Abstract
The direct fabrication of functional electronics on conformal surfaces enables efficient space utilization, higher integration density, and reduced structural weight in advanced electronic systems. While conformal electronics on planar and externally curved surfaces have been widely investigated, no effective approach has been developed for high-resolution fabrication on cavity inner surfaces. This limitation leads to substantial underutilization of inner-surface resources and restricts their functional potential. Inspired by the traditional Chinese art of inner-painted snuff bottles, we introduce a directional inner-surface printing method based on the principles of aerosol jet printing1,2 that maintains high printing resolution across a range of materials. Compared with conventional techniques, the method supports the direct fabrication of diverse functional electronics on inner surfaces with feature sizes as small as 11.58 ± 0.67 μm, including electronic structures within high-aspect-ratio ( > 10) cavities and stress-sensor arrays integrated into honeycomb architectures. This strategy enables the fabrication of high-resolution, integrated electronics in previously inaccessible areas, with potential applications in structural health monitoring, wearable devices, and biotechnology.
Subject terms: Mechanical engineering, Surface patterning
The work presents a directional inner-surface printing method that enables high-resolution fabrication of functional electronics on inner surfaces of cavities, allowing direct patterning and integration of devices such as sensors and coils in previously inaccessible areas.
Introduction
Efficient spatial utilization in functional devices is important for enhancing system integration, reducing structural weight, and enabling increasingly compact electronic systems. Direct fabrication of functional components onto target surfaces provides an effective route to overcome the spatial constraints associated with conventional assembly-based manufacturing3. Conformal printing technologies have attracted considerable attention because they enable the deposition of functional materials directly onto curved and non-planar surfaces4, while maintaining substrate integrity and facilitating multifunctional integration. Recent advances in conformal printing processes5,6, materials7,8, and device fabrication9 have improved the precision and reliability of conformal electronics, leading to applications in aerospace systems, automotive electronics, and wearable devices10. Despite these developments, current conformal manufacturing techniques remain largely limited to externally accessible or moderately curved surfaces. The direct fabrication of functional electronics on inner surfaces or within confined structural cavities remains a significant challenge.
At present, the fabrication of electronics within inaccessible internal geometries generally relies on indirect manufacturing followed by assembly. Approaches such as component mounting11, transfer printing12,13, and flexible circuit integration are commonly used to incorporate pre-fabricated devices into complex structures. However, these manufacture-first, assemble-later strategies often involve multiple processing steps and alignment procedures, which can limit design flexibility and complicate device implementation. The absence of a direct printing approach capable of accessing and patterning inner surfaces restricts the integration of electronics within complex three-dimensional (3D) structures. Therefore, developing a manufacturing strategy that enables direct and conformal patterning on inner surfaces without disassembly or secondary assembly remains an important objective.
In this work, we demonstrate a directional inner-surface printing (DISP) strategy for material deposition in confined 3D spaces. Inspired by the ancient Chinese art14 of inner-painted snuff bottles (Fig. 1a), in which artisans create reverse paintings through a bottle’s narrow neck using specialized hooked brushes (Fig. 1b), DISP is developed based on the principles of aerosol jet printing1 and employs a bent-nozzle design to redirect focused aerosol streams toward otherwise inaccessible inner surfaces. Combined with a high-precision multi-axis motion platform, the method enables accurate trajectory control and conformal material deposition within complex cavity structures while maintaining high printing resolution across a range of functional materials. We systematically investigate the effects of bent-nozzle geometry on printing performance through experiments and computational fluid dynamics (CFD) simulations, revealing the mechanisms governing directional aerosol transport and deposition. The DISP approach enables high-resolution patterning with feature sizes down to 11.58 ± 0.67 μm and supports direct fabrication within high-aspect-ratio ( > 10) cavities. Using this approach, we fabricate a range of functional devices on inner surfaces, including microstructures, induction coils, heating elements, temperature sensors, and distributed stress-sensor arrays within honeycomb structures. These results demonstrate the capability of DISP for utilizing previously inaccessible inner surfaces and support the integration of functional electronics in applications such as structural health monitoring, wearable systems, and biotechnology.
Fig. 1. DISP enables patterning on inner surfaces.

