We study the long-time asymptotics for the solution of the modified Camassa–Holm (mCH) equation with step-like initial data.

\begin{align*} &m_{t}+\left (m\left (u^{2}-u_{x}^{2}\right )\right )_{x}=0, \quad m=u-u_{xx}, \\[3pt] & {u(x,0)=u_0(x)\to \left \{ \begin{array}{l@{\quad}l} 1/c_+, &\ x\to +\infty, \\[3pt] 1/c_-, &\ x\to -\infty, \end{array}\right .} \end{align*}

$c_+$

$c_-$

$(y,t)$

$(\xi, c)$

$c=c_+/c_-$

$\{ (\xi, c)\,:\, \xi \in \mathbb{R}, \ c\gt 0, \ \xi =y/t\}$

$u(y,t)$

$\mathcal{O}(t^{-2})$

$\mathcal{O}(t^{-1})$

Wave impact on solid structures is a well-studied phenomenon, but almost exclusively for the case that the impacting liquid (e.g. water) is surrounded by a non-condensable gas (such as air). In this study we turn to wave impact in a boiling liquid, a liquid that is in thermal equilibrium with its own vapour, which is of key relevance to the transport of cryogenic liquids, such as liquified natural gas and liquid hydrogen in the near future. More specifically, we use the Atmosphere facility at MARIN, NL, to prepare water/water vapour systems at different temperatures along the vapour curve. Here, we perform wave impact experiments by generating a soliton in a flume contained within the autoclave of the facility. A bathymetry profile interacts with the soliton, leading to a breaking wave that impacts onto a vertical wall, where we measure the pressures occurring during impact by means of $100$ embedded pressure sensors. In boiling liquids, we report wave impact pressures that are up to two orders of magnitude larger than those measured in comparable water–air experiments. We trace these pressures back to the collapse of the entrapped vapour pocket, which we semi-quantitatively describe using a simplified hemicylindrical vapour bubble model, which is in good agreement with the experimental findings. Finally, this allows us to predict the relevance of our findings for the transport of cryogenic liquids in huge overseas carriers where wave impact due to sloshing is the dominant cause of hydrodynamic load of containment systems in cargo tanks.

We study the dynamics of a thin liquid sheet that flows upwards along the sides of a vertically aligned, impacting plate. Upon impact of the vertical solid plate onto a liquid pool, the liquid film is ejected and subsequently continues to flow over the solid surface while the plate enters the water. With increasing impact velocity, the liquid film is observed to rise up faster and higher. We focus on the time evolution of the liquid film height and the thickness of its upper rim and discuss their dynamics in detail. Similar to findings in previous literature on sheet fragmentation during drop impact, we find the rim thickness to be governed by the local instantaneous capillary number based on gravity and the deceleration of the liquid sheet, showing that the retraction of the rim is primarily due to capillarity. In contrast, for the liquid film height, we demonstrate that the viscous dissipation in the thin boundary layer is the dominant factor for the vertical deceleration of the liquid sheet, by modelling the time evolution of the film height and showing that the influences of capillarity, gravity and deceleration due to the air phase are all negligible compared with the viscous term. Finally, we introduce characteristic viscous time and length scales based on the initial rim thickness and show that the maximum height of the film and the corresponding time can be determined from these viscous scales.

Observers were randomized to time and location across two different Neonatal Intensive Care Units (NICUs) to count hand hygiene opportunities (HHOs). Mean hourly HHO was lower at night and during use of precautions, and higher in shared rooms. HHO benchmarks can support implementation of group electronic monitoring systems in NICUs.

Identifying the absence of situation awareness (SA) in air traffic controllers is critical since it directly affects their hazard perception. This study aims to introduce and validate a multimodal methodology employing electroencephalogram (EEG) and eye-tracking to investigate SA variation within specific air traffic control contexts. Data from 28 participants executing the experiment involving three different SA-probe tests illustrated the conceptual relationship between EEG and eye-tracking indicators and SA variations, using behavioural data as a proxy. The results indicated that both EEG and eye-tracking metrics correlated positively with the SA levels required, that is, the frequency spectrum in the β (13–30 Hz) and γ (30–50 Hz) bands, alongside the fixation/saccade-based indicators and pupil dilation increased in response to higher SA levels. This research has substantial implications for investigating SA using a human-centric approach via psychophysiological indicators, revealing the intrinsic interactions between the human capability envelope and SA, contributing to the development of a real-time monitoring system of SA variations for air transportation safety research.

