Single-cell tornado-like vortices (TLVs) exhibit periodic wandering fluctuations around the time-averaged vortex core, a phenomenon known as vortex wandering, which constitutes the most prominent periodic behaviour in such flows. The coupling between vortex motion and wandering creates complex swirl dynamics, posing significant analytical challenges. However, the limited availability of experimental studies on vortex wandering decomposition hampers a deeper understanding of this phenomenon. To address this gap, a tornado simulator was designed to generate a controllable single-cell TLV, and high-frequency velocity data were obtained using particle image velocimetry. A sparsity-promoting dynamic mode decomposition (sp-DMD) method was developed to decouple coherent structures and analyse dynamic characteristics. Results show that as the swirl ratio increases, the vortex structure becomes more diffuse, with significant reductions in intensity. Vortex wandering is present across all swirl conditions, with its periodicity strongly modulated by the swirl ratio. Importantly, sp-DMD identified two primary modes, the time-averaged mode (first mode), representing the dominant rotational vortex motion, and the vortex-wandering-dominated modes (second and third conjugate modes), which correspond to persistent periodic velocity fluctuations and contribute the most significant pulsations. These modes exhibit a pair of oppositely rotating vortices symmetrically revolving around the central flow axis. Visualisations of the Q criterion reveal a symmetric dipole pattern. This suggests that rotational and shear effects are likely responsible for the periodic movement of the vortex core. Furthermore, as the swirl ratio increases, the energy of the vortex-wandering-dominated modes diminishes, and motion transitions from high-energy, organised dynamics to low-energy, disordered behaviour.

This paper presents a detailed technical overview of the femtosecond precision timing and synchronization systems implemented at the Shanghai high repetition rate XFEL and extreme light facility (SHINE). These systems are designed to deliver stabilized optical references to multiple receiver clients, ensuring high-precision synchronization between the optical master oscillator (OMO) and optical/RF subsystems. The core components include an OMO, fiber length stabilizers and laser-to-laser synchronization modules that achieve femtosecond-level accuracy. Our discussion extends to the various subsystems that comprise the synchronization infrastructure, including the OMO, fiber length stabilizer and advanced phase detection techniques. Finally, we highlight ongoing research and development efforts aimed at enhancing the functionality and efficiency of these systems, thereby contributing to the advancement of X-ray free-electron laser technology and its applications in scientific research.

This paper numerically investigates the heat transport and bifurcation of natural convection in a differentially heated cavity filled with entangled polymer solution combined with the boundary layer and kinetic energy budget analysis. The polymers are described by the Rolie-Poly model, which effectively captures the rheological response of entangled polymers. The results indicate that the competition between its shear-thinning and elasticity dominates the flow structures and heat transfer rate. The addition of polymers tends to enhance the heat transfer as the polymer viscosity ratio ($\beta$) decreases or the relaxation time ratio ($\xi$) increases. The amount of heat transfer enhancement (HTE) behaves non-monotonically, which first increases significantly and then remains almost constant or decreases slightly with the Weissenberg number ($Wi$). The critical $Wi$ gradually increases with the increasing $\xi$, where the maximum HTE reaches approximately $64.9\,\%$ at $\beta = 0.1$. It is interesting that even at low Rayleigh numbers, the flow transitions from laminar to periodic flows in scenarios with strong elasticity. The bifurcation is subcritical and exhibits a typical hysteresis loop. Then, the bifurcation routes driven by inertia and elasticity are examined by direct numerical simulations. These results are illustrated by time histories, Fourier spectra analysis and spatial structures observed at varying time intervals. The kinetic energy budget indicates that the stretch of the polymers leads to great energy exchange between polymers and flow structures, which plays a crucial role in the hysteresis phenomenon. This dynamic behaviour contributes to the strongly self-sustained and self-enhancing processes in the flow.

Ultra-thin liquid sheets generated by impinging two liquid jets are crucial high-repetition-rate targets for laser ion acceleration and ultra-fast physics, and serve widely as barrier-free samples for structural biochemistry. The impact of liquid viscosity on sheet thickness should be comprehended fully to exploit its potential. Here, we demonstrate experimentally that viscosity significantly influences thickness distribution, while surface tension primarily governs shape. We propose a thickness model based on momentum exchange and mass transport within the radial flow, which agrees well with the experiments. These results provide deeper insights into the behaviour of liquid sheets and enable accurate thickness control for various applications, including atomization nozzles and laser-driven particle sources.

