Deformation occurs in a thin liquid film when it is subjected to a non-uniform electric field, which is referred to as the electrohydrodynamic patterning. Due to the development of a non-uniform electrical force along the surface, the film would evolve into microstructures/nanostructures. In this work, a linear and a nonlinear model are proposed to thoroughly investigate the steady state (i.e. equilibrium state) of the electrohydrodynamic deformation of thin liquid film. It is found that the deformation is closely dependent on the electric Bond number BoE. Interestingly, when BoE is larger than a critical value, the film would be deformed remarkably and get in contact with the top template. To model the ‘contact’ between the liquid film and the solid template, the disjoining pressure is incorporated into the numerical model. From the nonlinear numerical model, a hysteresis deformation is revealed, i.e. the film may have different equilibrium states depending on whether the voltage is increased or decreased. To analyse the stability of these multiple equilibrium states, the Lyapunov functional is employed to characterise the system’s free energy. According to the Lyapunov functional analysis, at most three equilibrium states can be formed. Among them, one is stable, another is metastable and the third one is unstable. Finally, the model is extended to study the three-dimensional deformation of the electrohydrodynamic patterning.

Turbulent mixing driven by the reshocked Richtmyer–Meshkov (RM) instability plays a critical role in numerous natural phenomena and engineering applications. As the most fundamental physical quantity characterizing the mixing process, the mixing width transitions from linear to power-law growth following the initial shock. However, there is a notable absence of quantitative models for predicting the pronounced compression of initial interface perturbations or mixing regions at the moment of shock impact. This gap has restricted the development of integrated algebraic models to only the pre- and post-shock evolution stages. To address this limitation, the present study develops a predictive model for the compression of the mixing width induced by shocks. Based on the general principle of growth rate decomposition proposed by Li et al. (Phy. Rev. E, vol. 103, issue 5, 2021, 053109), two distinct types of shock-induced compression processes are identified, differentiated by the dominant mechanism governing their evolution: light–heavy and heavy–light shock-induced compression. For light–heavy interactions, both stretching (compression) and penetration mechanisms are influential, whereas heavy–light interactions are governed predominantly by the stretching (compression) mechanism. To characterize these mechanisms, the average velocity difference between the extremities of the mixing zone is quantified, and a physical model of RM mixing is utilized. A quantitative theoretical model is subsequently formulated through the independent algebraic modelling of these two mechanisms. The proposed model demonstrates excellent agreement with numerical simulations of reshocked RM mixing, offering valuable insights for the development of integrated algebraic models for mixing width evolution.

This paper investigates the behaviour of turbulence production in adverse pressure gradient (APG) turbulent boundary layers (TBLs), including the range of pressure gradients from zero-pressure-gradient (ZPG) to separation, moderate and high Reynolds numbers, and equilibrium and non-equilibrium flows. The main focus is on predicting the values and positions of turbulence production peaks. Based on the unique ability of turbulence production to describe energy exchange, the idea that the ratios of the mean flow length scales to the turbulence length scales are locally smallest near peaks is proposed. Thereby, the ratios of length scales are defined for the inner and outer regions, respectively, as well as the ratios of time scales for further consideration of local information. The ratios in the inner region are found to reach the same constant value in different APG TBLs. Like turbulence production in the ZPG TBL, turbulence production in APG TBLs is shown to have a certain invariance of the inner peak. The value and position of the inner peak can also be predicted quantitatively. In contrast, the ratios in the outer region cannot be determined with unique coefficients, which accounts for the different self-similarity properties of the inner and outer regions. The outer time scale ratios establish a link between mean flow and turbulence, thus participating in the discussion on half-power laws. The present results support the existence of a half-power-law region that is not immediately adjacent to the overlapping region.

