Cross-diffusion waves resulting from multiscale, multi-physics instabilities: theory

Abstract. We propose a multiscale approach for coupling multi-physics processes across the scales. 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 overall stress field incompatible with accelerations from feedbacks of generalized THMC thermodynamic forces trigger fluxes another kind. Cross-diffusion terms in 4×4 diffusion matrix are shown to lead multiple diffusional P and S wave equations as coupled solutions. Uncertainties location meso-scale material instabilities captured wave-scale correlation probability amplitudes. Cross-diffusional have unusual dispersion patterns and, although they assume solitary state, do not behave like solitons but show complex interactions collide. Their characteristic wavenumber constant speed define mesoscopic internal time–space relations entirely defined coefficients reaction–cross-diffusion equations. A companion paper proposes an application theory earthquakes showing excitation reactions can, through extreme effect cross-diffusional operator, energy cascade connecting large small scales solid-state turbulence.