This study combines experimental observations and numerical simulations to comprehensively analyse the interface evolution of confined droplets in microfluidic devices with flow-focusing junctions under different aspect ratios. Microchannels with aspect ratios of 1, 1/2 and 1/3 are designed, where droplets are generated at the first flow-focusing junction, and three distinct flow patterns – no breakup, single breakup and multiple breakups – are observed at the second flow-focusing junction. The relationship between droplet length and flow parameters is established, investigating the effects of capillary number and channel aspect ratio on droplet breakup behaviour. It is found that the scaling exponent of the minimum neck thickness increases with the continuous phase flow rate. Numerical simulations are carried out to illustrate the shape evolution of a droplet in three-dimensional space, allowing the calculation of the curvature distribution of the interface. The scaling exponent of the mean radius of curvature in a channel with an aspect ratio of 1 differs from that in a channel with an aspect ratio of less than 1. These findings provide theoretical support for understanding droplet breakup dynamics and lay a foundation for optimising microfluidic device design and structural innovation.

This study presents a novel investigation into the vortex dynamics of flow around a near-wall rectangular cylinder based on direct numerical simulation at $Re=1000$, marking the first in-depth exploration of these phenomena. By varying aspect ratios ($L/D = 5$, $10$, $15$) and gap ratios ($G/D = 0.1$, $0.3$, $0.9$), the study reveals the vortex dynamics influenced by the near-wall effect, considering the incoming laminar boundary layer flow. Both $L/D$ and $G/D$ significantly influence vortex dynamics, leading to behaviours not observed in previous bluff body flows. As $G/D$ increases, the streamwise scale of the upper leading edge (ULE) recirculation grows, delaying flow reattachment. At smaller $G/D$, lower leading edge (LLE) recirculation is suppressed, with upper Kelvin–Helmholtz vortices merging to form the ULE vortex, followed by instability, differing from conventional flow dynamics. Larger $G/D$ promotes the formation of an LLE shear layer. An intriguing finding at $L/D = 5$ and $G/D = 0.1$ is the backward flow of fluid from the downstream region to the upper side of the cylinder. At $G/D = 0.3$, double-trailing-edge vortices emerge for larger $L/D$, with two distinct flow behaviours associated with two interactions between gap flow and wall recirculation. These interactions lead to different multiple flow separations. For $G/D = 0.9$, the secondary vortex (SV) from the plate wall induces the formation of a tertiary vortex from the lower side of the cylinder. Double-SVs are observed at $L/D = 5$. Frequency locking is observed in most cases, but is suppressed at $L/D = 10$ and $G/D = 0.9$, where competing shedding modes lead to two distinct evolutions of the SV.

A high-energy pulsed vacuum ultraviolet (VUV) solid-state laser at 177 nm with high peak power by the sixth harmonic of a neodymium-doped yttrium aluminum garnet (Nd:YAG) amplifier in a KBe2BO3F2 prism-coupled device was demonstrated. The ultraviolet (UV) pump laser is a 352 ps pulsed, spatial top-hat super-Gaussian beam at 355 nm. A high energy of a 7.12 mJ VUV laser at 177 nm is obtained with a pulse width of 255 ps, indicating a peak power of 28 MW, and the conversion efficiency is 9.42% from 355 to 177 nm. The measured results fitted well with the theoretical prediction. It is the highest pulse energy and highest peak power ever reported in the VUV range for any solid-state lasers. The high-energy, high-peak-power, and high-spatial-uniformity VUV laser is of great interest for ultra-fine machining and particle-size measurements using UV in-line Fraunhofer holography diagnostics.

The large number of patients with ankle injuries and the high incidence make ankle rehabilitation an urgent health problem. However, there is a certain degree of difference between the motion of most ankle rehabilitation robots and the actual axis of the human ankle. To achieve more precise ankle joint rehabilitation training, this paper proposes a novel 3-PUU/R parallel ankle rehabilitation mechanism that integrates with the human ankle joint axis. Moreover, it provides comprehensive ankle joint motion necessary for effective rehabilitation. The mechanism has four degrees of freedom (DOFs), enabling plantarflexion/dorsiflexion, eversion/inversion, internal rotation/external rotation, and dorsal extension of the ankle joint. First, based on the DOFs of the human ankle joint and the variation pattern of the joint axes, a 3-PUU/R parallel ankle joint rehabilitation mechanism is designed. Based on the screw theory, the inverse kinematics inverse, complete Jacobian matrix, singular characteristics, and workspace analysis of the mechanism are conducted. Subsequently, the motion performance of the mechanism is analyzed based on the motion/force transmission indices and the constraint indices. Then, the performance of the mechanism is optimized according to human physiological characteristics, with the motion/force transmission ratio and workspace range as optimization objectives. Finally, a physical prototype of the proposed robot was developed, and experimental tests were performed to evaluate the above performance of the proposed robot. This study provides a good prospect for improving the comfort and safety of ankle joint rehabilitation from the perspective of human-machine axis matching.

