This study investigates the coupled aeroelastic dynamics and performance enhancement of thin flexible wings equipped with multiple distributed feathers, motivated by bio-inspired design of agile micro-air and unmanned aerial vehicles. A multi-body aeroelastic framework is developed by coupling an incompressible Navier-Stokes solver with large-eddy simulation in an arbitrary Lagrangian-Eulerian frame and a flexible multi-body structural model. The aeroelastic solver is applied to examine the aerodynamic performance of thin flexible wings without feathers, with a single leading-edge feather and with multiple overlapping feathers over a range of angles of attack, feather preset angles and feather lengths at Re = 2500. The results show that multi-feather configurations reorganize leading-edge vortex dynamics, yielding higher lift and lift-to-drag ratios than membrane-only wings. This is particularly evident in pre-stall and transitional regimes, where the design also keeps drag penalties moderate and reduces force fluctuations. A shallow positive preset angle combined with an intermediate feather length establishes a soft chordwise slot that sustains a gently convecting leading-edge vortex, accelerates pressure recovery and improves aerodynamic efficiency. When feathers become too long or too steep, blockage effects re-inflate drag and degrade performance. A new empirical scaling relation incorporating bounded feather coverage and preset-angle modifiers is proposed to predict the maximum membrane deformation under a Weber-number backbone. These findings provide quantitative guidelines for designing feathered morphing membrane wings with tunable lift, efficiency and stability across a wide angle-of-attack envelope.

Angle encoders enable high-accuracy and reliable angular measurements by the signal interpolation of light interference, in which the signal error plays an important role in limiting the measurement accuracy. To improve the accuracy of angle encoders, an error compensation model that extracts the signal error feature and further reconstructs the signal is established by variational mode decomposition (VMD) method. The VMD is used to adaptively decompose the error data into k intrinsic mode function (IMF), improving the signal error extracting efficiency. By analysis of the information contained in the IMF, an error compensation model is established, and the signal could be reconstructed by the error compensation to improve the measurement accuracy. It is found that, after the compensation, the mean, peak, and standard deviation of the error, could be reduced to 0.1739 '', and 0.6846 '', respectively.

Programmable and precise assembly of low-dimensional nanomaterials is the long-standing bottleneck for fabricating anisotropic flexible electronics, which provides physical support for sensing both strain magnitude and direction, and are critical for soft robotics and human-machine interfaces. However, existing strategies suffer from low alignment efficiency, poor spatial programmability, and complex fabrication. Here, a programmable dielectrophoretic (DEP) assembly methodology is reported, leveraging structured electric fields and serrated electrodes to achieve spatially selective, oriented deposition of carbon nanotubes (CNTs). Through theoretical analysis of the CNTs' motion behavior and impedance testing to quantify alignment degree, the electric field parameters are optimized. Meanwhile, combining with the design of a serrated electrode, the assembly efficiency of CNTs is also significantly improved (<90 s). As a proof-of-concept, the fabricated anisotropic strain sensor exhibits a sensitivity ratio of 16.52 between parallel and perpendicular directions and maintains robust durability over 2000 cycles. To demonstrate the utility of this programmable assembly, the CNTs are configured as a right-angle sensor array, which is capable of detecting the magnitude and direction of strain within the 180° range. This work not only extends the development of dielectrophoresis in the manufacturing of anisotropic composites but also offers new avenues for developing high-performance, multifunctional flexible electronics.

Grating roughness imposes fundamental limitations on the achievable accuracy of optical encoders in precision displacement measurement. To address the potential accuracy that the encoders could achieve, diffraction models describing both surface roughness and line edge roughness are developed to quantitatively characterize their impact on optical imaging. Leveraging Fresnel diffraction, the dependence between random grating roughness and the resulting imaging field is analytically formulated, enabling reliable retrieval of displacement information from the measured signals. To further evaluate roughness-induced measurement uncertainty, an accuracy prediction model by the Monte Carlo statistical framework is established to imply the grating roughness dependence of the achievable accuracy. The model exhibits excellent concordance with experimental measurements: 95.6% of the measured maximum errors fall within the 95% confidence interval of the predicted values, while all experimental results remain confined to a deviation range between -10% and +5%. Beyond predictive capability, the proposed model provides physical insight into the mechanisms through which roughness degrades measurement accuracy, thereby identifying the dominant factors that must be controlled during grating fabrication. Consequently, the model enables more accurate assessment of in-service grating performance and supports reliability-oriented design for future optical encoder applications. Overall, this work establishes a theoretical foundation for precision grating fabrication and performance evaluation, offering practical guidance for enhancing measurement accuracy in high-precision metrology systems.

