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Reaction-diffusion waves in hydro-mechanically coupled porous solids as a precursor to instabilities
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  • Qingpei Sun,
  • Manman Hu,
  • Christoph Eckart Schrank,
  • Klaus Regenauer- Lieb
Qingpei Sun
University of Hong Kong
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Manman Hu
University of Hong Kong

Corresponding Author:mmhu@hku.hk

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Christoph Eckart Schrank
Queensland University of Technology
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Klaus Regenauer- Lieb
UNSW Sydney
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Here, we extend the Fisher-Kolmogorov-Petrovsky-Piskunov equation to capture the interplay of multiscale and multiphysics coupled processes. We use a minimum of two coupled reaction-diffusion equations with additional nonlocal terms that describe the coupling between scales through mutual cross-diffusivities and regularise the ill-posed reaction-self-diffusion system. Applying bifurcation theory we suggest that geological patterns can be interpreted as physical representations of two classes of well-known instabilities: Turing instability, Hopf bifurcation, and a new class of complex soliton-like waves. The new class appears for small fluid release reactions rates which may, for negligible self-diffusion, lead to an extreme focusing of wave intensity into a short sharp earthquake-like event. We propose a first step approach for detection of these dissipative waves, expected to precede a large scale instability.