Toroidal bubbles (TBs) represent cases of vortex rings with a gas–liquid interface where a gas vortex ring is encased within a liquid vortex ring, and can serve as effective media for mass conveyance, process mixing, noise reduction and reaction regulation. In this study, we carry out a systematic study on the interaction between a TB and a free surface. According to the high-speed photographic images from the experiments, we identify strong and weak interactions in terms of the normalized maximum free surface deformation $h_{max}^*$. Then, we perform numerical simulations based on the volume of fluid (VOF) method in the OpenFOAM platform. Based on both the experimental and the numerical results, we conclude that the Froude number, $Fr$, determines the main characteristics during the interaction process. The TB–free surface interaction is essentially the interaction between the liquid vortex ring enveloping the TB and the free surface, supplemented by the TB's complex behaviour. Next, we establish the scaling law of $h_{max}^*$ based on the energy balance condition. Based on this, we provide the critical $Fr$ and the slenderness of the TB, $\eta$, for identifying the strong and weak interactions, and a parametric plot of the interactions in terms of $Fr$ and $\eta$.

Deep learning (DL) has been widely used in bearing fault diagnosis. In particular, convolutional neural networks (CNNs) improve diagnosis accuracy by extracting excellent fault features. However, CNN lacks an explicit learning mechanism to distinguish between different fault characteristics in the input signal to the diagnosis results. This article presents a new end-to-end depth framework called multi-head self-attention convolution neural network (MSA-CNN) for bearing fault diagnosis. Firstly, we adopt a data pre-processing method that directly converts one-dimensional (1D) original signals into two-dimensional (2D) grayscale images, which is simple to implement and preserves the complete information of the original signal. Secondly, multi-head self-attention (MSA) is first constructed to aggregate the global information and adaptively assign weights to the input signal's features. Thirdly, the CNN with small-scale kernels extracted detailed local features. Finally, the learned high-level representations are fed into the full connect (FC) layer for fault diagnosis. The performance of the MSA-CNN is validated on different datasets. The results show that the proposed MSA-CNN can significantly improve fault diagnosis accuracy compared with the other state-of-the-art methods and has excellent noise immunity performance.

Carboxylesterases (CarEs) is an important detoxification enzyme system in phase Ⅰ participating in insecticides resistance. In our previous study, SlCarE054, a CarEs gene from lepidoptera class, was screened out to be upregulated in a pyrethroids and organophosphates resistant population. Its overexpression was verified in two field-collected populations of Spodoptera litura (Lepidoptera: Noctuidae) resistant to pyrethroids and organophosphates by qRT-PCR. Spatiotemporal expression results showed that SlCarE054 was highly expressed in the pupae stage and the digestive tissue midgut. To further explore its role in pyrethroids and organophosphates resistance, its metabolism activity to insecticides was determined by UPLC. Its recombinant protein showed significant metabolism activity to cyhalothrin and fenvalerate, but not to phoxim or chlorpyrifos. The metabolic activity of SlCarE054 to β-cypermethrin showed stereoselectivity, with higher metabolic activity to θ-cypermethrin than the enantiomer α-cypermethrin. The metabolite of β-cypermethrin was identified as 3-phenoxybenzaldehyde. Further modelling and docking analysis indicated that β-cypermethrin, cyhalothrin and fenvalerate could bind with the catalytic triad of the 3D structure of SlCarE054. The interaction of β-cypermethrin with SlCarE054 also showed the lowest binding energy. Our work provides evidence that SlCarE054 play roles in β-cypermethrin resistance in S. litura.