Rhopalosiphum padi is an important grain pest, causing severe losses during crop production. As a systemic insecticide, flonicamid can control piercing-sucking pests efficiently. In our study, the lethal effects of flonicamid on the biological traits of R. padi were investigated via a life table approach. Flonicamid is highly efficiently toxic to R. padi, with an LC50 of 9.068 mg L−1. The adult longevity and fecundity of the R. padi F0 generation were markedly reduced under the LC25 and LC50 concentrations of flonicamid exposure. In addition, negative transgenerational effects on R. padi were observed under exposure to lethal concentrations of flonicamid, with noticeable decreases in the reproductive period, adult longevity, total longevity, and total fecundity of the F1 generation under the LC25 concentration of flonicamid. Furthermore, the third nymph stage (N3), preadult stage, duration of the adult pre-reproductive period, duration of the total pre-reproductive period, reproductive period, adult longevity, total longevity, and total fecundity of the F1 generation were significantly lower under treatment with the LC50 concentration of flonicamid. The life table parameters were subsequently analysed, revealing that the intrinsic rate of increase (rm) and the net reproductive rate (R0) were significantly lower but that the finite rate of increase (λ) and the mean generation time (T) were not significantly different under the LC25 and LC50 concentrations of flonicamid. These data are beneficial for grain aphid control and are critical for exploring the role of flonicamid in the integrated management of this key pest.

A compact microstrip eight-channel diplexer based on quad-mode stepped impedance resonator (QMSIR) is proposed in this paper. The proposed diplexer is composed by two second-order quad-band bandpass filters (BPFs) and common-port distributed coupling matching circuit. Each quad-band BPF is formed by two coupled-QMSIRs controlling the passband characteristics. By introducing multiple coupling paths between input and output ports, the isolation between the eight channels is performed. For demonstration, an eight-channel diplexer based on QMSIR is designed and fabricated with microstrip technology. The use of the QMSIR can lead to significant size reduction for the multiplexer, this is because the required resonator number is reduced. As a result, the diplexer occupies a compact size of 0.083λ2, which is smaller than most of the eight-channel diplexers that have been proposed. And the 3 dB fractional bandwidth is 97% (2.5–7.2 GHz). Measurement results correlate well with the simulated predictions, showing that a good isolation of better than 20 dB and upper stopband of better than 10 dB.

The bevelled nozzle is a promising noise control approach and has been tested to suppress the noise levels in supersonic circular jets, but not in rectangular jets so far. In this study, implicit large-eddy simulations are performed to analyse the noise control of supersonic rectangular jets with single- and double-bevelled nozzles. Three nozzle pressure ratios ($NPR = 2.3$, 3.0 and 5.0) are considered to form two over-expanded cold jets and one under-expanded cold jet, exhausted from a baseline convergent–divergent rectangular nozzle with an aspect ratio of 2.0. Results show that, with the increase of $NPR$, the oscillation of the jet plume is switched from a symmetrical mode to a flapping mode (preferential in the minor-axis plane), then to a helical mode, together with a reduction of the screech frequency. The amplitude of the screech tone is the strongest in the flapping jet, and the turbulent mixing noise is the most prominent in the helically oscillating jet. The single-bevelled nozzle induces asymmetric shock-cell structures and deflects the jet plumes, and the double-bevelled nozzle primarily enables the enhancement of the shear-layer mixing and shortens the lengths of the jet potential cores. With the bevelled nozzles, the gross thrusts of the baseline nozzle are increased by $0.05 \sim 7.38$ %. Details on the characteristics of far-field noise in the jets with/without the bevel cuts and their noise control mechanisms are discussed using the Ffowcs Williams–Hawkings acoustic analogy, dynamic mode decomposition and spatio-temporal Fourier transformation. Results suggest that the noise control has a close relationship with the destruction of well-organized coherent structures and the suppression of upstream-propagating guided-jet modes, which interrupt the feedback mechanism accounting for the generation of screech tones in the supersonic rectangular jets.