a Traditional Chinese snuff bottles are decorated by painting on their inner surfaces using specialized hooked brushes. b Artisans create reverse paintings through the bottle’s narrow neck, enabling patterning within confined 3D spaces. c Schematic illustration of aerosol generation and transport in the DISP process. Aerosol droplets are generated by an ultrasonic atomizer and carried by a carrier gas to the printhead, where they are focused by a coaxial sheath gas. d Schematic of DISP using a bent nozzle, which extends into cavity structures and delivers aerosol to inner wall surfaces that are inaccessible to conventional straight nozzles. e As the nozzle moves relative to the substrate, aerosol droplets are deposited onto the inner surface to form predefined patterns. f The emblem of Northwestern Polytechnical University is printed on the inner surface of a transparent glass bottle, demonstrating inner-surface patterning using DISP. Some graphical elements in panels a and b were adapted from resources obtained from Magnific.com.
Results
Bent nozzle design and printing mechanism
In the DISP process, liquid ink is atomized into microdroplets by an ultrasonic atomizer and transported by a carrier gas to the nozzle, where a coaxial sheath gas focuses the droplets into a directed aerosol stream (Fig. 1c). The bent nozzle extends into cavity structures, enabling aerosol delivery to inner wall surfaces that are inaccessible to conventional straight nozzles (Fig. 1d). Within the nozzle, the aerosol stream is redirected through the bending segment, further focused by the contraction of the focusing segment, and subsequently ejected through the outlet at high velocity (Fig. 1e). As the nozzle moves relative to the substrate, aerosol droplets are deposited onto the inner surface to form predefined patterns. Unlike straight nozzles, which require substrate reorientation and generally permit only oblique deposition on semi-enclosed surfaces, bent nozzles enable direct deposition onto inner surfaces by redirecting the aerosol stream while maintaining its focused characteristics. Because the aerosol stream is transported by gas flow and is directionally insensitive, it can be redirected and deposited vertically onto inner surfaces without compromising patterning capability (Supplementary Fig. 1). As a demonstration, the emblem of Northwestern Polytechnical University was printed on the inner surface of a glass bottle using blue ink (Fig. 1f and Supplementary Movie 1).
The bent nozzle consists of four functional segments: a connection segment, an extension segment, a bending segment, and a focusing segment (Fig. 2a). The connection segment securely attaches the nozzle to the aerosol generation system, providing a stable and leak-free interface. The extension segment increases the nozzle's reach, enabling access to deeper or more confined regions within cavities. The bending segment redirects the aerosol stream at a prescribed angle, allowing directional control of material deposition. The focusing segment employs a sheath gas flow to confine and stabilize the aerosol jet, thereby improving printing precision and resolution. To investigate the influence of nozzle geometry on printing performance, experimental studies and numerical simulations were conducted to evaluate the effects of three key structural parameters—extended length, bending angle, and focusing length—on the morphology of printed lines. As shown in Fig. 2b, each parameter was varied across eight discrete levels: extended length from 30 to 100 mm in 10 mm increments, bending angle from 0° to 105° in 15° increments, and focusing length from 4 to 11 mm in 1 mm increments, with initial baseline values set to 30 mm, 90°, and 7 mm, respectively. In all experimental configurations, the focusing segment of the nozzle was maintained perpendicular to the inclined substrate under fixed process parameters and a constant working distance (Supplementary Table 1and Supplementary Fig. 2a), ensuring consistent aerosol impingement conditions. The aerosol stream remained well collimated after being redirected through the bending segment (Supplementary Fig. 2b and Supplementary Movie 2), which is important for maintaining printing precision. The width and height of the printed lines were quantitatively measured using white-light interferometry (Supplementary Fig. 3), while overall line morphology was assessed via optical microscopy (Supplementary Fig. 4).
Fig. 2. Bent nozzle design and printing mechanism.

a Schematic of the bent nozzle design consisting of four functional segments. b The structural parameters of the nozzle, including extended length, bending angle, and focusing length, were varied across eight discrete levels. c Boundary condition setup for CFD and DPM simulations. Effects of nozzle structural parameters on printed-line morphology in experiments and simulations: extended length (d), bending angle (f), and focusing length (h). Effects of nozzle structural parameters on the cross-sectional profiles of printed lines: extended length (e), bending angle (g), and focusing length (i). Width-Exp, experimental line width; Width-CFD, simulated line width from CFD–DPM model; Height-Exp, experimental line height. Data are presented as mean ± standard deviation (SD); error bars indicate SD; n = 4. Width-Exp, experimentally measured line width; Width-CFD, simulated line width from the CFD–DPM model; Height-Exp, experimentally measured line height.
