This paper presents a novel robust control method for a hip-assist exoskeleton robot’s joint module, addressing dynamic performance under variable loads. The proposed approach integrates traditional PID control with robust, model-based strategies, utilizing the system’s dynamic model and a Lyapunov-based robust controller to handle uncertainties. This method not only enhances traditional PID control but also offers practical advantages in implementation. Theoretical analysis confirms the system’s uniform boundedness and ultimate boundedness. A Matlab prototype was developed for simulation, demonstrating the control scheme’s feasibility and effectiveness. Numerical simulations show that the proposed fractional-order hybrid PD (FHPD) controller significantly reduces tracking error by 58.70% compared to the traditional PID controller, 55.41% compared to the MPD controller, and 32.32% compared to ADRC, highlighting its superior tracking performance and stability.

The emergence, on the Loess Plateau of Central China, of settlements enclosed by circular ditches has engendered lively debate about the function of these (often extensive) ditch systems. Here, the authors report on a suite of new dates and sedimentological analyses from the late Yangshao (5300–4800 BP) triple-ditch system at the Shuanghuaishu site, Henan Province. Exploitation of natural topographic variations, and evidence for ditch maintenance and varied water flows, suggests a key function in hydrological management, while temporal overlap in the use of these three ditches reveals the large scale of this endeavour to adapt to the pressures of the natural environment.

This study utilises large-eddy simulation with the actuator line model to examine the effects of the tip speed ratio (TSR) on the wake-meandering characteristics of a wind turbine in uniform and turbulent inflows. It is shown that as the TSR grows, the onset position of the wake meandering moves closer to the rotor, and the magnitude of wake oscillation is stronger. This aligns with previous work showing that a higher TSR can accelerate the instability and breakdown of tip vortices. Without a nacelle, the Strouhal number of the wake meandering is found to be independent of the TSR under both the uniform and turbulent inflows. However, with a relatively large nacelle, the Strouhal number first increases and then decreases with TSR. Therefore, the current discovery elucidates the crucial role of the nacelle and clarifies the origin of the TSR dependence of the Strouhal number in wake meandering. In addition, the characteristic frequency of the wake meandering under the turbulent inflow is much smaller than that under the uniform inflow, because of the significant influence of the freestream turbulence. Furthermore, the proper orthogonal decomposition (POD) and spectral POD (SPOD) methods are employed to study the spatiotemporal characteristics of the meandering wake and its TSR dependence. It is found that the tip and root vortices are the prominent wake structures under the uniform inflow, whereas more complex multiscale structures from the interaction between the freestream turbulence and tip/root vortices exist under the turbulent inflow. Moreover, an amplitude modulation phenomenon of the POD time coefficients at the optimal TSR is observed in the uniform inflow case. Finally, a reduced-order model is constructed for predicting the wake dynamics by combining the SPOD and the ‘sparse identification of nonlinear dynamics’ algorithm with high accuracy and interpretability.

Trailing-edge serrations inspired by owls are capable of reducing broadband noise. In this study, the wall-resolved large-eddy simulations (LES) are carried out on the flow over NACA-0012 airfoil with additional serrated trailing edges. The computations are conducted with the high-order flux reconstruction method on unstructured meshes. Three kinds of serrations with different lengths are studied and compared with the straight trailing-edge case, and all three types of serration achieved a certain degree of noise reduction. Presently, the medium-length serration achieves the best noise reduction effect. The maximum decrease of overall sound pressure level is approximately 2.4 dB, implying that the length of serration has a substantial impact on the noise reduction effect. The serration has no significant effect on the upstream turbulence statistics, but it changes the flow structure near the serration, such as inducing side vortex pairs attached to the serration edges. Moreover, dynamic mode decomposition shows that the pressure structures vary with the serration length. For the most unstable hydrodynamic wave, the spanwise coherence of the mode structure of pressure in the upstream boundary layer is weakened. In addition, serrations can redistribute the dipole sources on the surfaces of airfoil and serrations. The destructive interference is enhanced to some extent, which is favourable for noise reduction. In contrast with LES simulations, the pure dipole analysis shows that the longest serration case seems to be the best. Furthermore, a recently developed noise theory is used to evaluate the influence of serrations on the flow noise sources qualitatively and quantitatively. It is found that the serrations can mitigate noise source intensity near the serration edges but increase the source intensity in the near wake. The combined effect of serration on the dipole source and flow noise source determines the overall noise reduction effect. To conclude, destructive interference plays a primary role in suppressing noise radiation by serrated trailing edges, and the dual effect of flow noise sources should be considered in future serration designs. As the influence of turbulence structure will make it more difficult to find the optimal serration parameters, the position of high-fidelity simulation will become increasingly important.