Motivated by the work initiated by Chapman [‘Determinants of Legendre symbol matrices’, Acta Arith. 115 (2004), 231–244], we investigate some arithmetical properties of generalised Legendre matrices over finite fields. For example, letting $a_1,\ldots ,a_{(q-1)/2}$ be all the nonzero squares in the finite field $\mathbb {F}_q$ containing q elements with $2\nmid q$, we give the explicit value of the determinant $D_{(q-1)/2}=\det [(a_i+a_j)^{(q-3)/2}]_{1\le i,j\le (q-1)/2}$. In particular, if $q=p$ is a prime greater than $3$, then

$$ \begin{align*}\bigg(\frac{\det D_{(p-1)/2}}{p}\bigg)= \begin{cases} 1 & \mbox{if}\ p\equiv1\pmod4,\\ (-1)^{(h(-p)+1)/2} & \mbox{if}\ p\equiv 3\pmod4\ \text{and}\ p>3, \end{cases}\end{align*} $$

where $(\frac {\cdot }{p})$ is the Legendre symbol and $h(-p)$ is the class number of $\mathbb {Q}(\sqrt {-p})$.

This paper retrospectively analysed the prevalence of macrolide-resistant Mycoplasma pneumoniae (MRMP) in some parts of China. Between January 2013 and December 2019, we collected 4,145 respiratory samples, including pharyngeal swabs and alveolar lavage fluid. The highest PCR-positive rate of M. pneumoniae was 74.5% in Beijing, the highest resistance rate was 100% in Shanghai, and Gansu was the lowest with 20%. The highest PCR-positive rate of M. pneumoniae was 74.5% in 2013, and the highest MRMP was 97.4% in 2019; the PCR-positive rate of M. pneumoniae for adults in Beijing was 17.9% and the MRMP was 10.48%. Among the children diagnosed with community-acquired pneumonia (CAP), the PCR-positive and macrolide-resistant rates of M. pneumoniae were both higher in the severe ones. A2063G in domain V of 23S rRNA was the major macrolide-resistant mutation, accounting for more than 90%. The MIC values of all MRMP to erythromycin and azithromycin were ≥ 64 μg/ml, and the MICs of tetracycline and levofloxacin were ≤ 0.5 μg/ml and ≤ 1 μg/ml, respectively. The macrolide resistance varied in different regions and years. Among inpatients, the macrolide-resistant rate was higher in severe pneumonia. A2063G was the common mutation, and we found no resistance to tetracycline and levofloxacin.

The numerical investigation focuses on the flow patterns around a rectangular cylinder with three aspect ratios ($L/D=5$, $10$, $15$) at a Reynolds number of $1000$. The study delves into the dynamics of vortices, their associated frequencies, the evolution of the boundary layer and the decay of the wake. Kelvin–Helmholtz (KH) vortices originate from the leading edge (LE) shear layer and transform into hairpin vortices. Specifically, at $L/D=5$, three KH vortices merge into a single LE vortex. However, at $L/D=10$ and $15$, two KH vortices combine to form a LE vortex, with the rapid formation of hairpin vortex packets. A fractional harmonic arises due to feedback from the split LE shear layer moving upstream, triggering interaction with the reverse flow. Trailing edge (TE) vortices shed, creating a Kármán-like street in the wake. The intensity of wake oscillation at $L/D=5$ surpasses that in the other two cases. Boundary layer transition occurs after the saturation of disturbance energy for $L/D=10$ and $15$, but not for $L/D=5$. The low-frequency disturbances are selected to generate streaks inside the boundary layer. The TE vortex shedding induces the formation of a favourable pressure gradient, accelerating the flow and fostering boundary layer relaminarization. The self-similarity of the velocity defect is observed in all three wakes, accompanied by the decay of disturbance energy. Importantly, the decrease in the shedding frequency of LE (TE) vortices significantly contributes to the overall decay of disturbance energy. This comprehensive exploration provides insights into complex flow phenomena and their underlying dynamics.

The laboratory generation and diagnosis of uniform near-critical-density (NCD) plasmas play critical roles in various studies and applications, such as fusion science, high energy density physics, astrophysics as well as relativistic electron beam generation. Here we successfully generated the quasistatic NCD plasma sample by heating a low-density tri-cellulose acetate (TCA) foam with the high-power-laser-driven hohlraum radiation. The temperature of the hohlraum is determined to be 20 eV by analyzing the spectra obtained with the transmission grating spectrometer. The single-order diffraction grating was employed to eliminate the high-order disturbance. The temperature of the heated foam is determined to be T = 16.8 ± 1.1 eV by analyzing the high-resolution spectra obtained with a flat-field grating spectrometer. The electron density of the heated foam is about $N_e=4.0\pm 0.3\times {10}^{20}{\text{cm}}^{-3}$ under the reasonable assumption of constant mass density.

