Cross-diffusion waves in hydro-poro-mechanics

Hu, Manman; Schrank, Christoph; Regenauer-Lieb, Klaus

doi:10.1016/j.jmps.2019.05.015

Cited by 26 publications

(53 citation statements)

References 29 publications

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“…By extending the diagonal diffusion matrix through the cross-diffusion coefficients in equation 31, a new cross-diffusion wave phenomenon is revealed that incorporates chemical waves at its lowest scale (Regenauer-Lieb et al, 2020). For the simple case of hydro-mechanical (HM) coupling, we have recently reported that the upscaled volumetric chemical strains can result in a hydromechanically coupled cross-diffusional pressure wave phenomenon (Hu et al, 2019).…”

Section: Cross-diffusion and Its Role In Coupling Of Instabilities Acmentioning

confidence: 99%

“…Of specific interest for the earthquake problem is the aspect of the fate of the accelerations carried by the waves (Regenauer-Lieb et al, 2020) for cases where the wave collides and collapse after the collision. In experiments carried out with collapsing puffed rice particles (Guillard et al, 2015) cross-diffusion waves were detected (Hu et al, 2019) which release an acoustic emission when annihilating after collision with the top surface. We propose that for a homogeneous plastic zone as shown in Figure (??…”

Section: Cross-diffusion Waveformsmentioning

confidence: 99%

“…The special role of cross diffusion for the emergence of Turing patterns is their capability to generate spatial periodicity (Berenstein and Beta, 2012), an aspect that is often overlooked in the analysis of Turing patterns. The upscaled Korteweg-de Vries equation does not necessarily honour the co-dependence between the diffusion and reaction rate constants of the cross-diffusion process, and results need to be investigated with caution (Hu et al, 2019;Vanag and Epstein, 2009). Turing patterns appear because around the bifurcation point in the reaction-self-diffusion system, linearly unstable eigenfunctions exist that grow exponentially with time.…”

Section: Cross-diffusion Collisionsmentioning

confidence: 99%

“…Working Hypothesis: This paper develops the hypothesis that patterns in our planet encode information of dissipative structures in the form of standing waves that can appear when a cross-diffusion term is added to reaction-diffusion equations (Berenstein and Beta, 2012). We develop a continuation of a solid mechanical cross-diffusion formulation in which slow damage waves (Hu et al, 2019) have been identified as a precursor phenomenon to macroscopic failure of porous materials under load. The failure pattern induced by these waves imprints a characteristic bar-code like signature around the main failure zone.…”

Section: Introductionmentioning

confidence: 99%

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Cross-Diffusion Waves as a trigger for multiscale, multiphysics Instabilities: Application to earthquakes

Regenauer‐Lieb

Schrank

et al. 2020

Preprint

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Abstract. Theoretical approaches to earthquake instabilities propose shear-dominated instabilities as a source mechanism. Here we take a fresh look at the role of possible volumetric instabilities preceding a shear instability. We investigate the phenomena that may prepare earthquake instabilities using the coupling of Thermo-Hydro-Mechano-Chemical reaction-diffusion equations in a THMC diffusion matrix. We show that the off-diagonal cross-diffusivities can give rise to a new class of waves known as cross-diffusion waves. Their unique property is that for critical conditions cross-diffusion waves can funnel wave energy into a quasi-stationary wave focus from large to small-scale. The equivalent extreme event in ocean waves and optical fibres leads to the appearance of rogue waves and high energy pulses of light in lasers. In the context of hydromechanical coupling, a rogue wave would appear as a sudden fluid pressure spike on the future fault plane. This is here interpreted as a trigger for the ultimate (shear) seismic moment release.

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Section: Cross-diffusion and Its Role In Coupling Of Instabilities Acmentioning

confidence: 99%

Section: Cross-diffusion Waveformsmentioning

confidence: 99%

Section: Cross-diffusion Collisionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Cross-Diffusion Waves as a trigger for multiscale, multiphysics Instabilities: Application to earthquakes

Regenauer‐Lieb

Schrank

et al. 2020

Preprint

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“…A review of the progress made in this field as well as a specific case study of rhythmic banding in marls can be found in the recent work of L'Heureux (L'Heureux, 2018;L'Heureux, 2013). The present work develops the key ideas into a geomechanical perspective building on an initial approach proposed for hydro-mechanical coupling (Hu et al, 2019;Alevizos et al, 2017;Regenauer-Lieb et al, 2016;Veveakis and Regenauer-Lieb, 2015;Regenauer-Lieb et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

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

Regenauer‐Lieb¹,

Hu²,

Schrank³

et al. 2020

Preprint

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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.

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The reaction–cross‐diffusion models for tissue growth

Pınar

2021

Math Methods in App Sciences

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The application of mathematics to fields such as biology, medicine, and biotechnology has resulted in quantitative relations, and mathematical biology, an interdisciplinary branch, has emerged. The considered models of cell/tissue growth are determined by cross-reaction-diffusion equations with possible transitions between malignant cells with different growth rates or healthy cells. For the considered models, the exact solutions in the explicit form were not obtained in the existing literature to our knowledge. Our main aim is to fill this gap by revealing their exact solutions. The obtained results have a major role in the literature so that the considered models are seen in a large scale of applications.

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Cross-diffusion waves in hydro-poro-mechanics

Cited by 26 publications

References 29 publications

Cross-Diffusion Waves as a trigger for multiscale, multiphysics Instabilities: Application to earthquakes

Cross-Diffusion Waves as a trigger for multiscale, multiphysics Instabilities: Application to earthquakes

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

The reaction–cross‐diffusion models for tissue growth

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