In this paper, we study the rapid transition in Richtmyer–Meshkov instability (RMI) with reshock through three-dimensional double-layer swirling vortex rings. The rapid transition in RMI with reshock has an essential influence on the evolution of supernovas and the ignition of inertial confinement fusion, which has been confirmed in numerical simulations and experiments in shock-tube and high-energy-density facilities over the past few years. Vortex evolution has been confirmed to dominate the late-time nonlinear development of the perturbed interface. However, few studies have investigated the three-dimensional characteristics and nonlinear interactions among vortex structures during the transition to turbulent flows. The coexistence of co-rotating and counter-rotating vortices is hypothesized to induce successive large-scale strain fields, which are the main driving sources for rapid development. The three-dimensional effect is reflected in the presence of local swirling motion in the azimuthal direction, and it decreases the translation velocity of a vortex ring. Large-, middle- and small-scale strain fields are employed to describe the development process of RMI with reshock, e.g. vorticity deposited by the reshock, formation of the coexistence of the co-rotating and counter-rotating vortices, iterative cascade under the amplification of the strain fields and viscous dissipation to internal energy. This provides theoretical suggestions for designing practical applications, such as the estimation of the hydrodynamic instability and mixing during the late-time acceleration phase of the inertial confinement fusion.

Traditional bulky and complex control devices such as remote control and ground station cannot meet the requirement of fast and flexible control of unmanned aerial vehicles (UAVs) in complex environments. Therefore, a data glove based on multi-sensor fusion is designed in this paper. In order to achieve the goal of gesture control of UAVs, the method can accurately recognize various gestures and convert them into corresponding UAV control commands. First, the wireless data glove fuses flexible fiber optic sensors and inertial sensors to construct a gesture dataset. Then, the trained neural network model is deployed to the STM32 microcontroller-based data glove for real-time gesture recognition, in which the convolutional neural network-Attention mechanism (CNN-Attention) network is used for static gesture recognition, and the convolutional neural network-bidirectional long and short-term memory (CNN-Bi-LSTM) network is used for dynamic gesture recognition. Finally, the gestures are converted into control commands and sent to the vehicle terminal to control the UAV. Through the UAV simulation test on the simulation platform, the average recognition accuracy of 32 static gestures reaches 99.7%, and the average recognition accuracy of 13 dynamic gestures reaches 99.9%, which indicates that the system’s gesture recognition effect is perfect. The task test in the scene constructed in the real environment shows that the UAV can respond to the gestures quickly, and the method proposed in this paper can realize the real-time stable control of the UAV on the terminal side.

A multifunctional optical diagnostic system, which includes an interferometer, a refractometer and a multi-frame shadowgraph, has been developed at the Shenguang-II upgrade laser facility to characterize underdense plasmas in experiments of the double-cone ignition scheme of inertial confinement fusion. The system employs a 266 nm laser as the probe to minimize the refraction effect and allows for flexible switching among three modes of the interferometer, refractometer and multi-frame shadowgraph. The multifunctional module comprises a pair of beam splitters that attenuate the laser, shield stray light and configure the multi-frame and interferometric modules. By adjusting the distance and angle between the beam splitters, the system can be easily adjusted and switched between the modes. Diagnostic results demonstrate that the interferometer can reconstruct electron density below 1019 cm–3, while the refractometer can diagnose density approximately up to 1020 cm–3. The multi-frame shadowgraph is used to qualitatively characterize the temporal evolution of plasmas in the cases in which the interferometer and refractometer become ineffective.

Fiber Bragg grating-based Raman oscillators are capable of achieving targeted frequency conversion and brightness enhancement through the provision of gain via stimulated Raman scattering across a broad gain spectrum. This capability renders them an exemplary solution for the acquisition of high-brightness, specialized-wavelength lasers. Nonetheless, the output power of all-fiber Raman oscillators is typically limited to several hundred watts, primarily due to limitations in injectable pump power and the influence of higher-order Raman effects, which is inadequate for certain application demands. In this study, we introduce an innovative approach by employing a graded-index fiber with a core diameter of up to 150 μm as the Raman gain medium. This strategy not only enhances the injectable pump power but also mitigates higher-order Raman effects. Consequently, we have successfully attained an output power of 1780 W for the all-fiber Raman laser at 1130 nm, representing the highest output power in Raman fiber oscillators with any configuration reported to date.