This study elucidated the impacts of coenzyme Q10 (COQ10) supplementation in a high-fat diet (HFD) on growth, lipid metabolism and mitochondrial function in spotted seabass (Lateolabrax maculatus). Totally five diets were formulated: a diet with normal fat content (11 % lipid, NFD), a HFD (17 % lipid) and three additional diets by supplementing 5, 20 or 80 mg/kg of COQ10 to the HFD. After an 8-week culture period, samples were collected and analysed. The results demonstrated that COQ10 inclusion prevented the HFD-induced deterioration of growth performance and feed utilisation. COQ10 alleviated the deposition of saturated fatty acids following HFD intake and promoted the assimilation of n-3 and n-6 PUFA. Moreover, COQ10 administration inhibited the surge in serum transaminase activity and reduced hepatic lipid content following HFD ingestion, which was consistent with the results of oil red O staining. In addition, HFD feeding led to reduced hepatic citrate synthase and succinate dehydrogenase activities and decreased ATP content. Notably, COQ10 administration improved these indices and up-regulated the expression of mitochondrial biogenesis-related genes (pgc-1α, pgc-1β, nrf-1, tfam) and autophagy-related genes (pink1, mul1, atg5). In summary, supplementing 20–80 mg/kg of COQ10 in the HFD promoted growth performance, alleviated hepatic fat accumulation and enhanced liver mitochondrial function in spotted seabass.

This paper introduces an equivalent series mechanism model to improve ankle rehabilitation robots’ ability to recurrence the complex movements of the anthropo-ankle and enhance human-machine locomotion compatibility. The model emulates the true anatomical architecture of the ankle joint and is integrated with a parallel rehabilitative mechanism. The rehabilitative robot includes dual virtual motion centers to mimic the ankle joint’s intricate motion, accommodate individual patient variations, and address the rehabilitation requirements of both right and left feet. Firstly, a serial equivalence model of anthropo-ankle is developed based on the kinematic and anatomical characteristics of the human ankle. The type design for the 4-degree of freedom (4-DOF) parallel ankle rehabilitative robot is then conducted on the basis of the kinematical and restrictive properties of the anthropo-ankle equivalence kinematic model. Secondly, the mechanism’s motion properties allow it to be equivalent to a series branch chain, enabling the establishment of an inverse kinematics model. The kinematical performance of the mechanisms is analyzed using the transmissibility and constrainability indices, followed by workspace analysis and dimensional optimization of the rehabilitative mechanism. Finally, a human-machine coupled rehabilitative simulation model is developed using OpenSim biomechanics software to evaluate the recovery effect.

This study explored the relationship between multifaceted multilingualism and cognitive shifting through a task-switching paradigm using fMRI. Multilingualism was modeled from both convergent (i.e., integrated multilingual index) and divergent (i.e., L2 proficiency, interpreting training, language entropy) perspectives. Participants identified letters or numbers based on task cues, with Repeat trials maintaining the same task and Switch trials requiring a different task. Switch cost (Switch–Repeat) was used to reflect shifting demands. Better task-switching performance was associated with a higher integrated multilingual index and interpreting training. Neuroimaging indicated that multilinguals predominantly engaged left-hemisphere regions for switching, with extensive multilingual experience requiring fewer neural resources for switch cost (i.e., more efficient processing for cognitive control). During task switching, brain connectivity was regulated locally by L2 proficiency, and globally by interpreting training. These findings underscore the importance of considering multifaceted multilingual experience to understand its impact on cognitive function and brain activity.

Unmanned aerial vehicle (UAV) formations for bearing-only passive detection are increasingly important in modern military confrontations, and the array of the formation is one of the decisive factors affecting the detection accuracy of the system. How to plan the optimal geometric array in bearing-only detection is a complex nondeterministic polynomial problem, and this paper proposed the distributed stochastic subgradient projection algorithm (DSSPA) with layered constraints to solve this challenge. Firstly, based on the constraints of safe flight altitude and fixed baseline, the UAV formation is layered, and the system model for bearing-only cooperative localisation is constructed and analysed. Then, the calculation formula for geometric dilution of precision (GDOP) in the observation plane is provided, this nonlinear objective function is appropriately simplified to obtain its quadratic form, ensuring that it can be adapted and used efficiently in the system model. Finally, the proposed distributed stochastic subgradient projection algorithm (DSSPA) combines the idea of stochastic gradient descent with the projection method. By performing a projection operation on each feasible solution, it ensures that the updated parameters can satisfy the constraints while efficiently solving the convex optimisation problem of array planning. In addition to theoretical proof, this paper also conducts three simulation experiments of different scales, validating the effectiveness and superiority of the proposed method for bearing-only detection array planning in UAV formations. This research provides essential guidance and technical reference for the deployment of UAV formations and path planning of detection platforms.

