Developing Reynolds-averaged Navier–Stokes (RANS) turbulence models that remain accurate across diverse flow regimes is a long-standing challenge. In this work, we propose a novel framework, termed the progressive mixture-of-experts (PMoE), designed to enable continual learning for RANS turbulence modelling. The framework employs a modular autoencoder-based router to associate each flow scenario with a specialised turbulence model, referred to as an expert. When a new flow regime cannot be adequately represented by the existing router and expert set, a new expert together with its routing component can be introduced at low cost, without modifying or degrading previously trained ones, thereby naturally avoiding catastrophic forgetting. The framework is applied to a range of flows with distinct physical characteristics, including aerofoil wake, channel, periodic hill and square duct flows. The resulting PMoE model effectively integrates multiple experts and achieves improved predictive accuracy across both seen and unseen test cases that differ in operating conditions or configurations. Owing to sparse activation, model expansion does not incur additional computational cost during inference. The proposed framework therefore provides a scalable pathway towards lifelong-learning turbulence models for industrial computational fluid dynamics.

The Paleocene-Eocene Thermal Maximum (PETM, ∼56 Ma) marks a rapid, intense warming event at the Paleocene-Eocene boundary. However, the terrestrial record of the PETM is limited, and its paleoenvironmental impacts are debated. This study examines the effects of the PETM on terrestrial lake environments using mineralogical, inorganic and organic geochemical analyses of the Paleocene Kongdian Formation’s organic-rich rocks from the Bohai Bay Basin. Findings show that global PETM warming drove regional aridification and evaporation, while carbonate isotopic signals (negative δ13C, positive δ18O) are consistent with enhanced hydrological cycling and salinity fluctuations, reflecting the interplay between global climate forcing and local hydrological responses. Nutrient influx during the PETM boosted paleoproductivity. Arid-adapted organisms like Podocarpidites and Ephedripites also became present. The PETM experienced heightened seasonal variance and climatic extremes, with elevated temperatures causing increased evaporation and salinity during dry seasons, indicating greater aridity. Seasonal precipitation likely intensified due to monsoonal rains or the tropical convergence zone’s northward movement. Pollen from the Bohai Bay Basin indicates both significant episodic precipitation and increased aridity, reflecting complex climatic interactions. Increased detrital kaolinite content during the PETM suggests intensified physical weathering and erosion in kaolinite-bearing catchment areas, driven by episodic heavy rainfall. Our sedimentological observations (e.g., laminated shale cyclicity and detrital mineral assemblages) indicate sporadic heavy rainfall events, enhancing physical weathering and altering detrital sediment mineral content in the Bohai Bay Basin.

This work experimentally investigates Richtmyer–Meshkov (RM) turbulence driven by a cylindrical converging shock using time-resolved planar laser-induced fluorescence. An automatically retractable plate is developed to generate membraneless yet sharp interfaces characterised by random short-wavelength perturbations and controllable long-wavelength components. Five initial interfaces are examined: one with random short-wavelength perturbations, and four with these random perturbations superimposed with single-mode long-wavelength perturbations of controlled amplitude and wavenumber. The shocked interface in the converging configuration exhibits strongly unsteady motion: it initially moves inwards uniformly, then decelerates, moves outwards following reshock, and finally decelerates again with noticeable oscillations. The interface initially develops with a well-defined morphology, but quickly transitions to turbulent mixing after reshock. Both reshock and Rayleigh–Taylor instability, unique to converging RM flows, significantly influence the mixing layer evolution. The mixing width exhibits significantly higher post-reshock growth rates compared with the planar counterpart. Scalar mixedness analysis indicates that the random-perturbation case achieves significantly higher homogenisation efficiency than single-mode cases, whereas the mean scalar dissipation rate follows a similar temporal pattern regardless of initial morphology. The initial perturbation spectrum strongly influences the timing of turbulent transition: the high-wavenumber single-mode case reaches the empirical threshold earliest, followed by the random-perturbation case, while the low-wavenumber single-mode cases exhibit substantially delayed or incomplete transition. Scalar energy spectra further highlight that initial perturbations critically affect the efficiency of turbulent cascade and the small-scale energy distribution.

The collisions between elongated particles in turbulence play an important role in various natural and industrial processes. In this study, we establish a theoretical model to estimate the collision kernels of monodisperse elongated passive particles in homogeneous isotropic turbulence. The model is composed of two terms: the collision kernel with fixed relative angles and the angular-volumetric number density of neighbouring pairs, where we first derive under the Gaussian hypothesis of the fluid velocity gradients and then incorporate a non-Gaussianity factor into the formulations. The collision kernels obtained by the present model are in a good agreement with that of direct numerical simulations. Moreover, our model provides insights into the mechanism of the relative alignment between nearby particle pairs and the chain formation in turbulence, from the perspective of particle collisions.