Reward processing dysfunctions are considered a candidate mechanism underlying anhedonia and apathy in depression. Neuroimaging studies have documented that neurofunctional alterations in mesocorticolimbic circuits may neurally mediate these dysfunctions. However, common and distinct neurofunctional alterations during motivational and hedonic evaluation of monetary and natural rewards in depression have not been systematically examined. Here, we capitalized on pre-registered neuroimaging meta-analyses to (1) establish general reward-related neural alterations in depression, (2) determine common and distinct alterations during the receipt and anticipation of monetary v. natural rewards, and, (3) characterize the differences on the behavioral, network, and molecular level. The pre-registered meta-analysis (https://osf.io/ay3r9) included 633 depressed patients and 644 healthy controls and revealed generally decreased subgenual anterior cingulate cortex and striatal reactivity toward rewards in depression. Subsequent comparative analyses indicated that monetary rewards led to decreased hedonic reactivity in the right ventral caudate while natural rewards led to decreased reactivity in the bilateral putamen in depressed individuals. These regions exhibited distinguishable profiles on the behavioral, network, and molecular level. Further analyses demonstrated that the right thalamus and left putamen showed decreased activation during the anticipation of monetary reward. The present results indicate that distinguishable neurofunctional alterations may neurally mediate reward-processing alterations in depression, in particular, with respect to monetary and natural rewards. Given that natural rewards prevail in everyday life, our findings suggest that reward-type specific interventions are warranted and challenge the generalizability of experimental tasks employing monetary incentives to capture reward dysregulations in everyday life.

Constraining the timing and extent of Quaternary glaciations in the Tibetan Plateau (TP) is significant for the reconstruction of paleoclimatic environment and understanding the interrelationships among climate, tectonics, and glacial systems. We investigated the late Quaternary glacial history of the Qinggulong and Juequ valleys in the Taniantaweng Mountains, southeastern TP, using cosmogenic 10Be surface exposure dating. Four major glacial events were identified based on 26 10Be ages. The exposure ages of the oldest late Quaternary glaciation correspond to Marine Oxygen Isotope Stage (MIS) 6. The maximum glacial extent was dated to 48.5–41.1 ka (MIS 3), during the last glaciation, and was more advanced than that of the last glacial maximum (LGM). Geochronology and geomorphological evidence indicate that multiple glacial fluctuations occurred in the study area during the Early–Middle Holocene. These glacial fluctuations likely were driven by the North Atlantic climate oscillations, summer solar insolation variability, Asian summer monsoon intensity, and CO2 concentration.

To alleviate the growth inhibition, and intestinal damage of Chinese mitten crab (Eriocheir sinensis) induced by low fishmeal diets (LF), an 8-week feeding trial was conducted to evaluate the addition of dietary soybean-derived bioactive peptides (SBP) in LF diets on the regulation of growth, digestion and intestinal health. The crabs were fed isonitrogenous and isoenergetic conventional diet and LF diets (10 % fishmeal replaced by soybean meal, LF) supplemented with 0, 1 %, 2 %, 4 % and 6 % SBP, respectively. The results showed that LF diet inhibited growth while inclusion of SBP quadratically remitted the growth inhibition induced by LF. For digestive function, increasing addition level of SBP quadratically improved the α-amylase and trypsin activities. For antioxidant function, LF group significantly increased the malondialdehyde content, while SBP linearly decreased the malondialdehyde level and cubically increased the anti-superoxide anion activity and total antioxidant capacity level. For intestinal health, the peritrophic membrane (PM) almost completely separated from the inner wall of the intestinal lumen, the epithelial cells reduced, the muscularis became thinner and the apoptotic signals increased in LF group; with SBP addition, the intestinal morphology was improved, with the PM adhering to the inner wall of the intestinal lumen, an increase in the number of epithelial cells and an increase in the thickness of the muscularis. Additionally, there was a decrease in apoptotic signals. Dietary SBP also increased the expression of PT and Crustin1 quadratically and decreased the expression of ALF1 linearly, ALF3 and ILF2 quadratically.