Asymptotic expansions of the maximum likelihood estimator (MLE) and weighted likelihood estimator (WLE) of an examinee’s ability are derived while item parameter estimators are treated as covariates measured with error. The asymptotic formulae present the amount of bias of the ability estimators due to the uncertainty of item parameter estimators. A numerical example is presented to illustrate how to apply the formulae to evaluate the impact of uncertainty about item parameters on ability estimation and the appropriateness of estimating ability using the regular MLE or WLE method.

Let $[a_1(x),a_2(x),\ldots ,a_n(x),\ldots ]$ be the continued fraction expansion of $x\in [0,1)$ and $q_n(x)$ be the denominator of its nth convergent. The irrationality exponent and Khintchine exponent of x are respectively defined by

$$ \begin{align*} \overline{v}(x)=2+\limsup_{n\to\infty}\frac{\log a_{n+1}(x)}{\log q_n(x)} \quad \text{and}\quad \gamma(x)=\lim_{n\to\infty}\frac{1}{n}\sum_{i=1}^{n}\log a_i(x). \end{align*} $$

We study the multifractal spectrum of the irrationality exponent and the Khintchine exponent for continued fractions with nondecreasing partial quotients. For any $v>2$, we completely determine the Hausdorff dimensions of the sets $\{x\in [0,1): a_1(x)\leq a_2(x)\leq \cdots , \overline {v}(x)=v\}$ and

$$ \begin{align*}\bigg\{x\in[0,1): a_1(x)\leq a_2(x)\leq\cdots, \lim\limits_{n\to\infty}\frac{\log a_1(x)+\log a_2(x)+\cdots+\log a_n(x)}{\psi(n)}=1\bigg\},\end{align*} $$

where $\psi :\mathbb {N}\rightarrow \mathbb {R}^+$ is a function satisfying $\psi (n)\to \infty $ as $n\to \infty $.

The material removal rate (MRR) serves as a crucial indicator in the chemical mechanical polishing (CMP) process of semiconductor wafers. Currently, the mainstream method to ascertain the MRR through offline measurements proves time inefficient and struggles to represent process variability accurately. An efficient MRR prediction model based on stacking ensemble learning that integrates models with disparate architectures was proposed in this study. First, the processing signals collected during wafer polishing, as available in the PHM2016 dataset, were analyzed and preprocessed to extract statistical and neighbor domain features. Subsequently, Pearson correlation coefficient analysis (PCCA) and principal component analysis (PCA) were employed to fuse the extracted features. Ultimately, random forest (RF), light gradient boosting machine (LightGBM), and backpropagation neural network (BPNN) with hyperparameters optimized by the Bayesian Optimization Algorithm were integrated to establish an MRR prediction model based on stacking ensemble learning. The developed model was verified on the PHM2016 benchmark test set, and a Mean Square Error (MSE) of 7.72 and a coefficient of determination (R2) of 95.82% were achieved. This indicates that the stacking ensemble learning based model, integrated with base models of disparate architectures, offers considerable potential for real-time MRR prediction in the CMP process of semiconductor wafers.

The tension distribution problem of cable-driven parallel robots is inevitable in real-time control. Currently, iterative algorithms or geometric algorithms are commonly used to solve this problem. Iterative algorithms are difficult to improve in real-time performance, and the tension obtained by geometric algorithms may not be continuous. In this paper, a novel tension distribution method for four-cable, 3-DOF cable-driven parallel robots is proposed based on the wave equation. The tension calculated by this method is continuous and differentiable, without the need for iterative computation or geometric centroid calculations, thus exhibiting good real-time performance. Furthermore, the feasibility and rationality of this algorithm are theoretically proven. Finally, the real-time performance and continuity of cable tension are analyzed through a specific numerical example.