Installation-induced eccentricity and tilt are major sources of angular measurement error in rotary grating encoders, while existing self-calibration methods often require multiple reading heads or external reference instruments. This paper proposes an online angular self-calibration method for a polar-coordinate encoder that simultaneously measures rotation angle and radial displacement using a single polar-coordinate reading head. A coupled eccentricity-tilt error model is established, and the installation parameters are identified online from radial displacement measurements by solving an overdetermined linear system. The identified parameters are then incorporated into an angular compensation model for online error correction under varying mounting conditions. Conditioning and perturbation analyses demonstrate that the proposed identification method has good numerical stability and robustness. Experiments performed on an air-bearing calibration platform show that, under a fixed installation condition, the maximum angular error is reduced from 8.65 arcsec to 0.84 arcsec after compensation, corresponding to an approximately 90% reduction. In five repeated reinstallation tests, the residual angular errors after compensation range from 0.67 arcsec to 0.88 arcsec, with a mean value of 0.78 arcsec. A measurement uncertainty analysis based on the experimental results gives a combined standard uncertainty of 0.15 arcsec and an expanded uncertainty of 0.30 arcsec (k = 2). These results demonstrate that the proposed method provides an effective and practical solution for online suppression of installation-induced angular errors in high-precision rotary grating encoders.

High-precision displacement measurement places stringent requirements on error modeling for absolute optical encoders. In practical industrial environments, encoder errors exhibit multi-scale characteristics and spatially varying non-stationary behavior due to coupled physical mechanisms. Conventional compensation methods often struggle to maintain stability in smooth regions while accurately capturing locally complex structures. To address this challenge, this paper proposes an adaptive multi-kernel radial basis function (MK-RBF) modeling framework for high-precision encoder error compensation. The proposed approach enhances scale coverage through cooperative multi-kernel representation and introduces structural adaptivity to accommodate spatial complexity variations. A scale-consistency regulation strategy and a complexity-driven resolution allocation mechanism are incorporated to improve numerical robustness and modeling accuracy. Experimental results demonstrate that the proposed method achieves superior residual stability and lower root-mean-square error compared with piecewise fitting, EMD-based methods, and single-kernel RBF models. According to the VDI 3441 (1997) evaluation standard, positional uncertainty is reduced to 2.8 mu m and repeatability is improved to 1.0 mu m, confirming the robustness and practical applicability of the proposed framework under complex error conditions.

Conventional phase-shifting detection system enables compact quadrature signal acquisition; however, it suffers from severe sensitivity to angular perturbations induced by spatial positional shifts of non-collinear beams. Here, we present a robust spatial phase-shifting interference detection method using spatial interference fringes and a dual-detector configuration arranged along the fringe normal direction. A physical model for quadrature signal acquisition is established, in which the robustness is quantitatively characterized by the ratio of the projected fringe periods along the detector axis before and after angular perturbation. The analysis demonstrates that under a specific homologous angular perturbation of 0.005 degrees, the relative deviation of the longitudinal fringe interference geometric configuration is 3 & times; 107 times that of the optimized transverse fringe interference geometric configuration. The optimized transverse fringe interference geometric configuration can maintain the ratio at a level extremely close to 1, thereby ensuring stable phase matching and signal orthogonality. The proposed method is applied to a grating interferometer and validated through simulations and experiments. The optimized system achieves a maximum residual error of 21.29 nm and a maximum standard deviation of 12.71 nm over a 300 & micro;m measurement range, demonstrating enhanced robustness and suitability for compact grating interferometric displacement measurement system.

