TY - JOUR
T1 - Cross-diffusion waves resulting from multiscale, multi-physics instabilities
T2 - Theory
AU - Regenauer-Lieb, Klaus
AU - Hu, Manman
AU - Schrank, Christoph
AU - Chen, Xiao
AU - Clavijo, Santiago Peña
AU - Kelka, Ulrich
AU - Karrech, Ali
AU - Gaede, Oliver
AU - Blach, Tomasz
AU - Roshan, Hamid
AU - Jacquey, Antoine B.
PY - 2021/4/16
Y1 - 2021/4/16
N2 - We propose a multiscale approach for coupling multi-physics processes across the scales. The physics is based on discrete phenomena, triggered by local thermohydro-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. A companion paper proposes an application of the theory to earthquakes showing that excitation waves triggered by local reactions can, through an extreme effect of a cross-diffusional wave operator, lead to an energy cascade connecting large and small scales and cause solid-state turbulence.
AB - We propose a multiscale approach for coupling multi-physics processes across the scales. The physics is based on discrete phenomena, triggered by local thermohydro-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. A companion paper proposes an application of the theory to earthquakes showing that excitation waves triggered by local reactions can, through an extreme effect of a cross-diffusional wave operator, lead to an energy cascade connecting large and small scales and cause solid-state turbulence.
UR - http://www.scopus.com/inward/record.url?scp=85104258402&partnerID=8YFLogxK
U2 - 10.5194/se-12-869-2021
DO - 10.5194/se-12-869-2021
M3 - Article
AN - SCOPUS:85104258402
SN - 1869-9510
VL - 12
SP - 869
EP - 883
JO - Solid Earth
JF - Solid Earth
IS - 4
ER -