Additionally, a 3D CFD framework was developed to model and elucidate the aerodynamic interactions governing aerosol droplet transport and deposition within a nozzle containing a bending segment, as illustrated in Fig. 2c. A Lagrangian discrete phase model (DPM) was used to simulate aerosol droplet trajectories and predict deposition lines on the substrate (Supplementary Fig. 5and Supplementary Movie 3). The simulated line width showed good agreement with experimentally measured values. As the extended length increased from 30 mm to 100 mm, the measured printed-line profiles showed only slight fluctuations (Fig. 2d, e and Supplementary Fig. 6), while the overall velocity fields within the fluid domain and the aerosol trajectories within the bending segment remained essentially unchanged (Supplementary Fig. 7 and Supplementary Fig. 8), indicating that the extended length has a negligible effect on the printed line morphology. As the bending angle increases from 0° to 105°, the average line width and its corresponding standard deviation gradually increase while the line height decreases (Fig. 2f, g and Supplementary Fig. 9). This trend arises from the increased deflection of the aerosol stream toward the outer wall within the bending and focusing segments (Supplementary Figs. 10 and 11). Such stream divergence at larger bending angles causes stronger flow disturbances, leading to wider line widths and a slight increase in porosity. Consequently, the resistivity increases slightly, consistent with the observed morphological changes (Supplementary Fig. 12). However, the wrap-around effect of the sheath gas prevents direct contact between the aerosol stream and the inner wall of the bent nozzle, enabling directional control of aerosol stream deposition onto the inclined substrate. As the focusing length increases from 4 to 11 mm, the printed line width decreases and height increases (Fig. 2h, i and Supplementary Fig. 13), with minimal influence on the overall velocity fields and aerosol trajectories (Supplementary Figs. 14 and 15), possibly due to enhanced droplet coalescence at longer focusing lengths. At short focusing lengths (4–6 mm), the printed lines exhibit overspray and asymmetric tailing due to insufficient focusing of larger droplets, which is progressively mitigated as the focusing length increases and the aerosol stream becomes more collimated15. However, excessively long focusing lengths may reduce droplet inertia, leading to lateral dispersion and broader deposition lines. In addition, the effects of working distance, carrier gas flow rate, and focusing ratio follow trends typical of aerosol-based printing systems1. Increasing the working distance results in wider and flatter lines, a higher gas flow rate increases both line width and height, and a higher focusing ratio produces narrower and taller lines (Supplementary Figs. 16 and 17).
Patterning capabilities and functional applications of the DISP method
To evaluate the patterning capability of DISP on inner surfaces, spiral lines were printed on the inner surface of a long glass tube (length: 200 mm; inner diameter: 20 mm) using a 90° bent nozzle (Fig. 3aand Supplementary Movie 4). Figure 3b shows a localized view of the resulting helical pattern, with individual spiral lines exhibiting a width of approximately 100 μm. By synchronizing the Z-axis translation speed with the rotational speed of the platform, the pitch and density of the spiral lines were precisely controlled, demonstrating the capability of DISP to print within high-aspect-ratio ( > 10) structures. In addition, seven 3 mm-wide colored rings were printed on the inner surface of a 26 mm-diameter glass bottle using inks with different color formulations (Fig. 3c). To demonstrate the high-resolution capability of DISP, fine line patterns arranged in concentric squares within a 1 mm × 1 mm area were printed on a vertically oriented glass substrate (Fig. 3dand Supplementary Movie 5) using a 161 μm nozzle, achieving a minimum feature width of 11.58 ± 0.67 μm (Fig. 3e). Even at this minimum feature size, the printed lines maintained electrical conductivity and functional performance (Supplementary Fig. 18 and Supplementary Table 2).
Fig. 3. Inner-surface patterning capability of the DISP method.

a Conformal printing of spiral lines on the inner surface of a high-aspect-ratio glass tube. b Local view of a spiral pattern, showing a single-line width of approximately 100 μm. c Colored concentric rings printed on the inner surface of a bottle using seven different inks. d High-resolution line patterns printed on a vertical substrate, with a minimum feature width of 11.58 ± 0.67 μm (e).