Thermal switches gain intense interest for dynamic thermal management of electronics, battery, and space applications under variable operating conditions. However, current approaches have limitations such as sharp state transition (binary "on" and "off" states, ×2) and being unable to simultaneously achieve self-initiated thermal startup and real-time responsiveness. Here, a dual-mode thermal switch with a passive thermal diode and active magnetic-gated switching characteristics is proposed and demonstrated using a branched interface and discrete plugs. Where passive-mode provides an asymmetric difference of 21.47 K, active-mode achieves multiple tuned freedom (×19). In contrast with conventional research, these switches provide an opportunity for thermal circuits to dissipate more heat of 11.83 K/mm on a small scale and control almost 20 thermal transients (5.5-9.5 times). Higher thermal regulation flexibility not only offers potential for dynamic control of operating temperatures, including some atypical environments (e.g., hot winter day), but also renders thermal switches amenable for scenarios where external stimuli, excluding temperature fluctuation, cannot manually intervene.

The vibration of solid surfaces is universal in nature and industry, giving rise to the multifarious dynamics of droplets on them. The dynamic behaviors of nanofluid droplets impacting on hydrophilic vibrating solid surfaces have been explored by molecular dynamics (MD). Specifically, the coupled effects of droplet properties and substrate vibration dynamics have been examined. Four impacting modes: Adhesion and Oscillation mode (AO mode), Up and Down mode (UD mode), Rebound mode (R mode), and Impact breakup mode (IB mode) are identified by analyzing the droplet's morphological evolution and energy conversion. In high frequency-high amplitude (fH, AH) regions, the IB mode is triggered, resulting in a rebounding droplet with large kinetic energy. The R mode is achieved at the large vibration Weber number (Wev) and is adjustable by the Weber number of droplet (We). A classification model of nanofluid droplet impacting behavior has been established to forecast the morphological evolution on vibration surfaces by We and Wev. Especially, the empirical criterion has been given to build the integrity and rebound configurations of impacting nanofluid droplets on a vibration surface, as (Wev/ We)1/2 = n. This study offers molecular insights into the physics of nanofluid droplets impacting on hydrophilic vibrating surfaces, devoting itself to exploring the manageable dynamic behaviors of vibrating droplets in droplet atomization, surface acoustic wave (SAW) devices, nanofluidic systems, and droplet-based 3D printing.

The degradation of measurement accuracy caused by the edge blurriness of the optical imaging due to the grating roughness poses a significant challenge in the development of precision optical encoders. In this study, a mathematical model based on Fresnel diffraction is established to address the roughness dependence of the optical spatial resolution after grating reflection, which reveals the limit on measurement accuracy of optical encoders. The edge blurriness of the optical imaging after grating reflection is quantified by the edge spread function, and the blurred edge induced by the grating roughness is further obtained, which bridges the final measurement accuracy by optical encoders and the grating profiles (determined by the manufacturing process). The accuracy of the roughness mathematical model was experimentally validated by comparing the width of the blurred interval, with the discrepancy between the experimental and calculated values remaining below 0.014 mu m. Compared with previous methods, a unified model was established that incorporates multiple roughness and provides a standard framework for evaluating grating measurement accuracy. Additionally, accuracy compensation was performed based on the mathematical model, resulting in a reduction of the period subdivision error to 11.23 % of its original value. The model provides a promising method to improve the measurement accuracy by compensating for the optical error induced by the grating roughness.

High-speed motion of the reading head in grating interferometers induces rarefied gas flow perturbations in narrow-confined microstructure spaces with micro- and nano-periodic structures, leading to the fluctuations of air-refractive index and nanometer-scale interferometric measurement errors. To address this, an integrated fluid-solid-optical framework combining the Information Preservation Direct Simulation Monte Carlo (IP-DSMC) method, a modified Edl & eacute;n refractive index model, and a ray-tracing method is developed. The IP-DSMC method is implemented within the OpenFOAM framework and validated against benchmark Couette flow cases. This study systematically characterizes the effects of Knudsen numbers and geometric parameters on flow perturbations and interferometric measurement errors. Results reveal that interferometric measurement errors are highly sensitive to refractive index non-uniformities induced by flow perturbations, jointly governed by rarefaction effects and microstructure geometries. A dynamic fluctuation model of air-refractive index incorporating Kn- and geometry-dependent corrections achieves high accuracy, showing that pressure-driven fluctuations of air-refractive index dominate interferometric measurement errors, reaching 13.2 nm at Kn is 0.25. The ray-tracing result confirms the reduction of the optical path difference with rising Kn, while geometric effects are secondary. This study provides a foundation for the error compensation in the high-precision grating interferometer under rarefied flow conditions.

