Gravity compensation, widely employed in mechanisms such as manipulators and exoskeletons, serves to minimize unnecessary energy consumption. Enhancing the performance of gravity compensation mechanisms (GCMs) is therefore of significant practical importance. One promising approach is the development of novel design methodologies. Existing GCMs utilizing cable-pulley units exhibit limitations in terms of structural compactness and efficiency. To address these issues, this paper proposes an innovative X-type gravity compensation unit featuring an adjustable cable sequencing arrangement. The application of this unit to a passive waist exoskeleton (PWE) is further introduced. Given the potential influence of pulley size and positioning on the actual spring elongation, a pulley-angle error model is established to analyze the effect of varying pulley positions. Simulations confirm the validity of the model and demonstrate that pulley size is a non-negligible factor in system performance. Finally, an experimental platform is constructed to evaluate the performance of the PWE. Experimental results indicate a notable improvement in exoskeleton performance attributable to the unique design of the X-type unit.

Intercropping cereals and legumes may enhance system productivity by simultaneously producing grain for human consumption and crop residues for livestock feed. This study evaluated the effects of maize (Zea mays) intercropped with cowpea (Vigna unguiculata) or mucuna (Mucuna pruriens) on soil moisture dynamics, grain and forage yields, and household food and feed self-sufficiency under varying rainfall conditions. The experiment was conducted on five farms in Mutoko District, Zimbabwe, during the 2021/22 and 2022/23 growing seasons using a Randomized Complete Block Design with five treatments: sole maize, sole cowpea, sole mucuna, maize–cowpea intercropping, and maize–mucuna intercropping. Soil moisture was measured biweekly to 1.8 m depth. Each season, experimental sites were classified according to seasonal rainfall as dry (<450 mm), average (450–600 mm), or wet seasons (>600 mm).Intercropping performance was influenced by rainfall. Sole mucuna utilized more soil moisture than other cropping systems. In dry and average seasons, sole maize yielded 1,812 kg ha−1 of grain, 103% more than maize intercrops, and met annual household maize requirements. In wet seasons, maize–cowpea intercropping produced higher maize grain yields (3,273 kg ha−1) than sole maize (2,372 kg ha−1), with a land equivalent ratio of 2.18. Mid-season dry spells reduced grain yields across treatments but had limited effects on stover production. During wet seasons, mucuna-based systems generated the highest forage and crude protein yields, sufficient to feed five cattle during the dry season. These findings highlight that maize–legume intercropping can enhance food and feed production during relatively wet seasons

Individual patient data meta-analyses (IPDMAs) provide powerful tools for synthesizing evidence across studies, yet methods for addressing unmeasured confounding in observational IPDMAs with survival outcomes are rarely implemented. Instrumental variable (IV) approaches offer causal inference capabilities but face practical challenges in hierarchical data structures, particularly the lack of standard diagnostics for instrument strength in nonlinear mixed-effects models. We adapt and evaluate a frequentist mixed-effects two-stage residual inclusion (2SRI) framework for survival IPDMAs, extending traditional IV methods to accommodate study-level and temporal clustering while handling time-to-event outcomes through Cox proportional hazards models. Because classical F-statistics are unavailable for logistic mixed-effects first-stage models, we propose the Wald $\chi ^2$ statistic as a practical instrument-strength diagnostic and empirically characterize its relationship to estimator performance. Through a comprehensive simulation study with 48 scenarios—varying unmeasured confounding (weak to very strong), instrument–treatment association strength (0.3–1.0), and cross-study IV allocation patterns—we evaluated 2SRI against naive mixed-effects Cox models using bias, coverage, variance, and mean squared error. The design was anchored to realistic IPDMA structure (10 studies, $N \approx 4,357$) from pooled Ebola data, with 1,000 replications per scenario. Results show that under weak confounding, naive models dominate on all metrics. With moderate-to-strong confounding and realized Wald $\chi ^2$ exceeding 150–200, mixed-effects 2SRI substantially reduces bias and achieves near-nominal coverage, though with inflated variance. We provide empirical guideposts linking realized first-stage strength to expected performance, enabling analysts to judge when 2SRI will outperform conventional approaches in hierarchical survival IPDMAs. All simulations assume a common treatment effect across studies. Performance under heterogeneous effects remains to be established.

Droplet impingement is one of the most common phenomena in nature. However, the impact dynamics of droplets on structured heterogeneous wettability surfaces remain little explored. In this work, an investigation is conducted into the droplet impact on heterogeneous wettability surfaces composed of superhydrophobic micropillars on a hydrophilic substrate, by using an improved phase-field lattice Boltzmann model. In particular, the effects of surface geometry and impact conditions on droplet bouncing and wetting behaviours are scrutinised. Four distinct impact outcomes are identified: complete bouncing, pancake bouncing, partial wetting and complete wetting. Based on the competition among capillary, inertial and viscous forces, an analytical model is proposed to predict the maximum droplet penetration depth within the pillar gaps. A transition diagram is constructed to distinguish these different impact outcomes, with regime boundaries derived from the proposed analytical model. Finally, from the perspective of energy analysis, both the evolution of the energy budget and the surface energy distribution during the droplet impact process are revealed. These findings provide guidance for the design of heterogeneous wettability surfaces, enabling predictable control over droplet bouncing and wetting behaviours.

This study investigates the unsteady oscillation cycle of sheet and tip vortex cavitation over an elliptical NACA $66_2$-415 hydrofoil using high-speed imaging and time-resolved tomographic particle image velocimetry. Synchronised measurements of radiated noise are conducted. The oscillation cycle consists of three phases, involving growth and collapse of the sheet and tip vortex cavitation, followed by intermittent rebounding of the tip vortex cavity. The collapse of the sheet cavity is triggered by a side-entrant jet, leading to the formation of the cloud and secondary vortex cavitation. The interaction between the secondary and tip vortex cavities further promotes the collapse of the latter. The three-dimensional instantaneous flow organisation indicates that the evolution of cavitation affects the centre displacement, deformation and breakdown of the tip vortex. Spanwise vortices emerge and interact with the tip vortex after the growth phase, causing violent fluctuations of the tip vortex during the collapse phase. The intense interaction between these vortices enhances the perturbation growth and promotes tip vortex breakdown. Proper orthogonal decomposition analysis reveals that the dominant unstable modes near the hydrofoil tip correspond to the displacement and deformation types. In addition to the suction-side shear layer, the vortex interaction region also exhibits intense production of turbulent kinetic energy. The temporal variation of sound pressure over an oscillation cycle indicates a strong correlation with the cavity morphology.