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- New
- Research Article
- 10.1080/17538947.2026.2663668
- Jul 1, 2026
- International Journal of Digital Earth
- Zhipeng Gui + 10 more
Spatial clustering is a powerful technique for exploratory spatial data analysis and has been widely used in geoscience, economics, and social sciences. However, spatial clustering still faces challenges, such as complex data distribution, parameter sensitivity, and noise interference. In this paper, we propose a robust spatial clustering algorithm by Network Edge Pruning and Internal Connection (NEPIC). Specifically, Delaunay Triangulation Network (DTN) is leveraged to establish the spatial proximity relationships between geographical entities. Four geometric features, edge length, expansion ratio, gravitation consistency, and connection strength, are adopted to distinguish Intra- and Cross-Cluster Edges (ICEs, CCEs). An initial clustering can be obtained through CCE pruning. Internal and boundary points are further identified, and connections involving boundary points are temporarily removed to separate weakly connected clusters. The final clusters are formed by connecting internal points and reassigning each boundary point to the cluster of its nearest internal neighbor. To demonstrate the effectiveness, we compared NEPIC with four typical baselines, including K-means, DBSCAN, ASCDT, and CDC, across six synthetic datasets. The results exhibited its advantage in clustering accuracy and parameter robustness. Moreover, we applied NEPIC in a real-world case to unravel the spatial patterns of global terrorist incidents and interpret the development trends of Syrian terrorism.
- New
- Research Article
- 10.1016/j.ast.2026.111880
- Jul 1, 2026
- Aerospace Science and Technology
- Zeyang Xiao + 5 more
Analysis of the effects of expansion ratio on the structure and infrared radiation characteristics of engine under-expanded plume under different altitudes
- New
- Research Article
- 10.1021/acs.langmuir.6c02144
- Jun 23, 2026
- Langmuir : the ACS journal of surfaces and colloids
- Lei Wang + 4 more
In this study, biodegradable porous poly(ethylene adipate-co-terephthalate) (PEAT) foam materials with excellent properties were prepared using supercritical carbon dioxide foaming technology. First, PEAT with varying molecular weights underwent systematic characterization to understand molecular weight's impact on PEAT properties. Subsequently, the effects of different foaming processes and molecular weight on PEAT foam's foaming performance, solubility, compressive properties, cell structure, and degradation behavior were thoroughly investigated. Experimental results confirmed that PEAT exhibits exceptional foaming capability. Uniform and intact cellular structures can be well retained even after complete aging and shrinkage. All PEAT foams exhibited high expansion ratios, with the maximum reaching approximately 36.69 times. However, due to its linear structure and weak melt strength, the PEAT foam experienced significant shrinkage. Carbon dioxide solubility tests revealed that high-molecular-weight PEAT materials demonstrated superior CO2 dissolution capacity. Notably, compared to the low-molecular-weight PEAT foam, the high-molecular-weight PEAT foam exhibits superior compressive strength and compressive modulus. After 10 compression cycles, it retains excellent compressive strength and elasticity. Furthermore, the PEAT foam demonstrates outstanding biodegradability, achieving a weight loss of 64.03% within a 10 day degradation cycle. These results confirm that the PEAT foam produced via supercritical carbon dioxide foaming technology not only achieves ultrahigh expansion ratios and outstanding compressive properties but also aligns with contemporary societal demands for eco-friendliness and cost-effectiveness. This material combines excellent comprehensive performance with practical application potential, offering prospects for further research and engineering implementation.