High-order diffraction is preferred to nanoscale displacement measurement by linear optical encoder. The diffraction efficiency at high orders, however, is limited. In this Letter, a high-order diffraction grating with an isosceles triangle profile in cross-section is proposed, and it could achieve over 40% in the diffraction efficiency of the ±4th order. Fabricated by anisotropic etching of Si (100) and followed by replication, the grating period is 4.82 μm and the symmetrical side angle for diffraction is 46.1°. Experiments indicate that, by the interference of ±4th order (optical subdivision is 8 times), the positioning accuracy in 1 mm travel length is 37.1 nm, the repeatability is 3.7 nm, and the stability is 3.6 nm @ 60 s, which are measured by the standard deviation (σ).

This paper presents a comprehensive review of the development and advancements in ultra-precision grating displacement sensors, emphasizing their fundamental measurement theories, technology evolutions, device development, current applications, and future trends. Grating displacement sensors, utilizing optical interference and photoelectric conversion principles, deliver exceptional resolution and accuracy, making them vital in high-precision fields such as semiconductor manufacturing, aerospace, advanced metrology, and microfabrication. The review examines key innovations in grating sensor technologies, including the integration of digital interference measurement methods, advanced signal demodulation techniques, and the application of pseudo-random binary codes for absolute displacement measurements. Furthermore, the paper assesses the impact of novel materials, sensor designs, and miniaturization on sensor performance, particularly in enhancing sensitivity, reducing environmental susceptibility, and improving long-term stability. A comparison of domestic and international research progress in grating sensor technologies is provided, identifying critical gaps and emerging research areas. Looking ahead, the outlook for the field underscores the potential for integration into digital twin techniques, artificial intelligence (AI), and hybrid sensor systems that combine displacement measurement with other sensing capabilities. The paper concludes by addressing challenges in the field, such as improving the signal-to-noise (SNR) ratio, enhancing sensor integration, and reducing production costs, while also spotlighting opportunities for further innovations to meet the escalating demands for ultra-precision measurements in next-generation manufacturing and other advanced applications. This review aims to provide a thorough understanding of the current state of ultra-precision grating displacement sensors and their potential to shape the future of high-precision measurement technologies.

The multi-diffractions model is commonly used to increase the optical subdivision factor. However, in practical applications, as the diffraction order increases, this model requires the size of the mirror above the scale grating to be larger, resulting in the reading unit being too bulky. In addition, the general multiple diffractions arrangement direction is arranged along the relative movement direction of the scale grating and the reading unit, which reduces the measurement range of the scale grating. More importantly, in the current blazed grating interferometer, the incident light beam is generally perpendicular to the grating’s macroscopic surface, which means that the maximum diffraction efficiency characteristics of the blazed grating are not fully utilized. To address these issues, we developed a novel multiple diffractions model. It arranges multiple diffraction positions along the direction of the grating ruling lines and directs the incident light beam onto the blazed grating groove surface at a near-Littrow angle. By slightly adjusting the inclination angle of the beam, the number of diffractions can be controlled. The operating principles of the proposed model are thoroughly elucidated. Subsequently, the corresponding experimental setup is constructed to validate the effectiveness of its optical subdivision and assess the accuracy of its displacement measurements. The results indicate that the measurement model can achieve optical subdivision up to 14 times, with the measurement accuracy reaching 46.54 nm within a travel range of 0.2 mm and 134.42 nm within a travel range of 1 mm. If the corresponding gain material can be inserted between the grating and the reflector to maintain a constant optical power of the diffracted beam, this model presents the potential for substantial optical subdivision multiples when the beam is vertically incident on the surface of the grating groove via the partial reflector. This may establish a fundamental optical design framework for future research on optical subdivision cavities.

