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© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

  11 Aug 2020

11 Aug 2020

Review status
A revised version of this preprint is currently under review for the journal SE.

Cross-Diffusion Waves as a trigger for Multiscale, Multi-Physics Instabilities: Theory

Klaus Regenauer-Lieb1, Manman Hu2, Christoph Schrank3, Xiao Chen1, Santiago Peña Clavijo1, Ulrich Kelka4, Ali Karrech5, Oliver Gaede3, Tomasz Blach1, Hamid Roshan1, and Antoine Jacquey6 Klaus Regenauer-Lieb et al.
  • 1School of Minerals and Energy Resources Engineering, UNSW, Sydney, NSW 2052, Australia
  • 2Department of Civil Engineering, The University of Hong Kong, Hong Kong
  • 3Science and Engineering Faculty, Queensland University of Technology, Brisbane, QLD, 4001, Australia
  • 4CSIRO, ARRC Technology Park, Kensington, WA 6151, Australia
  • 5School of Engineering, University of Western Australia, Crawley, WA 6009, Australia
  • 6Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

Abstract. We propose a non-local, meso-scale approach for coupling multiphysics processes across scale. The physics is based on discrete phenomena, triggered by local Thermo-Hydro-Mechano-Chemical (THMC) instabilities, that cause cross-diffusion (quasi-soliton) acceleration waves. These waves nucleate when the overall stress field is incompatible with accelerations from local feedbacks of generalized THMC thermodynamic forces that trigger generalized thermodynamic fluxes of another kind. Cross-diffusion terms in the 4 × 4 THMC diffusion matrix are shown to lead to multiple diffusional P- and S-wave equations as coupled THMC solutions. Uncertainties in the location of meso-scale material instabilities are captured by a wave-scale correlation of probability amplitudes. Cross-diffusional waves have unusual dispersion patterns and, although they assume a solitary state, do not behave like solitons but show complex interactions when they collide. Their characteristic wavenumber and constant speed define mesoscopic internal material time-space relations entirely defined by the coefficients of the coupled THMC reaction-cross-diffusion equations. For extreme conditions, cross-diffusion waves can lead to an energy cascade connecting large and small-scales and cause solid-state turbulence.

Klaus Regenauer-Lieb et al.

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Klaus Regenauer-Lieb et al.

Klaus Regenauer-Lieb et al.


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Latest update: 01 Dec 2020
Publications Copernicus
Short summary
In this paper we expand on a recent discovery of slow cross-diffusion hydromechanical waves cast into a new concise reaction-diffusion equation for thermo-, hydro-, mechano-, chemical coupling (THMC). We introduce the new concept of acceleration waves linking multiphysics phenomena across scales. They are also encountered in systems where quantum particles interact, such as in quantum optics.
In this paper we expand on a recent discovery of slow cross-diffusion hydromechanical waves cast...