We present an experimental study on controlling the number of vortices and the torque in a Taylor–Couette flow of water for Reynolds numbers from 660 to 1320. Different flow states are achieved in the annulus of width $d$ between the inner rotating and outer stationary cylinders through manipulating the initial height of the water annulus. We show that the torque exerted on the inner cylinder of the Taylor–Couette system can be reduced by up to 20 % by controlling the flow at a state where fewer than the nominal number of vortices develop between the cylinders. This flow state is achieved by starting the system with an initial water annulus height $h_0$ (which nominally corresponds to $h_0/d$ vortices), then gradually adding water into the annulus while the inner cylinder keeps rotating. During this filling process the flow topology is so persistent that the number of vortices does not increase; instead, the vortices are greatly stretched in the axial (vertical) direction. We show that this state with stretched vortices is sustainable until the vortices are stretched to around 2.05 times their nominal size. Our experiments reveal that by manipulating the initial height of the liquid annulus we are able to generate different flow states and demonstrate how the different flow states manifest themselves in global momentum transport.

U.S. multinational enterprises repatriated over $300 billion under the 2004 tax holiday. The repatriated funds can improve debt financing environment of nonrepatriating firms, especially those that are financially constrained. We document that such an externality of the tax holiday increases debt financing and consequently investments for financially constrained nonrepatriating firms relative to less constrained nonrepatriating firms. Using private loan market data, we further confirm a link from repatriated funds to increased debt financing for financially constrained nonrepatriating firms. Overall, the 2004 tax holiday appears to have benefited the U.S. economy through its positive externality on the debt market.

Isolated gametes can be used to investigate fertilization mechanisms, and probe distant hybridization between different species. Pollen grains of wheat and Setaria viridis are tricellular, containing sperm cells at anthesis. Sperm from these plants were isolated by breaking open pollen grains in a osmotic solution. Wheat ovules were digested in an enzyme solution for 20 min, and then transferred to an isolation solution without enzymes to separate egg cells from ovules. The fusion of wheat egg cells with wheat and S. viridis sperm was conducted using an electro-fusion apparatus. Under suitable osmotic pressure (10% mannitol), calcium concentration of 0.001% (CaCl2·2H2O), and a 30–35 V alternating electric field for 15 s, egg cells and sperm adhered to each other and became arranged in a line. Electroporation of the plasma membrane of egg cells and sperm using a 300–500 V direct-current electric field (45 µs amplitude pulse) caused them to fuse.

Direct numerical simulation is conducted to uncover the response of a supersonic turbulent boundary layer to streamwise concave curvature and the related physical mechanisms at a Mach number of 2.95. Streamwise variations of mean flow properties, turbulence statistics and turbulent structures are analysed. A method to define the boundary layer thickness based on the principal strain rate is proposed, which is applicable for boundary layers subjected to wall-normal pressure and velocity gradients. While the wall friction grows with the wall turning, the friction velocity decreases. A logarithmic region with constant slope exists in the concave boundary layer. However, with smaller slope, it is located lower than that of the flat boundary layer. Streamwise varying trends of the velocity and the principal strain rate within different wall-normal regions are different. The turbulence level is promoted by the concave curvature. Due to the increased turbulence generation in the outer layer, secondary bumps are noted in the profiles of streamwise and spanwise turbulence intensity. Peak positions in profiles of wall-normal turbulence intensity and Reynolds shear stress are pushed outward because of the same reason. Attributed to the Görtler instability, the streamwise extended vortices within the hairpin packets are intensified and more vortices are generated. Through accumulations of these vortices with a similar sense of rotation, large-scale streamwise roll cells are formed. Originated from the very large-scale motions and by promoting the ejection, sweep and spanwise events, the formation of large-scale streamwise roll cells is the physical cause of the alterations of the mean properties and turbulence statistics. The roll cells further give rise to the vortex generation. The large number of hairpin vortices formed in the near-wall region lead to the improved wall-normal correlation of turbulence in the concave boundary layer.