Microstructure-patterned channels based on sheathless inertial microfluidics have emerged as promising platforms for the migration and separation of multi-size particle mixtures, which is critical for point-of-care testing in the biomedical and environmental fields. This work proposes a quantitative strategy for multi-size particle migration and separation using the microstructure-patterned microchannel. First, we developed a design pattern of the lateral microstructures within a reverse wavy microchannel that enhanced the Dean drag force and inertial lift force. The number of lateral microstructures had a significant impact on the migration positions of small particles where the Dean drag force exceeded the inertial lift force. Next, the mechanism of single-size particle migration positions and multiple-size particle separation dynamics dominated by the enhanced Dean drag force was explored. Moreover, the coupled effects of flow rate, particle size and design pattern within microstructure-patterned microchannels were investigated. The optimal design pattern for the migration and separation of multi-size particle mixtures varied depending on the flow rate. Furthermore, a quantitative strategy was identified and verified for customizing the multi-size migration and separation using a novel explicit scaling factor. This study provides a tuning mechanism and customization strategy for the migration and separation of targeted particles in microstructure-patterned microchannels, which has great potential for practical application in the field of inertial microfluidics.

A blazed grating interferometer with high-fold optical subdivision is proposed based on the optical path design of Mach-Zehnder interferometer. In the designed measurement system, multiple diffractions are achieved on the blazed grating surface, fully leveraging the high diffraction efficiency of the blazed grating and avoiding the presence of non-coplanar beams. Furthermore, in order to avoid beam deformation resulting from multiple diffractions, the light path structure returning along the same path is constructed, and this design doubles the optical subdivision fold factor. The experimental results show that 14-fold optical subdivision can be realized in this measurement system, and the maximum calibration difference can reach 34.47 nm within a 0.2 mm travel and 101.07 nm within a 2 mm travel. The designed blazed grating interferometer has the characteristics of a simple structural layout, high-fold optical subdivision and high measurement performance, which lay the groundwork for actual product development.

This study explores the antibiofilm potential of slippery covalently attached liquid-like surfaces, revealing their remarkable ability to inhibit biofilm formation over extended periods, regardless of their hydrophobic or hydrophilic nature. We engineered permanently bound liquid-like solid surfaces with exceptional slipperiness, defined by ultralow contact angle hysteresis, and assessed their effectiveness against two nosocomial pathogens, Pseudomonas aeruginosa (PAO1) and Staphylococcus epidermidis (FH8). These surfaces achieved a 3-5 order of magnitude reduction in biofilm formation compared to polydimethylsiloxane under both static and dynamic culture conditions over 14 days. Impressively, both the hydrophobic and hydrophilic slippery liquid-like solid surfaces significantly outperformed the widely used antimicrobial coatings containing silver particles in the long term in both static and dynamic cultures. These slippery surfaces also outperformed emerging antibiofilm surfaces such as liquid-infused surfaces in extended periods of dynamic cultures. We have demonstrated that ultralow liquid-solid friction, characterized as ultralow contact angle hysteresis, is an important predictor of the long-term antibiofilm performance of both hydrophobic and hydrophilic slippery covalently attached liquid-like surfaces, particularly in dynamic cultures. This work elucidates the interfacial mechanisms and scientific principles underpinning the design of advanced antibiofilm surfaces capable of maintaining a superior performance over the long-term.

This study investigates the aeroelastic characteristics of multi-segment thin flexible structures with deflected flaps, focusing on their aerodynamic and hydrodynamic performance as well as vortex dynamics. These multi-segment structures, which can adapt their geometry through flap deflection, exhibit enhanced aerodynamic, hydrodynamic, and maneuvering capabilities across a range of flow conditions. A variational multibody aeroelastic modeling framework is employed to simulate the coupled fluid-membrane-flap dynamics as a function of the leading- and trailing-edge flap deflection angles. The lift, drag, and flow structures of the multi-segment system are analyzed under pre-stall and post-stall conditions to assess the influence of flap deflection. The results demonstrate that trailing-edge flap deflection improves lift performance under pre-stall conditions by modifying vortex structures, while leading-edge flap deflection promotes vortex attachment, enhancing lift performance in post-stall conditions. The thin structure forms streamlined shapes through flap deflection to reduce drag by optimizing the flow field. These findings underscore the importance of effective camber variation and the formation of leading-edge vortices in enhancing aerodynamic and hydrodynamic efficiency across varying flow conditions. The results provide valuable insights for optimizing morphing wing designs with deflected flaps, offering significant potential for improving maneuverability and efficiency in both aviation and underwater applications.