Hydraulic fracture (HF) propagation in naturally fractured formations is strongly influenced by local stress states near pre-existing natural fractures (NFs). The role of NF-induced shear deformation and stress redistribution in controlling HF trajectories remains poorly characterized. This study investigates how NF-induced stress redistribution governs HF-NF interactions through coupled laboratory experiments and poroelastic extended finite element simulations on intact and pre-fractured PMMA specimens under plane-strain conditions. Digital image correlation provides full-field measurements of displacement and strain evolution during mechanical loading and hydraulic fracturing. Under fixed-base, lateral confinement, and vertical compression boundary conditions, inclined NFs induce asymmetric stress redistribution and shear deformation, generating distinct local stress states prior to fluid injection. The results demonstrate that the HF trajectory is governed by the sign and spatial distribution of shear stress and shear strain components generated by NF orientation relative to the far-field maximum principal stress. Shear deformation that promotes compressive stress development adjacent to the NF causes the HF to deflect away, whereas shear deformation that reduces the effective normal stress along the NF promotes fracture attraction and linkage. Corresponding numerical reproduction of HF curvature in pre-fractured specimens requires mixed-mode (Mode I-II) fracture energy release criteria, while the intact specimen propagates in pure Mode I. Overall, the findings reveal a transition from tensile opening to shear-assisted mixed-mode propagation as local stress states evolve due to the presence of NFs, providing a mechanistic basis for predicting and controlling fracture trajectories in subsurface stimulation and storage applications.

Elastically accommodated grain-boundary sliding (EAGBS) is a plausible source of upper-mantle seismic attenuation and dispersion, yet classical theory predicts a localized Debye-like peak that is absent or only weakly expressed in dry olivine experiments. Here we test whether microstructural heterogeneity can explain this discrepancy using 2-D finite-element simulations on periodic Voronoi tessellations. We find that irregular grain geometry changes the baseline EAGBS response relative to the regular hexagonal benchmark, but increasing grain-size variance alone produces only modest changes in modulus and peak height, with little spectral broadening. In contrast, a broad distribution of grain-boundary viscosities progressively suppresses and broadens the Debye-like loss peak into a weak background spanning a wide frequency interval. This broadening arises from the superposition of many localized relaxation processes with distinct characteristic timescales and motivates a reduced-order 0-D description of the aggregate response. These results suggest that the absence of a pronounced EAGBS peak in dry olivine does not necessarily imply the absence of EAGBS mechanism itself. If grain boundaries sample a sufficiently broad viscosity distribution, the macroscopic EAGBS contribution may appear experimentally only as part of a broad attenuation background, while still remaining relevant for upper-mantle seismic attenuation and velocity dispersion.

Earthquakes propagating faster than the shear wave-speed are commonly thought to undergo a super-shear transition upon which they discontinuously jump from the sub-Rayleigh regime to the super-shear one. The super-Rayleigh regime, i.e., the range of propagation speeds between the Rayleigh and shear wave-speeds, is regarded as "forbidden" by the two-dimensional classical rupture theory. Here, we revisit the assumptions underlying the classical theory and develop a rupture theory that takes into account the dependence of the fault strength (frictional resistance) on the slip rate. The theory quantitatively agrees with numerical simulations nearly up to the Rayleigh wave-speed. Yet, very close to the latter, two-dimensional rupture solutions change their character due to frictional rate nonlinearity and rupture continuously propagates through the "forbidden" super-Rayleigh range into the super-shear regime, without a sharp super-shear transition. These results demonstrate that frictional rate dependence, generically observed in experiments, can have profound implications for fast earthquake propagation.