We developed a two-phase lattice Boltzmann model by coupling the entropic multiple-relaxation-time (EMRT or KBC) collision operator enabling low fluid viscosity, with a source term (Wang et al. 2022, Phys. Rev. E vol. 105, no 4) to independently adjust surface tension. The coupling is implemented via the exact difference method (EDM), which allows full consideration of external-force effects on the entropic stabiliser in KBC, in contrast to the recent work of Wang et al. (2022 Phys. Rev. E vol. 105) and Xu et al. (2024 Comput. Math. Appl. vol. 159, 92–101). More importantly, we address a major drawback of the EDM by explicitly demonstrating how its high-order error terms influence the pressure tensor and surface tension. Using the developed model, we investigated droplet impact and splashing on a thin liquid film at a remarkably high Weber number of ${\textit{We}} = 5000$ and Reynolds number of ${\textit{Re}} = 5000$. Droplet impact and splashing on flat surfaces and mesh structures at very high ${\textit{Re}}$ (15 200) and ${\textit{We}}$ (1020) are also studied after validating four representative cases against experiments. For droplet impact on flat surfaces, hydrophobicity promotes the growth of peripheral instabilities, leading to fingering splashing. Corona splashing transitions to fingering splashing as the liquid–gas viscosity ratio increases. For droplet impact on mesh structures, large openings promote liquid penetration, whereas small openings enhance spreading. As the solid ratio increases, the maximum spreading ratio increases monotonically but nonlinearly, whereas the maximum penetrated liquid pillar length first rises and then drops. These simulations demonstrate the proposed model offers significant advantages for accurately capturing and elucidating complex droplet impact and splashing dynamics at high ${\textit{Re}}$ and ${\textit{We}}$.

Shipwrecks provide invaluable insights into human society and trade. Their unique preservation conditions also mean that they can serve as exceptional biobanks, recording traces of organisms carried aboard or arriving post wreck. Yet only limited research has explored the genetic potential of onboard sediments. Here, the authors present environmental and metagenomic analyses of sediments contained in a large amphora from the 150-year-old Yangzi Estuary II shipwreck. Weaving the results with historic texts, they reconstruct part of the history of the wrecked vessel, elucidating cargo-packing techniques, its likely season and port of sailing, and its ultimate submersion within the estuarine environment.

Theileria annulata causes tropical theileriosis in cattle, yet the molecular basis of host–parasite crosstalk across intracellular stages remains incompletely defined. We combined RNA sequencing and untargeted metabolomics to profile paired uninfected and infected bovine leukocytes (schizont stage) and erythrocytes (piroplasm stage), together with purified schizonts and piroplasms. Integrated analyses revealed pronounced, cell type-specific reprogramming. Infected leukocytes showed activation of immune signalling, amino acid metabolism and energy-producing pathways, consistent with leukocyte transformation, whereas infected erythrocytes preferentially engaged glutathione metabolism and redox homeostasis. Parasite stage comparisons uncovered extensive transcriptional and metabolic rewiring, including stage-biased expression of mitochondrial components, antioxidant systems and putative stage-regulated transcription factors. These coherent host–parasite adaptations likely facilitate parasite survival and persistence within distinct cellular niches. This work delineates a stage-resolved multi-omics landscape of T. annulata infection spanning host and parasite compartments and identifies signalling and metabolic pathways that merit functional validation as candidates for improved diagnostics and targeted interventions against bovine tropical theileriosis.

The emergence of large language models, exemplified by ChatGPT, has garnered growing attention for their potential to generate feedback in second language writing, particularly automated written corrective feedback (AWCF). In this study, we examined how prompt design – a generic prompt and two domain-specific prompts (zero-shot and one-shot) enriched with comprehensive domain knowledge about written corrective feedback (WCF) – influences ChatGPT’s ability to provide AWCF. The accuracy and coverage of ChatGPT’s feedback across these three prompts were benchmarked against Grammarly, a widely used traditional automated writing evaluation (AWE) tool. We find that ChatGPT’s ability in flagging language errors grew considerably with prompt sophistication driven by the integration of domain-specific knowledge and examples. While the generic prompt resulted in substantially lower performance than Grammarly, the zero-shot prompt achieved comparable results to it and the one-shot prompt surpassed it considerably in error detection. Notably, the most pronounced improvement in ChatGPT’s performance was observed in its detection of frequent error categories, including those of word choice or expression, direct translation, sentence structure and pronoun. Nonetheless, even with the most sophisticated prompt, ChatGPT still displayed certain limitations when compared to Grammarly. Our study has both theoretical and practical implications. Theoretically, it lends empirical evidence to Knoth et al.’s (2024) proposition to separate domain-specific AI literacy from generic AI literacy. Practically, it sheds light on the pedagogical application and technical development of AWE systems.

