Articles | Volume 12, issue 4
https://doi.org/10.5194/se-12-869-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/se-12-869-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
16 Apr 2021
Research article |
| 16 Apr 2021
| 16 Apr 2021
Cross-diffusion waves resulting from multiscale, multi-physics instabilities: theory
School of Minerals and Energy Resources Engineering, UNSW, Sydney, NSW, 2052, Australia
Manman Hu
Department of Civil Engineering, The University of Hong Kong, Hong Kong
Christoph Schrank
Science and Engineering Faculty, Queensland University of Technology, Brisbane, QLD, 4001, Australia
Xiao Chen
School of Minerals and Energy Resources Engineering, UNSW, Sydney, NSW, 2052, Australia
Santiago Peña Clavijo
School of Minerals and Energy Resources Engineering, UNSW, Sydney, NSW, 2052, Australia
Ulrich Kelka
CSIRO Deep Earth Imaging Future Science Platform, Kensington, WA, 6151, Australia
Ali Karrech
School of Engineering, University of Western Australia, Crawley, WA, 6009, Australia
Oliver Gaede
Science and Engineering Faculty, Queensland University of Technology, Brisbane, QLD, 4001, Australia
Tomasz Blach
School of Minerals and Energy Resources Engineering, UNSW, Sydney, NSW, 2052, Australia
Hamid Roshan
School of Minerals and Energy Resources Engineering, UNSW, Sydney, NSW, 2052, Australia
Antoine B. Jacquey
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
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Cited
15 citations as recorded by crossref.
- Cross-diffusion waves resulting from multiscale, multiphysics instabilities: application to earthquakes K. Regenauer-Lieb et al.
- Chemo-hydro-mechanics in a reactive rock under cylindrical fluid pressurization X. Tang & M. Hu
- Cross-scale dynamic interactions in compacting porous media as a trigger to pattern formation M. Hu et al.
- Onsager’s reciprocal relationship applied to multiphysics poromechanics K. Regenauer-Lieb & M. Hu
- Cross-diffusion waves by cellular automata modeling: Pattern formation in porous media Z. Zhu et al.
- Coefficients of Reaction‐Diffusion Processes Derived From Patterns in Rocks C. Liu et al.
- Solitary pulses and periodic wave trains in a bistable FitzHugh-Nagumo model with cross diffusion and cross advection E. Zemskov et al.
- Inversion of fluid-release rates from episodic tremor and slip signals in subduction zones via a coarse-grained reaction diffusion model Q. Sun et al.
- Shear banding as a dissipative structure from a thermodynamic viewpoint F. Nicot et al.
- Multiscale Representative Elementary Volume Determination in Complex Porous Media: An Integrated Hydrodynamic and Thermodynamic Modelling Approach S. Hussain et al.
- Understanding earthquake precursors: from subcritical instabilities to catastrophic events K. Regenauer-Lieb & M. Hu
- An alternative to the fault-valve model B. Hobbs & A. Ord
- Emergence of precursor instabilities in geo-processes: Insights from dense active matter K. Regenauer-Lieb & M. Hu
- The appearance of standing wave structures in the reaction medium during the diffusion development of the chain reaction process G. Sargsyan et al.
- Shear and compaction bands in porous rocks with a micromechanics-inspired non-local elastoplastic model J. Wu et al.
15 citations as recorded by crossref.
- Cross-diffusion waves resulting from multiscale, multiphysics instabilities: application to earthquakes K. Regenauer-Lieb et al.
- Chemo-hydro-mechanics in a reactive rock under cylindrical fluid pressurization X. Tang & M. Hu
- Cross-scale dynamic interactions in compacting porous media as a trigger to pattern formation M. Hu et al.
- Onsager’s reciprocal relationship applied to multiphysics poromechanics K. Regenauer-Lieb & M. Hu
- Cross-diffusion waves by cellular automata modeling: Pattern formation in porous media Z. Zhu et al.
- Coefficients of Reaction‐Diffusion Processes Derived From Patterns in Rocks C. Liu et al.
- Solitary pulses and periodic wave trains in a bistable FitzHugh-Nagumo model with cross diffusion and cross advection E. Zemskov et al.
- Inversion of fluid-release rates from episodic tremor and slip signals in subduction zones via a coarse-grained reaction diffusion model Q. Sun et al.
- Shear banding as a dissipative structure from a thermodynamic viewpoint F. Nicot et al.
- Multiscale Representative Elementary Volume Determination in Complex Porous Media: An Integrated Hydrodynamic and Thermodynamic Modelling Approach S. Hussain et al.
- Understanding earthquake precursors: from subcritical instabilities to catastrophic events K. Regenauer-Lieb & M. Hu
- An alternative to the fault-valve model B. Hobbs & A. Ord
- Emergence of precursor instabilities in geo-processes: Insights from dense active matter K. Regenauer-Lieb & M. Hu
- The appearance of standing wave structures in the reaction medium during the diffusion development of the chain reaction process G. Sargsyan et al.
- Shear and compaction bands in porous rocks with a micromechanics-inspired non-local elastoplastic model J. Wu et al.
Saved (final revised paper)
Latest update: 04 May 2026
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 THMC coupling. If waves are excited through the THMC reaction terms unbounded reactions can be captured by inclusion of statistical information from the lower scale through nonlocal reaction–diffusion equations. These cross-diffusion coefficients regularize extreme earthquake-like events (rogue waves) through a new form of quasi-soliton wave.
In this paper we expand on a recent discovery of slow cross-diffusion hydromechanical waves cast...