Leveraging the directional aerosol deposition mechanism and inner-surface patterning capability of DISP, several functional devices were further demonstrated. Figure 4a shows a 7 × 7 3D micropillar array fabricated on the inner wall of a transparent glass bottle. The micropillars were formed via layer-by-layer deposition of silver nanoparticle ink16,17, with a ceramic heating element providing localized heating near the outer surface of the bottle to enhance solvent evaporation (Supplementary Movie 6). Figure 4b provides a detailed view of the array within a 5 mm × 5 mm area, where each pillar has a diameter of approximately 240 μm and a height of 600 μm. Figure 4c and Fig. 4d demonstrate wireless LED illumination enabled by spiral structures printed on the inner surface, which function as the transmitter and receiver, respectively (Supplementary Movie 7). Figure 4e shows a heating coil printed on the inner surface of a vial, with its temperature profile measured by infrared thermography under a 24 V DC power supply (Fig. 4f). The coil reaches 100 °C within 60 s and stabilizes at 139 °C after 400 s of operation (Supplementary Movie 8). Figure 4g shows a 20 mm × 20 mm temperature sensor printed on the inner surface of a tall beaker, exhibiting a strong positive correlation between resistance and temperature (Fig. 4h, R2 = 0.9996). When the beaker is held by hand, the resistance stabilizes at 342.8 Ω, in good agreement with the calibration curve and consistent with typical human body temperature (Fig. 4i).
Fig. 4. Diverse functional applications of the DISP method.

a A 7×7 3D micropillar array was printed contactlessly on the inner surface of a transparent glass vial. b Detailed view of the micropillar array. Spiral coils conformally printed on the inner wall of a beaker serve as the transmitting (c) and receiving (d) ends for electromagnetic induction, enabling wireless illumination of an LED. Heating coil (e) is printed on the inner surface of a transparent glass vial, and its corresponding temperature-rise curve (f). Temperature sensor (g) printed on the lower inner surface of a tall beaker and its corresponding temperature–resistance characteristic curve (h), where R denotes resistance, T denotes temperature, and R2 represents the coefficient of determination of the linear fit. i Resistance response of the sensor when the beaker is held by hand.
Stress sensor array within a honeycomb structure
To further explore the capabilities of DISP, a 3D resistive stress sensor array was developed to monitor stress distribution within a flexible honeycomb substrate (Fig. 5a). The flexible honeycomb substrate was cast from polydimethylsiloxane (PDMS) in a CNC-machined mold (Supplementary Fig. 19a), with a polyethylene terephthalate (PET) film bonded to its hydrophobic surface using a silicone adhesive to maintain flexibility and compatibility with aqueous silver ink (Fig. 5b). A 4 × 4 array of independent sensing units (3.6 mm × 10 mm) was conformally printed onto the inner surface of the honeycomb substrate (Fig. 5c, Supplementary Fig. 19c and Supplementary Movie 9). The resistance of each sensing unit changes as the printed structures deform under applied stress18, enabling stress monitoring within the honeycomb architecture (Fig. 5d).
Fig. 5. Stress sensor array conformally printed on the inner surface of a PDMS honeycomb.

a Schematic of the distributed stress-sensing array integrated on the inner surface of a flexible honeycomb substrate. b Schematic illustration of the stress sensor packaging structure. c Arrangement of a 4 × 4 array of independent stress sensors printed on the inner surface of the honeycomb substrate. d Optical image of a single printed stress sensor. e Relative resistance change (ΔR/R0) under applied force of up to approximately 17 N. f Relative resistance change (ΔR/R0) under repeated loading–unloading cycles at a maximum force of approximately 17 N. g Spatial distribution of relative resistance change (ΔR/R0) under different mold geometries (N, P, and U).
Periodic loads were applied to the sensor array, and the corresponding resistance changes were recorded (Supplementary Fig. 20a). The relative resistance change (ΔR/R0) of each sensor was found to depend on the applied force and increased approximately linearly with the applied force (Fig. 5e). At an applied force of 17 N, the relative resistance change reached 0.34. To minimize mechanical crosstalk between adjacent sensors, a 3D-printed support structure consisting of 16 hexagonal columns was introduced to support the honeycomb substrate (Supplementary Fig. 20b). Multiple loading–unloading cycles on individual sensors demonstrated stable and repeatable resistance responses, with resistance recovering to its initial value after each unloading (Fig. 5fand Supplementary Fig. 21), confirming good durability and reversibility. Stress was applied and released to the 4 × 4 stress sensor array was loaded and unloaded using molds shaped as N, P, and U (representing the initials of the authors’ affiliation), with signals collected via a custom measurement system (Supplementary Fig. 22). The spatial distribution of relative resistance change across the sensor array clearly reproduced the imposed patterns (Fig. 5g and Supplementary Movie 10), demonstrating stable electromechanical performance and reliable stress mapping capability on inner surfaces.