High-concentrate diets are commonly used to enhance lamb growth performance; however, their long-term impacts on metabolic health, particularly fat deposition and liver function, remain a challenge. This study utilized an integrative multi-omics approach to explore the role of keystone rumen microbiota in modulating the rumen-liver-tail adipose axis under high-concentrate diets. Keystone rumen bacterial taxa, including Ruminococcus_gauvreauii, Syntrophococcus, Solobacterium, Bifidobacterium, and Ruminococcaceae_UCG-010, were identified as critical mediators linking dietary changes to tail fat deposition. Liver transcriptomic analysis revealed disrupted folate biosynthesis, regulated by key members of the AKR1C3 family (AKR1C23, AKR1C1, and PGFS), which played a pivotal role in glucose and fatty acid metabolism through the action of tetrahydrobiopterin. In tail adipose tissue, pathways associated with vitamin B6 metabolism and fatty acid elongation were significantly enriched, with pyridoxal 5’-phosphate and elongation-related genes (ELOVL3, HSD17B12, and FADS2) contributing to lipid biosynthesis and deposition. These findings establish a mechanistic framework for the rumen-liver-tail adipose axis, highlighting the influence of keystone rumen microbiota on host metabolism. This study offers novel insights into dietary interventions and microbial strategies to improve ruminant healthy production efficiency and meat quality.

In typical nature and engineering scenarios, such as supernova explosion and inertial confinement fusion, mixing flows induced by hydrodynamic interfacial instabilities are essentially compressible. Despite their significance, accurate predictive tools for these compressible flows remain scarce. For engineering applications, the Reynolds-averaged Navier–Stokes (RANS) simulation stands out as the most practical approach due to its outstanding computational efficiency. However, existing RANS studies focus primarily on cases where the compressible effect plays an insignificant role in mixing development, with quite limited attention given to scenarios with significant compressibility influence. Moreover, most of the existing RANS mixing models demonstrate significantly inaccurate predictions for the latter. This study develops a novel compressible RANS mixing model by incorporating physical compressibility corrections into the $K$–$L$–$\gamma$ mixing transition model recently proposed by Xie et al. (J. Fluid Mech. 1002, 2025, A31). Specifically, taking the density-stratified Rayleigh–Taylor mixing flows as representative compressible cases, we first analyse the limitations of the existing model for compressible flows, based on high-fidelity data and local instability criteria. Subsequently, the equation of state for a perfect gas is employed to derive comprehensive compressibility corrections. The crucial turbulent composition and heat fluxes are integrated into the closure of the key turbulent mass flux term of the turbulent kinetic energy equation. These corrections enable the model to accurately depict compressible mixing flows. Systematic validations confirm the efficacy of the proposed modelling scheme. This study offers a promising strategy for modelling compressible mixing flows, paving the way for more accurate predictions in complex scenarios.

The Richtmyer–Meshkov instability at gas interfaces with controllable initial perturbation spectra under reshock conditions is investigated both experimentally and theoretically. A soap-film method is adopted to generate well-defined single-, dual- and triple-mode air/SF$_6$ interfaces. By inserting an acrylic block into the test section, a reflected shock with controllable reshock timing is created. The results reveal a complex relationship between the post-reshock perturbation growth rate and the pre-reshock interface morphology. For single-mode interfaces, the post-reshock growth rate exhibits a strong dependence on pre-reshock conditions. In contrast, for multi-mode interfaces, this dependence weakens significantly due to mode-coupling effects. It is found that, following reshock, each fundamental mode develops independently and later is significantly influenced by mode-coupling effects. Based on this finding, we propose an empirical model that matches the initial linear growth rate and the asymptotic growth rate, accurately predicting the evolution of fundamental modes from early to late stages across all three configurations. Furthermore, a theoretical formula is derived, linking the empirical coefficient in the model of Charakhch’An (2020 J. Appl. Mech. Tech. Phys. vol. 41, no. 1, pp. 23–31) to the initial perturbation. This provides a unified framework to explain the varying dependence of post-reshock growth rates on pre-reshock morphology observed in previous experiments.

This paper considers two commuting smooth transformations on a Banach space and proves the sub-additivity of the measure theoretic entropies under mild conditions. Furthermore, some additional conditions are given for the equality of the entropies. This extends Hu’s work [Some ergodic properties of commuting diffeomorphisms. Ergod. Th. & Dynam. Sys. 13(1) (1993), 73–100] about commuting diffeomorphisms in a finite dimensional space to the case of systems on an infinite dimensional Banach space.