High-elevation environments present harsh challenges for the pursuit of agropastoral subsistence strategies and relatively little is known about the mechanisms early communities employed to adapt to such locations successfully. This article presents the sequential carbon and oxygen analysis of archaeological caprine teeth from Bangga (c. 3000–2200 BP), which is approximately 3750masl on the Tibetan Plateau. Made visible through this method, intra-tooth variation in isotopic composition allows insights into herding strategies that possibly included the provisioning of livestock with groundwater and agricultural fodder and summer grazing in saline or marsh environments. Such intensive provisioning differs markedly from lower-elevation agropastoralism.

Autonomous exploration in unknown environments has become a critical capability of mobile robots. Many methods often suffer from problems such as exploration goal selection based solely on information gain and inefficient tour optimization. Recent reinforcement learning-based methods do not consider full area coverage and the performance of transferring learned policy to new environments cannot be guaranteed. To address these issues, a dual-stage exploration method has been proposed, which combines spatial clustering of possible exploration goals and Traveling Salesman Problem (TSP) based tour planning on both local and global scales, aiming for efficient full-area exploration in highly convoluted environments. Our method involves two stages: exploration and relocation. During the exploration stage, we introduce to generate local navigation goal candidates straight from clusters of all possible local exploration goals. The local navigation goal is determined through tour planning, utilizing the TSP framework. Moreover, during the relocation stage, we suggest clustering all possible global exploration goals and applying TSP-based tour planning to efficiently direct the robot toward previously detected but yet-to-be-explored areas. The proposed method is validated in various challenging simulated and real-world environments. Experimental results demonstrate its effectiveness and efficiency. Videos and code are available at https://github.com/JiatongBao/exploration.

This study investigates the impact of molecular thermal fluctuations on compressible decaying isotropic turbulence using the unified stochastic particle (USP) method, encompassing both two-dimensional (2-D) and three-dimensional (3-D) scenarios. The findings reveal that the turbulent spectra of velocity and thermodynamic variables follow the wavenumber (k) scaling law of ${k}^{(d-1)}$ for different spatial dimensions $d$ within the high wavenumber range, indicating the impact of thermal fluctuations on small-scale turbulent statistics. With the application of Helmholtz decomposition, it is found that the thermal fluctuation spectra of solenoidal and compressible velocity components (${\boldsymbol {u}}_{s}$ and ${\boldsymbol {u}}_{c}$) follow an energy ratio of 1 : 1 for 2-D cases, while the ratio changes to 2 : 1 for 3-D cases. Comparisons between 3-D turbulent spectra obtained through USP simulations and direct numerical simulations of the Navier–Stokes equations demonstrate that thermal fluctuations dominate the spectra at length scales comparable to the Kolmogorov length scale. Additionally, the effect of thermal fluctuations on the spectrum of ${\boldsymbol {u}}_{c}$ is significantly influenced by variations in the turbulent Mach number. We further study the impact of thermal fluctuations on the predictability of turbulence. With initial differences caused by thermal fluctuations, different flow realizations display significant disparities in velocity and thermodynamic fields at larger scales after a certain period of time, which can be characterized by ‘inverse error cascades’. Moreover, the results suggest a strong correlation between the predictabilities of thermodynamic fields and the predictability of ${\boldsymbol {u}}_{c}$.

Various psychosocial and psychological interventions have been developed to reduce schizophrenia relapse prevention. A better understanding of these active interventions is important for clinical practice and for meaningful allocation of resources. However, no bibliometric analysis of this area has been conducted. Studies were retrieved from the Web of Science Core Collection database. The publication outputs and cooperation of institutions were visualized with Origin 2021. Global cooperation was visualized using ArcGIS Pro3.0. VOSviewer was used to generate visualizations of network of authors and keywords. The number of annual publications generally showed a fluctuating upward trend over the past 20 years. Germany published the most relevant articles (361, 26.76%). The Technical University of Munich was the most productive institution (70, 9.86%). Leucht Stefan published the most articles (46, 6.48%) and had the highest number of citations (4,375 citations). Schizophrenia Research published the most studies (39, 5.49%). Keywords were roughly classified into three clusters: cognitive behavioral therapy (CBT), family interventions and family psychoeducation and other factors related to interventions. The findings provided the current status of research on psychosocial and psychological interventions for schizophrenia relapse prevention from a bibliometric perspective. Recent research has mainly focused on CBT, family interventions and family psychoeducation.