Discussion
The next generation of engineering applications for 3D-printed conformal electronics requires more efficient use of available space within functional devices. To meet this need, directional direct-write deposition strategies are required, as accurate and controllable inner-surface patterning remains largely inaccessible using conventional straight-nozzle approaches. Here, we demonstrate a printing strategy that leverages directional control of aerosol jet deposition to fabricate conformal electronics on inner surfaces. The key feature of the design is the incorporation of a bending segment within the nozzle, enabling controlled redirection and deposition of aerosolized inks onto inclined or vertical inner surfaces. The effects of bent-nozzle structural parameters on printed-line morphology were systematically investigated through experiments and CFD simulations. The sheath gas forms a protective flow that prevents direct contact between the aerosol stream and the inner wall of the bent nozzle, thereby enabling stable material transport and deposition. This configuration enables controlled and gentle deposition onto inner surfaces, in contrast to high-energy or high-temperature processes such as plasma spraying19,20 or explosive spraying21.
Compared with existing conformal AJP methods (Supplementary Table 3), the DISP approach extends direct fabrication capability to high-aspect-ratio ( > 10) structures while maintaining high resolution ( < 11.58 ± 0.67 μm), non-contact operation, and broad material compatibility. Using this approach, 3D micropillar arrays, electromagnetic induction coils, heating coils, and temperature sensors were conformally printed on the inner surfaces of complex structures. In addition, a 4 × 4 stress sensor array printed on the inner surface of the honeycomb substrate enables in situ monitoring and visualization of internal stress distribution. These results demonstrate that DISP enables the fabrication of functional electronics on otherwise inaccessible surfaces and may support applications in structural health monitoring, wearable devices, and biotechnology.
Methods
Materials of aerosol inks
Seven water-based colored inks were purchased from M&G Stationery (Shanghai, China). The inks exhibit viscosities in the range of 2–5 cP, making them suitable for ultrasonic atomization-based aerosol generation. During deposition on inner surfaces, a ceramic heating plate was applied to the outer wall at the target region and maintained at 60 °C to promote rapid solvent evaporation and reduce ink spreading.
A water-based conductive silver nanoparticle ink (JS-A426) was supplied by NovaCentrix (Austin, TX, USA). The ink has a viscosity of 6–10 cP, making it compatible with ultrasonic atomization systems. It contains 50 wt% silver nanoparticles with an average particle size of 30–40 nm, dispersed in a proprietary solvent system consisting of isopropanol, ethylene glycol, diethylene glycol, and other hydrocarbon-based solvents. The ink exhibits high electrical conductivity and contains polymer additives to enhance adhesion to various substrates.
Bent nozzles manufacturing
The bent nozzle was designed in SolidWorks with a fully parametric, smooth geometry to minimize abrupt changes in cross-section and curvature. This design reduces flow disturbances and promotes a stable, collimated aerosol jet throughout the nozzle. The nozzles were fabricated via high-resolution stereolithography (SLA) using a Phrozen Sonic Mighty Revo 14K 3D printer (Phrozen) with a transparent photopolymer resin (Aqua-Clear, Phrozen). During fabrication, the nozzle orifice plane was maintained parallel to the build platform to ensure geometric fidelity across different bending angles, resulting in a consistent outlet diameter of 290 μm (Supplementary Fig. 23).
Experimental setup
All printing experiments were performed using a custom-built ultrasonic atomization aerosol printing system integrated with an IDS NanoJet aerosol generator (IDS Inc.). The system includes precision voltage controllers for modulating ultrasonic transducers and mass flow controllers (MFCs) for regulating N2 carrier gas flow. The printing platform provides sub-micron positioning accuracy and is controlled via G-code and ACS motion commands. Alignment was achieved through a pre-calibration procedure. For planar substrates, the sample was fixed on a holder aligned with the XYZ coordinate system. The nozzle was positioned at a reference feature, brought into slight contact, retracted to a predefined standoff distance, and the toolpath was generated based on the planar geometry. For cylindrical substrates, the sample was mounted on a rotational stage aligned with the Z-axis to ensure coaxial alignment. The nozzle was then positioned at a reference inner-surface point, brought into slight contact, retracted to the predefined standoff distance, and the toolpath was generated based on the 3D geometry. Toolpaths were generated by converting AutoCAD DXF files into machine instructions using proprietary software. Prior to use, each ink was mixed for 10 min in a planetary mixer (THINKY ARM-310, Thinky Corporation) to ensure homogeneous dispersion. Unless otherwise stated, glass microscope slides were used as substrates for line morphology characterization. After printing, samples with silver nanoparticle patterns were thermally sintered in a convection oven at 200 °C for 1 h. All glassware (beakers, test tubes, and vials) used for inner-surface printing was made of high-temperature-resistant borosilicate glass.
