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Cross-diffusion waves by cellular automata modeling: Pattern formation in porous media.

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Summary
This summary is machine-generated.

This study introduces a new cross-diffusion framework to model pattern formation in porous materials. The model efficiently simulates deformation bands, revealing how external forces drive pattern evolution in complex systems.

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Area of Science:

  • Geophysics and Materials Science
  • Multiscale and Multiphysics Phenomena

Background:

  • Porous earth materials display large-scale deformation patterns, like deformation bands, arising from intricate small-scale interactions.
  • Understanding these multiscale phenomena requires advanced modeling techniques that bridge microscale physics with macroscale behavior.

Purpose of the Study:

  • To introduce a novel cross-diffusion framework for simulating multiscale, multiphysics pattern formation in porous media.
  • To develop a microphysics-enriched continuum approach for accurate prediction of deformation band evolution.
  • To investigate the dynamics of "cross-diffusion waves" in porous materials.

Main Methods:

  • Development of a cross-diffusion framework inspired by multi-species chemical systems.
  • Implementation of a microphysics-enriched continuum approach.
  • Utilization of a cellular automata algorithm for discretizing porous network structures, enhancing computational efficiency.

Main Results:

  • The proposed framework accurately predicts the formation and evolution of deformation patterns.
  • Substantial computational efficiency was achieved in simulating pattern formation.
  • External thermodynamic forces were shown to initiate pattern formation in cross-coupled dynamic systems.
  • The propagation speed of deformation bands is governed by cross-diffusion and a cross-reaction coefficient.

Conclusions:

  • The study presents a generic framework for pattern formation in cross-coupled multi-constituent reactive systems.
  • Cross-diffusion plays a critical role in the dynamics of instabilities like "cross-diffusion waves" in porous media.
  • The findings have implications for understanding phenomena observed in materials such as dry snow.