We investigate the natural oscillations of sessile drops with a central trapped bubble on a plane using linear potential flow theory, considering both free and pinned contact lines. The system is governed by the contact angle $\alpha$ and the ratio $\tau$ of inner to outer contact line radii. For bubble-containing (BC) hemispherical drops with free contact lines (referred to as free BC semi-drops), the modes mirror half of those in concentric spherical BC drops due to plane symmetry. These modes are labelled ‘plus’ (with greater inner surface deformation) and ‘minus’ (with greater outer surface deformation). As $\tau \to 0$, minus modes converge to those of bubble-free drops. Results show that varying $\alpha$ from $90^\circ$ or pinning the contact line in free BC semi-drops alters the topology of spectral lines, turning original crossings of spectral lines between minus and plus modes into avoided crossings. This shift causes minus and plus modes to form spectral trends with avoided crossings, maintaining their original spectral shapes. In an avoided crossing, two coupled modes cannot be classified as plus or minus due to their comparable inner and outer surface deformations, resulting in mode beating when both are excited, as confirmed by our direct numerical simulations. This study on the impact of inner bubbles on the spectrum may help in predicting bubble size in opaque sessile drops.

The interaction between planar incident shocks and cylindrical boundary layers is prevalent in missiles equipped with inverted inlets, which typically leads to substantial three-dimensional flow separation and the formation of vortical flow. This study utilizes wind-tunnel experiments and theoretical analysis to elucidate the shock structure, surface topology and pressure distributions induced by a planar shock with finite width impinging on a cylinder wall at Mach 2.0. In the central region, a refraction phenomenon occurs as the transmitted shock bends within the boundary layer, generating a series of compression waves that coalesce into a shock, forming a ‘shock triangle’ structure. As the incident shock propagates backward along both sides, it gradually evolves into a Mach stem, where the transmitted shock refracts the expansion wave. The incident shock interacts with the boundary layer, resulting in the formation of a highly swept separation region that yields a pair of counter-rotating horseshoe-like vortices above the separation lines. These vortices facilitate the accumulation of low-energy fluid on both sides. Although the interaction of the symmetry plane aligns with free-interaction-theory, the separation shock angle away from the centre significantly deviates from the predicted value owing to the accumulation of low-energy fluids. The primary separation line and pressure distribution jointly exhibit an elliptical similarity on the cylindrical surface. Furthermore, the potential unsteady behaviour is assessed, and the Strouhal number of the low-frequency oscillation is found to be 0.0094, which is insufficient to trigger significant alterations in the flow field structure.

An experimental investigation is conducted to study the flow patterns, spectral properties and energy fluxes in thin-layer turbulence with varying system sizes and damping rates. It is found that although a system-size vortex (an indicator of spectral condensation) occurs for small system sizes and does not for large ones, the spectra for different system sizes consistently exhibit a scaling close to $k^{-3}$ in inverse cascade (another indicator of spectral condensation). On the other hand, under a fixed system size larger than the friction-dominated length scale, the energy spectrum in the inverse cascade range changes from $k^{-3}$ to $k^{-5/3}$ as the damping rate increases, suggesting that the friction-dominated length scale may not be a suitable parameter for predicting spectral transition. At lower damping rates and large system sizes, turbulent structures grow larger via inverse cascade, manifesting as long streamers, and the small-scale vortices are suppressed. This suppression leads to a reduction of energy flux at intermediate scales and a change in the spectral shape. The dimensionless Taylor microscale is found to exhibit a monotonic dependence on the damping rate. With the reduction in the damping rate, the Taylor microscale increases to become comparable with the forcing scale, and the spectrum in inverse cascade transits to a steeper scaling, $k^{-3}$, indicating that the dimensionless Taylor microscale may be used as a diagnostic parameter for spectral transition.