The trajectory tracking of Autonomous Underwater Vehicles (AUV) is an important research topic. However, in the traditional research into AUV trajectory tracking control, the AUV often follows human-set trajectories without obstacles, and trajectory planning and tracking are separated. Focusing on this separation, a trajectory re-planning controller based on Model Predictive Control (MPC) is designed and added into the trajectory tracking controller to form a new control system. Firstly, an obstacle avoidance function is set up for the design of an MPC trajectory re-planning controller, so that the re-planned trajectory produced by the re-planning controller can avoid obstacles. Then, the tracking controller in the MPC receives the re-planned trajectory and obtains the optimal tracking control law after calculating the object function with a Sequential Quadratic Programming (SQP) optimisation algorithm. Lastly, in a backstepping algorithm, the speed jump can be sharp while the MPC tracking controller can solve the speed jump problem. Simulation results of different obstacles and trajectories demonstrate the efficiency of the proposed MPC trajectory re-planning tracking control algorithm for AUVs.

The nonlinear absorption (NLA) properties of potassium dideuterium phosphate crystals at 515 nm under different excitation laser intensities are investigated with the Z-scan technique. Two critical intensities are highlighted: the critical intensity for exciting the NLA and the critical intensity of the multiphoton absorption mechanism transition. Experimental results indicate the existence of defect states located in the band gap, which can be manipulated by varying laser intensity. A model based on the change of multiphoton absorption mechanism induced by the transformation of defect species is proposed to interpret the experiments. Modeling results are in good agreement with the experiment data.

In this study, we propose a high order well-balanced weighted compact nonlinear (WCN) scheme for the gas dynamic equations under gravitational fields. The proposed scheme is an extension of the high order WCN schemes developed in (S. Zhang, S. Jiang, C.-W Shu, J. Comput. Phys. 227 (2008) 7294-7321). For the purpose of maintaining the exact steady state solution, the well-balanced technique in (Y. Xing, C.-W Shu, J. Sci. Comput. 54 (2013) 645-662) is employed to split the source term into two terms. The proposed scheme can maintain the isothermal equilibrium solution exactly, genuine high order accuracy and resolve small perturbations of the hydrostatic balance state on the coarse meshes. Furthermore, in order to capture the strong discontinuities and large gradients, the fifth-order upwind weighted nonlinear interpolations together with the fourth/sixth order cell-centered compact schemes with local characteristic projections are used to construct different WCN schemes. Several representative one- and two-dimensional examples are simulated to demonstrate the good performance of the proposed schemes.

In this study, a numerical framework of the high order well-balanced weighted compact nonlinear (WCN) schemes is proposed for the shallow water equations based on the work in [S. Zhang, S. Jiang, C.-W Shu, J. Comput. Phys. 227 (2008) 7294-7321]. We employ a special splitting technique for the source term proposed in [Y. Xing, C.-W Shu, J. Comput. Phys. 208 (2005) 206-227] to maintain the exact C-property, which can be proved theoretically. In the meantime, the genuine high order accuracy of the numerical scheme can be observed successfully, and small perturbation of the stationary state can be resolved and evolved well. In order to capture the strong discontinuities and large gradients, the fifth-order upwind weighted nonlinear interpolations together with the fourth/sixth order cell-centered compact scheme are used to construct different WCN schemes. In addition, the local characteristic projections are considered to further restrain the potential numerical oscillations. A variety of representative one- and two-dimensional examples are tested to demonstrate the good performance of the proposed schemes.