for analyzing complex spatial models of diffusion-limited processes (DLP).
  • The developed methods enhance the feasibility of studying DLP in large-scale simulations.
  • Findings have broad applicability in fields such as microbial dynamics, biomedical processes, and image analysis.