Research on stress damage induced by weaning and its underlying mechanisms in squabs is notably scarce. The study was designed to uncover the potential mechanisms behind the intestinal epithelial barrier impairment due to early weaning (EW) in squabs by evaluating the function of intestinal epithelial barrier, the balance of T helper cell (Th) subsets, and the link between them. A total of 160 hatched squabs were randomly assigned to two groups: one received artificial pigeon milk starting from day 7 post-hatching, while the other group continued to be nourished by their parent pigeons. Ileal tissue and serum samples from eight replicates were gathered for analyses at intervals of 1, 4, 7, 10, 14, and 21 days after weaning. Results showed that body weight of squabs in the EW group decreased significantly from 1 day after weaning and continued throughout the experiment period. The serum endotoxin, diamine oxidase of weaned squabs increased significantly. The mRNA expression of ileal tight junction proteins of weaned squabs was significantly downregulated at multiple time points from 1 to 21 days after weaning. Compared to squabs in the control group, the weaned squabs exhibited immune imbalances of Th1/Th2 and Th17/Treg in ileum, characterized by abnormal expression of specific transcription factors of Th1, Th2, Th17, and Treg, as well as abnormal concentrations of differentiation-inducing cytokines and effector cytokines. Mantel tests showed that the changes of factors related to the differentiation of Th17/Treg cell subsets were significantly correlated with the diamine oxidase, endotoxin level, and the CDLN1 mRNA expression. Summarily, EW could lead to impaired growth, compromised intestinal epithelial barrier function and an imbalance in the differentiation of Th cell subsets in squabs, among which the dysbalance between Th17 and Treg cells appeared to be more closely associated with the damage of the intestinal epithelial barrier function in early weaned squabs.

The literature shows that social media enhances individual stakeholders’ ability to directly influence firm behaviors, paying less attention to how it enables different stakeholder groups to influence firms collectively. Drawing on the stakeholder multiplicity perspective in stakeholder theory, this study theorizes and empirically demonstrates that social media can empower lower-salience stakeholders to drive the actions of higher-salience stakeholders to influence firm behaviors. By analyzing 506 consumer crises involving foreign and local companies in China from 2000 to 2020, we find that firms take more substantial responsibility when confronted with consumers’ social-media-based collective actions than when confronted with conventional channels of consumer complaints. This heightened responsibility stems mainly from collective actions’ tendency to spur law-enforcing agencies into addressing alleged firm misdeeds, demonstrating a stakeholder multiplicity effect of social media empowerment. We also identify the institutional contingency of this effect, showing that local governments’ bureaucratic capacity positively moderates collective actions’ effect on law-enforcing actions, whereas their intervention in firms’ operational decisions negatively moderates law-enforcing actions’ effect on firms’ responsibility assumption. This study extends the understanding of social media's relationship with stakeholder influence and consolidates the stakeholder multiplicity perspective in stakeholder theory.

We report the first measurement of turbulent mixing developing from the convergent Richtmyer–Meshkov (RM) instability using time-resolved planar laser-induced fluorescence in a semi-annular convergent shock tube. A membraneless yet sharp interface with random short-wavelength perturbations, but controllable long-wavelength perturbations, is created by an automatically retractable plate, enhancing the reproducibility and reliability of RM turbulence experiments. The cylindrical air/SF$_6$ interface formed is first subjected to a convergent shock, then to its reflected shock and subsequently transits to turbulent mixing. It is found that the mixing width after reshock has a linear growth rate more than twice the rate in planar geometry. Also, the mixing width does not present power-law growth at late stages as in a planar geometry. However, the scalar spectrum and transition criterion obtained are similar to their planar counterparts. These findings indicate that the geometric constraint greatly affects the large scales of the flow, while having a weaker effect on the small scales. It is also found that the reflected shock significantly increases both scale separation and Reynolds number, explaining the rapid transition to turbulence following reshock.

The proton–boron ${}^{11}{\text{B}}\left( {p,\alpha } \right)2\alpha $ reaction (p-11B) is an interesting alternative to the D-T reaction ${\text{D}}\left( {{\text{T}},{\text{n}}} \right)\alpha $ for fusion energy, since the primary reaction channel is aneutronic and all reaction partners are stable isotopes. We measured the α production yield using protons in the 120–260 keV energy range impinging onto a hydrogen–boron-mixed target, and for the first time present experimental evidence of an increase of α-particle yield relative to a pure boron target. The measured enhancement factor is approximately 30%. The experiment results indicate a higher reactivity, and that may lower the condition for p-11B fusion ignition.