The impact of a liquid droplet with another droplet or onto a solid surface are important basic processes that occur in many applications such as agricultural sprays and inkjet printing, and in nature such as pathogens transport by raindrops. We investigated the head-on collision of unequal-size droplets of the same liquid on wetting surfaces using the direct numerical simulations technique at different size ratios. The unsteady Navier–Stokes equations are solved and the liquid–gas interface is tracked using the geometric volume-of-fluid method. The numerical model is validated by comparing simulation results of two extreme cases of droplets bouncing with the experimental data from previous studies and the agreement is quite accurate. The validated model is employed to simulate droplets bouncing at several size ratios at different Weber numbers and Ohnesorge number. Two distinct regimes are identified, namely, the inertial regime, where the restitution coefficient is a constant value close to 0.3, the viscous regime, where the restitution coefficient declines. To understand the bouncing behaviour, the velocity field is analysed and an energy budget calculation is performed. The distribution of the sessile droplet energy is found to be important and the sessile droplet surface energy is calculated by its deformation characteristics such as crater depth. Finally, a scaling analysis is performed to rationalize the insensitivity of the coefficient of restitution in the inertial regime, and its decline in the viscous regime, at large size ratios.

In this work, the dynamics of two-dimensional rotating Janus drops in shear flow is studied numerically using a ternary-fluid diffuse interface method. The rotation of Janus drops is found to be closely related to their deformation. A new deformation parameter $D$ is proposed to assess the significance of the drop deformation. According to the maximum value of $D$ ($D_{max}$), the deformation of rotating Janus drops can be classified into linear deformation ($D_{max}\le 0.2$) and nonlinear deformation ($D_{max}> 0.2$). In particular, $D_{max}$ in the former depends linearly on the Reynolds and capillary numbers, which can be interpreted by a mass–spring model. Furthermore, the rotation period $t_R$ of a Janus drop is found to be more sensitive to the drop deformation than to the aspect ratio of the drop at equilibrium. By introducing a corrected shear rate and an aspect ratio of drop deformation, a rotation model for Janus drops is established based on Jeffery's theory for rigid particles, and it agrees well with our numerical results.

The dynamics of compound drops impacting on a flat substrate is numerically investigated using a ternary-fluid diffuse-interface method, with the aim of assessing the effect of a density difference between the inner and outer droplets (denoted by $\lambda$) on the evolution of the interfaces. With the help of numerical simulations, we find that, at the intermediate stage of drop impact, the inner droplet exhibits a self-similar deformation at $\lambda =1$ and relatively high Weber number, and experiences more or less a uniform acceleration for various $\lambda$. In particular, the acceleration magnitude at $\lambda \ne 1$ can be correlated with the acceleration at $\lambda =1$ and the Atwood number. When the inner droplet is denser than the outer one, a lamella occurs at the spreading front of the inner droplet. We present a scaling analysis of the thickness of the lamella, and the resultant theoretical prediction is in good agreement with numerical results. At the maximal spreading of the compound drop, a bulging structure is formed around the symmetry axis due to the presence of the inner droplet, thereby effectively reducing the liquid supply to the spreading front and leading to a decrease of maximal spreading ratio $\beta _{max}$ as compared with a pure drop. We proposed a corrected Weber number $We^*_\lambda$ by taking account of the combined effects of $\lambda$, volume fraction of the inner droplet, Weber number and morphology of the compound drop. Integrating $We^*_\lambda$ with the universal model of $\beta _{max}$ for impacting pure drops, we successfully build up a new model for predicting the maximal spreading ratio of impacting compound drops with various $\lambda$.

In this study, the length scaling for the boundary layer separation induced by two incident shock waves is experimentally and analytically investigated. The experiments are performed in a Mach 2.73 flow. A double-wedge shock generator with two deflection angles ($\alpha _1$ and $\alpha _2$) is employed to generate two incident shock waves. Two deflection angle combinations with an identical total deflection angle are adopted: ($\alpha _1 = 7^\circ$, $\alpha _2 = 5^\circ$) and ($\alpha _1 = 5^\circ$, $\alpha _2 = 7^\circ$). For each deflection angle combination, the flow features of the dual-incident shock wave–turbulent boundary layer interactions (dual-ISWTBLIs) under five shock wave distance conditions are examined via schlieren photography, wall-pressure measurements and surface oil-flow visualisation. The experimental results show that the separation point moves downstream with increasing shock wave distance ($d$). For the dual-ISWTBLIs exhibiting a coupling separation state, the upstream interaction length ($L_{int}$) of the separation region approximately linearly decreases with increasing $d$, and the decrease rate of $L_{int}$ with $d$ increases with the second deflection angle under the condition of an identical total deflection angle. Based on control volume analysis of mass and momentum conservations, the relation between $L_{int}$ and $d$ is analytically determined to be approximately linear for the dual-ISWTBLIs with a coupling separation region, and the slope of the linear relation obtained analytically agrees well with that obtained experimentally. Furthermore, a prediction method for $L_{int}$ of the dual-ISWTBLIs with a coupling separation region is proposed, and the relative error of the predicted $L_{int}$ in comparison with the experimental result is $\sim$10 %.

