As is known, zinc pollution has been a public environmental issue for a long time. Accordingly, the major objective of this study is to examine the effect of activated Firmiana simplex leaf on Zn(II) removal from aqueous solution. The result shows that activated Firmiana simplex leaf can remove Zn(II) effectively at 250°C due to the preservation of amine, carboxyl, and phosphate groups. Several factors were determined to have significant effects on the adsorption of Zn(II), including the adsorbent component, dosage, initial concentration, solution pH, temperature, and duration. Pseudo first order and pseudo second order kinetics equations were used to predict the kinetic and thermodynamic constants that reveal the endothermic and spontaneous nature of the adsorption. Using the Langmuir model, the maximum zinc adsorption capacity was calculated to be 55.096 mg/ g, which was subsequently confirmed by Fourier transformed infrared radiation (FT-IR) analyses and X-ray diffraction (XRD) spectra.

Theoretical approaches to earthquake instabilities propose shear-dominated source mechanisms. 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 or quasi-soliton waves. Their unique property is that for critical conditions cross-diffusion waves can funnel wave energy into a stationary wave focus from large to small scale. We show that the rich solution space of the reaction–cross-diffusion approach to earthquake instabilities can recover classical Turing instabilities (periodic in space instabilities), Hopf bifurcations (spring-slider-like earthquake models), and a new class of quasi-soliton waves. Only the quasi-soliton waves can lead to extreme focussing of the wave energy into short-wavelength instabilities of short duration. The equivalent extreme event in ocean waves and optical fibres leads to the appearance of “rogue waves” and high energy pulses of light in photonics. In the context of hydromechanical coupling, a rogue wave would appear as a sudden fluid pressure spike. This spike is likely to cause unstable slip on a pre-existing (near-critically stressed) fault acting as a trigger for the ultimate (shear) seismic moment release.

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 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.

Mineral precipitation can form complex patterns under non‐equilibrium conditions, in which two representative patterns are rhythmic Liesegang stripes and fractal dendrites. Interestingly, both patterns occur in the same rock formations, including various dendritic morphologies found in different rocks, such as limestone and sandstone. However, the underlying mechanism for selecting the vastly different mineral precipitation patterns remains unclear. We use a phase‐field model to reveal the mechanisms driving pattern selection in mineral precipitation. Simulations allow us to explore the effects of diffusion parameters on determining the dendritic morphologies. We also propose a general criterion to distinguish the resulting dendrites in simulations and field observations based on a qualitative visual distinction into three categories and a quantitative fractal dimension (FD) phase diagram. Using this model, we reproduce the classified dendrites in the field and invert for the key parameters that reflect the intrinsic material properties and geological environments. This study provides a quantitative tool for identifying the morphology selection mechanism with potential applications to geological field studies, exploration for resource evaluation, and other potential industrial applications.

Self‐organizing diffusion‐reaction systems naturally form complex patterns under far‐from‐equilibrium conditions. A representative example is the rhythmic concentration pattern of Fe‐oxides in Zebra rocks; these patterns include reddish‐brown stripes, rounded rods, and elliptical spots. Similar patterns are observed in the banded iron formations, which are presumed to have formed in the early earth under global glaciation. We propose that such patterns can be used directly (e.g., by computer‐vision‐analysis) to infer basic quantities relevant to their formation giving information on generalized chemical gradients. Here we present a phase‐field model that quantitatively captures the distinct Zebra rock patterns based on the concept of phase separation that describes the process forming Liesegang stripes. We find that diffusion coefficients (the bulk self‐diffusivities of the native species and the mobility of the reaction product) play an essential role in controlling the appearance of regular stripe patterns as well as the transition from stripes to spots. The numerical results are carefully benchmarked with well‐established empirical spacing law, width law, timing law and the Matalon‐Packter law. Using this model, we invert for the important process parameters originating from the intrinsic material properties, the self‐diffusivity ratio and the mobility of Fe‐oxides with a series of Zebra rock samples. This study allows a quantitative prediction of the generalized chemical gradients in mineralized source rocks without intrusive measurements, providing a better intuition for the mineral exploration space.