Computational model setup
The 3D CFD model of the bent nozzle was developed in SolidWorks and simulated using ANSYS Fluent. The fluid domain was extracted using ANSYS SpaceClaim, and boundary conditions were defined for the aerosol inlet, sheath gas inlet, inner wall, outlet, and inclined substrate. The realizable k–ε turbulence model was used to solve the governing equations throughout the flow domain. Parametric numerical studies were performed to investigate the effects of key nozzle parameters (extended length, bending angle, and focusing length) on gas velocity and flow distribution. The discrete phase model (DPM) was used to simulate aerosol particle trajectories during transport, redirection, and deposition, explicitly accounting for particle–fluid interactions within the bent nozzle geometry. The model also enabled the prediction of particle deposition patterns on the inclined substrate.
PDMS honeycomb substrate fabrication
The aluminum alloy master mold for the honeycomb structure was fabricated by CNC machining. Polydimethylsiloxane (PDMS) prepolymer (Sylgard 184, Dow Corning) was mixed with curing agent at a 10:1 mass ratio, degassed under vacuum for 30 min, and cast into the mold. The filled mold was further degassed for 30 min to remove trapped air bubbles and cured at 100 °C for 1 h. The cured PDMS honeycomb structure was demolded and cleaned sequentially with ethanol and deionized water.
Characterization of morphology and electrical properties
The cross-sectional morphology and line width of printed samples were characterized using a Sensofar S neox 3D optical profilometer (Sensofar). The reported line width and height values are averages from three sampling regions across four lines for each parameter set. Dimensional measurements were also performed using an optical microscope (HiROX RH-2000, Hirox Corporation). A commercially available driver board was used for electromagnetic induction coils (Supplementary Fig. 24). Non-contact temperature monitoring of heating coils was performed using a thermal imaging camera (Optris PI 650, Optris GmbH). Cyclic loading–unloading tests were conducted at a constant crosshead speed of 1 mm/s using a universal testing machine (AMETEK LS1, AMETEK Inc.). Real-time resistance of individual sensors was measured using a source meter (Keithley 2400, Tektronix) and recorded using ACurveTracer software. Sensor array signals were collected using a custom-built data acquisition system and processed to generate spatial resistance distribution maps.
Supplementary information
Description of Additional Supplementary Files
Source data
Acknowledgements
The authors thank the Key Laboratory of Aircraft High Performance Assembly at Northwestern Polytechnical University for support in DISP printing equipment.
Author contributions
C.Y., Z.X., and K.Z. conceived the idea and led research efforts. Z.X., W.Y., and Z.Y. performed the experiments. Z.X., K.Z., A.L., D.Y., and H.C. participated in the discussion of experimental results. Z.X. and A.L. carried out the numerical simulation experiment. Z.X. wrote the manuscript and designed the figures. A.L. and Y.N. participated in the design of the figures. C.Y. and Y.L. revised the manuscript and supervised the research. All authors reviewed and commented on the paper.
Peer review
Peer review information
Nature Communications thanks Liam Gillan, Jakub Krzemiński, Lin Zhang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.
Funding
The authors gratefully acknowledge support from the National Key R&D Program of China (Grant No. 2024YFB4609103), the National Natural Science Foundation of China (Grant No. U24A20131).
Data availability
The authors declare that all the data supporting the findings of this study are provided in the manuscript and its supplementary information files. Source data are provided with this paper.
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Contributor Information
Chenglin Yi, Email: yichenglin@nwpu.edu.cn.
Hui Cheng, Email: chenghui@nwpu.edu.cn.
Kaifu Zhang, Email: zhangkf@nwpu.edu.cn.
Supplementary information
The online version contains supplementary material available at https://doi.org/10.1038/s41467-026-76961-y.
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Associated Data
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Supplementary Materials
Description of Additional Supplementary Files
Data Availability Statement
The authors declare that all the data supporting the findings of this study are provided in the manuscript and its supplementary information files. Source data are provided with this paper.