Convection in Earth's outer core is driven by the release of heat and light elements at the inner core boundary. A key question is whether these buoyancy sources drive convection throughout the core, or whether a stable layer exists just below the core-mantle boundary (CMB). Recent simulations incorporating CMB heat flux heterogeneities propose locally stable ``regional inversion lenses'' (RILs) rather than a global layer, allowing stable and unstable regions to coexist. However, these simulations combine thermal and compositional anomalies, ignoring differences in diffusivities and boundary conditions. Here we simulate thermal, chemical, and thermochemical convection at Ekman number $E=10^{-5}$, with thermal and chemical flux Rayleigh numbers $\widetilde{Ra}_T=30-4000$ and $\widetilde{Ra}_ξ=30-100000$, and Prandtl numbers $Pr_T=1$ and $Pr_ξ=10$. Purely chemical simulations accumulate light elements below the CMB, forming locally stable regions near the poles or global layers, depending on $\widetilde{Ra}_ξ$. These chemically stratified regions persist in thermochemical simulations even when thermal forcing is destabilising. Introducing heterogeneous CMB heat flux produces thermally stratified RILs even with strongly destabilising compositional buoyancy. Our simulations reveal a diverse range of locations, properties, and morphologies of stable regions depending on $\widetilde{Ra}_T$ and $\widetilde{Ra}_ξ$, they can have a seismically detectable thickness and strength and might also have a signature in geomagnetic observations.

The differentiable physics paradigm may be leveraged as an a-posteriori approach for discovering turbulence closure models by embedding a neural network parameterization directly inside the solver and optimizing it given potentially sparse target data. This addresses a key limitation of a-priori learning where direct numerical simulation (DNS) data is used to approximate the subgrid stress with the assumption of a low-pass filter. Closures trained in this a-priori manner frequently lead to unstable deployments due to the mismatch between the assumed filter and the effect of numerical discretizations and coarse-graining. In comparison, while typically stable during deployment, a-posteriori learning incurs high computational costs due to the need to backpropagate through a large eddy simulation (LES) solver. Furthermore, a-posteriori methods are challenging to apply broadly since they require significant modification of existing solvers. Finally, both approaches are limited when generalization is desired across different numerical schemes with their implicit filtering characteristics. In this work, we present a deep-learning approach for turbulence closure modeling built on the continuous data assimilation framework. Our approach enables the a-priori training of closures using sparsely observed DNS data without modifying or differentiating through the LES solver, while preserving stability during deployment for the recovery of invariant statistics. We focus on the model's ability to adapt to different discretizations by explicitly conditioning it on the numerical scheme. We use two- and three-dimensional canonical cases to test our framework and show that the learned correction systematically tracks the discretization error of the coarse solver.

We introduce the toroh -- formally designated an Extreme Orographic Convective Event (EOCE) -- as a previously uncharacterised class of atmospheric hazard distinct from downbursts and conventional hailstorms. The toroh is a coherent hydraulic ice-piston formed when a convective system with anomalously narrow drop size distribution (mu ~ 20) undergoes explosive secondary ice production via the Hallett-Mossop mechanism, triggered by marine iodine ice-nucleating particles injected by a vortex or orographic resonance with an inselberg (Planalto Mirador, SC, Brazil). The piston collapses coherently into canyon terrain, producing a two-phase acoustic signature, seismic tremor M_L ~ 2-3, and a diagnostic erosion scar with zero fine-grained matrix. Piston cohesion is justified by ice sintering kinetics: tau_p ~ 0.04 s << tau_sint = 1-10 s, and sintered tensile strength ~10^4 Pa exceeds aerodynamic fragmentation pressure ~10^3 Pa. We propose EOCE as a candidate mechanism for four persistent geological anomalies: (1) erosional amphitheatres in resistant bedrock; (2) heavy mineral concentration in canyon lag deposits; (3) spatiotemporal heterogeneity of the Great Unconformity, incompatible with uniform Snowball Earth glaciation; (4) the nutrient pulse preceding the Cambrian Explosion. In pristine pre-industrial conditions, EOCE frequency is estimated at 1-10 per century per canyon -- sufficient for independent geomythological encoding in ~18 culturally isolated traditions. The Adams Event (Laschamp, ~42 ka) amplified this baseline 10-100x; 20th-century tetraethyl-lead aerosols suppressed it below observational threshold. A 3D anelastic bin-microphysics model and testable predictions are presented. Code: this https URL