To explore the effect of yield stress on the secondary breakup of gel drops, experimental and theoretical investigations are carried out by employing a high-speed camera. A unique hemline-type breakup, as a modified behaviour of sheet-thinning breakup, occurs when the air velocity increases to a high region. The edges of the drops constantly deform into thin membranes when the high-velocity air skims over the gel drops. These membranes vibrate vertically, and breaking points occur at high amplitudes, causing the formation of reticular fragments. The results of linear stability analysis indicated that the yield stress of the gel drops has an influence on the formation and breakup of the gel membranes. The breakup regime map and breakup times are also studied.

The Palaeo-Mesozoic geodynamic evolution of the Tangjia–Sumdo accretionary complex belt, which separates the North and South Lhasa Terrane, remains controversial. Moreover, the lack of geological records restricts the understanding of the evolution of the Sumdo Palaeo-Tethys Ocean from the middle Permian until the middle Triassic. Here we present zircon U–Pb geochronology, whole-rock geochemistry and Sr–Nd–Hf isotopic compositions of the Yeqing gabbro. Zircon U–Pb geochronology yields ages from 254 ± 1 to 249 ± 1 Ma. In situ Hf isotopic analyses yield ϵ Hf(t) values of −0.2 to +6.3. These samples have high TiO2 (3.69 wt %) and P2O5 (0.78 wt %) contents, with typical patterns like ocean island basalt (OIB). Besides, they are classified as high-Nb basalts (HNBs) based on the high content of Nb (45.3–113.5 ppm). Whole-rock Sr–Nd isotopic compositions are similar to OIB, with initial 87Sr/86Sr of 0.7047–0.7054, 143Nd/144Nd of 0.512526–0.512647 and ϵ Nd(t) of 0.3–2.7. These signatures suggest that the Yeqing gabbro is mainly derived from low-degree melting of the garnet lherzolite mantle. Based on field observations of HNBs intruding into the continental margin and their geochemical characteristics, we infer that the Yeqing gabbro was generated in a subduction environment. Combined with the regional geology of the subduction environment and the evolution of oceanic islands in the Sumdo Palaeo-Tethys Ocean, we propose that the Yeqing gabbro may represent a product of the asthenosphere upwelling through a slab window produced by subduction of seismic ridge in the Sumdo Palaeo-Tethys Ocean, called plume – subduction-zone interaction, during the late Permian to early Triassic.

Viruses completely rely on the energy and metabolic systems of host cells for life activities. Viral infections usually lead to cytopathic effects and host diseases. To date, there are still no specific clinical vaccines or drugs against most viral infections. Therefore, understanding the molecular and cellular mechanisms of viral infections is of great significance to prevent and treat viral diseases. A variety of viral infections are related to the p38 MAPK signalling pathway, and p38 is an important host factor in virus-infected cells. Here, we introduce the different signalling pathways of p38 activation and then summarise how different viruses induce p38 phosphorylation. Finally, we provide a general summary of the effect of p38 activation on virus replication. Our review provides integrated data on p38 activation and viral infections and describes the potential application of targeting p38 as an antiviral strategy.