Robot pick-and-place for unknown objects is still a very challenging research topic. This paper proposes a multi-modal learning method for robot one-shot imitation of pick-and-place tasks. This method aims to enhance the generality of industrial robots while reducing the amount of data and training costs the one-shot imitation method relies on. The method first categorizes human demonstration videos into different tasks, and these tasks are classified into six types to symbolize as many types of pick-and-place tasks as possible. Second, the method generates multi-modal prompts and finally predicts the action of the robot and completes the symbolic pick-and-place task in industrial production. A carefully curated dataset is created to complement the method. The dataset consists of human demonstration videos and instance images focused on real-world scenes and industrial tasks, which fosters adaptable and efficient learning. Experimental results demonstrate favorable success rates and loss results both in simulation environments and real-world experiments, confirming its effectiveness and practicality.

In this article, we study the following Schrödinger equation

\begin{align*}\begin{cases}-\Delta u -\frac{\mu}{|x|^2} u+\lambda u =f(u), &\text{in}~ \mathbb{R}^N\backslash\{0\},\\\int_{\mathbb{R}^{N}}|u|^{2}\mathrm{d} x=a, & u\in H^1(\mathbb{R}^{N}),\end{cases}\end{align*}

where $N\geq 3$, a > 0, and $\mu \lt \frac{(N-2)^2}{4}$. Here $\frac{1}{|x|^2} $ represents the Hardy potential (or ‘inverse-square potential’), λ is a Lagrange multiplier, and the nonlinearity function f satisfies the general Sobolev critical growth condition. Our main goal is to demonstrate the existence of normalized ground state solutions for this equation when $0 \lt \mu \lt \frac{(N-2)^2}{4}$. We also analyse the behaviour of solutions as $\mu\to0^+$ and derive the existence of normalized ground state solutions for the limiting case where µ = 0. Finally, we investigate the existence of normalized solutions when µ < 0 and analyse the asymptotic behaviour of solutions as $\mu\to 0^-$.

This study investigates the correlation between the fluctuating wall heat flux, and the distribution and transport of Reynolds shear stress and turbulent heat flux in compressible boundary layers at Mach number 5.86 and friction Reynolds number 420, with a relatively weaker and a stronger wall cooling imposed. As illustrated from the probability density functions of the wall-heat-flux perturbations, with increasing wall cooling, the extreme wall heat flux is intensified and tends to be more negatively skewed. To examine the role of the extreme events in the transport of the momentum and heat, conditional analysis of the extreme positive and negative wall-heat-flux-perturbation events is conducted. In most regions of the boundary layer, the positive events are predominantly associated with an increase in Reynolds shear stress and a decrease in turbulent heat flux. Joint probability density functions of velocity and wall-heat-flux perturbations in the near-wall region indicate that the extreme positive events tend to be more correlated with ejections, which is particularly evident in the stronger wall-cooling case. To further shed light on the underlying mechanisms of the connections between wall heat flux and transport budgets, a transport equation for turbulent heat flux is derived, in a similar manner to that for Reynolds shear stress. The energy balance is inspected, with conditional analysis applied to budget terms and mean flow properties so as to quantify the correlation between wall-heat-flux fluctuations and energy evolution.

The associations between obesity and liver diseases are complex and diverse. To explore the causal relationships between obesity and liver diseases, we applied two-sample Mendelian randomisation (MR) and multivariable MR analysis. The data of exposures (BMI and WHRadjBMI) and outcomes (liver diseases and liver function biomarker) were obtained from the open genome-wide association study database. A two-sample MR study revealed that the genetically predicted BMI and WHRadjBMI were associated with non-alcoholic fatty liver disease, liver fibrosis and autoimmune hepatitis. Obesity was not associated with primary biliary cholangitis, liver failure, liver cell carcinoma, viral hepatitis and secondary malignant neoplasm of liver. A higher WHRadjBMI was associated with higher levels of biomarkers of lipid accumulation and metabolic disorders. These findings indicated independent causal roles of obesity in non-alcoholic fatty liver disease, liver fibrosis and impaired liver metabolic function rather than in viral or autoimmune liver disease.