The geometry of compound sessile drops at equilibrium on a flat substrate can exhibit a variety of complicated morphological configurations. In this paper, we first investigate the configuration boundaries of the compound sessile drops in a wide parameter space, where a specific configuration is not stable outside its boundaries. Then, we focus on the transitions among the axisymmetric configurations, i.e. encapsulation, lens and collars. The configuration transitions result from the variation of the wettability of the substrate and the volume ratio of the two component droplets. With the help of theoretical analysis and numerical simulations, we obtain previously unidentified criteria for the onset of configuration transition, identify the irreversible and reversible configuration transitions, reveal the dynamic behaviours of configuration transitions that are not accessible to theoretical analysis, and provide a further step towards the ultimate purpose of such work, which is the controllable reconfiguration of the compound sessile drops.

Interstitial cells of Cajal (ICC) play an essential role in the motility of the gastrointestinal tract, and they have been identified in many laboratory animals and in humans. However, the information of ICC in lower animals is still very limited. In the present study, ICC were identified in the gastric muscularis mucosae of an amphibian—the Chinese giant salamander, by c-Kit immunohistochemistry and transmission electron microscopy. ICC showed c-Kit immunoreactivity and had spindle-shaped cell bodies and 1–2 long processes. ICC were located between smooth muscle cells (SMC) in gastric muscularis mucosae. Ultrastructurally, ICC appeared as polygon-, spindle-, and awl-shaped with long cytoplasmic prolongations between SMC. ICC had distinctive characteristics, such as nuclei with peripheral electron-dense heterochromatin, caveolae, and abundant intracytoplasmatic vacuoles, mitochondria, and rough endoplasmic reticula. Moreover, lamellar bodies and two types of condensed granules were observed in the cytoplasm of ICC. Notably, ICC establish close contacts with each other. Moreover, ICC establish gap junctions with SMC. In addition, ICC were frequently observed close to nerve fibers. In summary, the present study demonstrated the presence of ICC in the gastric muscularis mucosae of the Chinese giant salamander.

Metal additive manufacturing (AM) provides a platform for microstructure optimization via process control, but establishing a quantitative processing-microstructure linkage necessitates an efficient scheme for microstructure representation and regeneration. Here, we present a deep learning framework to quantitatively analyze the microstructural variations of metals fabricated by AM under different processing conditions. The principal microstructural descriptors are extracted directly from the electron backscatter diffraction patterns, enabling a quantitative measure of the microstructure differences in a reduced representation domain. We also demonstrate the capability of predicting new microstructures within the representation domain using a regeneration neural network, from which we are able to explore the physical insights into the implicitly expressed microstructure descriptors by mapping the regenerated microstructures as a function of principal component values. We validate the effectiveness of the framework using samples fabricated by a solid-state AM technology, additive friction stir deposition, which typically results in equiaxed microstructures.

The study of the petrogenesis of some magmatic rocks with special geochemical attributes provides effective information for us to explore the deep geodynamic background of their formation. A series of granitic porphyry dykes have been found in the mélange zone of the Asa region in southern Tibet, whose genesis may be closely related to the evolution of the Meso-Tethyan Ocean. Regional geodynamic evolution is investigated by whole-rock geochemical analysis, zircon U–Pb dating and Lu–Hf isotopic analysis of two porphyritic granites. The Asa porphyritic granites have high SiO2 (74.29–78.65 wt %) and alkalis (Na2O + K2O = 6.51–9.35 wt %) contents, and low Al2O3 (11.60–14.51 wt %), CaO (0.04–0.19 wt MgO (0.01–0.10 wt %) contents. They are enriched in Zr, Nb, Ce, Y and Hf and depleted in Ti, Ba, Sr and P, consistent with A-type granites. The samples are relatively rich in LREEs, with LREE/HREE ratios of 1.73–3.04. They display negative Eu anomalies (Eu/Eu* = 0.24–0.28) and obvious Ce anomalies in some samples. Zircon U–Pb analyses show that the porphyritic granites formed in late Early Cretaceous time, 107.4 to 105.5 Ma. Zircon εHf(t) values are in the range of 6.9 to 12.0. These data indicate that the porphyritic granites were sourced from interaction between mantle-derived and juvenile lower crust-derived melts, with the addition of oceanic sediment-derived melts. This occurred when the subducting Bangong–Nujiang oceanic crust split to create a slab window. Rising asthenosphere triggered re-melting of lower crust basalts, resulting in the formation of the late Early Cretaceous A-type granites around Asa.