- Research Article
- 10.1007/s11604-026-02027-0
- Jun 11, 2026
- Japanese journal of radiology
- Chong Meng + 10 more
Spontaneous isolated superior mesenteric artery dissection (SISMAD) is traditionally diagnosed via CT angiography (CTA) structural features, but localized biological inflammation remains poorly characterized. We aimed to characterize the radial spatial gradient of perivascular adipose tissue (PVAT) in SISMAD and evaluate a composite Vascular Inflammation Index (VII) as an auxiliary indicator of local inflammatory activity. In this retrospective study (2016-2025), 55 patients with SISMAD and 110 symptomatic controls were evaluated. PVAT volume, mean attenuation, and standard deviation (SD) were quantified across cumulative radial shells (0-1 to 0-5mm) from the SMA wall. A composite VII, integrating volume burden, expansion kinetics, and tissue texture, was developed. Multivariable logistic regression and bootstrap analysis (1000 iterations) assessed independent predictors and incremental diagnostic value. Participants (mean age, 50.4 years ± 15.9) included SISMAD patients who had higher white blood cell counts than controls (10.7 ± 5.2 vs. 8.7 ± 4.0 × 109/L; P = 0.017). PVAT volume was significantly higher in SISMAD (0-5mm: 10.1 mm3 ± 5.1 vs. 6.8 mm3 ± 4.0; P < 0.001). SISMAD patients exhibited aggressive radial expansion (expansion ratio: 12.5 vs. 8.6; P = 0.032) and lower 3-mm heterogeneity (22.8 vs. 24.1 HU; P = 0.046), suggesting an edema-induced homogenization effect. The VII achieved an AUC of 0.800 (95% CI 0.723, 0.878) for the identification of SISMAD-associated periarterial involvement and was the independent predictor of SISMAD (OR, 3.23; P < 0.001). Adding VII to the clinical model (Age, Gender, BMI, and WBC) significantly improved performance (AUC, 0.892 vs. 0.857; P = 0.038; increment, 0.035). A seven-day inflammatory plateau was identified post-onset. Automated radial spatial profiling of PVAT reveals a distinct volumetric and kinetic inflammatory signature in SISMAD. The integrated VII provides a quantitative biological assessment that complements structural CTA diagnosis.
- Research Article
- 10.1080/23799927.2026.2687108
- Jun 9, 2026
- International Journal of Computer Mathematics: Computer Systems Theory
- M A Shanooja + 1 more
<bold></bold> This paper proposes a novel symmetric block cipher over the large prime field GF (2521-1) for secure and efficient big data encryption. Unlike traditional cryptosystems using fixed S-boxes, the scheme employs a key-dependent transformation based on multiplicative inverses, removing the need for static lookup tables. Although inversion is generally costly, our optimized method uses a single binary right-shift inversion per block, with subsequent inverses computed via complement and cyclic shifts. This enhances security while maintaining flexibility and scalability. The cipher is spatially efficient, supporting encryption and decryption on the same platform without additional overhead. We assess the performance of the proposed scheme by analyzing its security, processing speed, avalanche effect, memory consumption, throughput, and expansion ratio, all of which yield competitive results. Its scalability is further validated through simulations using a 127-bit block size. Additionally, an in-depth theoretical analysis of security and computational complexity confirms the scheme’s strength and efficiency, making it well-suited for big data encryption.
- Research Article
- 10.1002/adma.202522073
- Jun 1, 2026
- Advanced materials (Deerfield Beach, Fla.)
- Adelais Trapali + 7 more
In the past decade, 3D-printed cellular materials have witnessed an impressive advancement affording a wealth of remarkable mechanical properties, such as negative Poisson's ratio, negative compressibility, and negative coefficient of thermal expansion (CTE). Recent efforts in this field have been increasingly considered 4D-printed metastructures, which leverage shape-morphing properties of stimuli-responsive materials. Here, we introduce a new class of 4D-printed metamaterials based on bistable spin crossover (SCO) molecular materials. These systems synergistically couple dissimilar materials at different size scales to harness mismatched thermomechanical properties-specifically differential thermal expansion and stiffness-to generate large directional deformations upon heating or cooling. Through a combination of theoretical modeling and experimental validation, we demonstrate that our SCO-based 4D-printed structures can achieve programmable motions, including positive and negative expansion. The associated CTE reaches peak values of ca. +14400 and -11400ppm/°C, respectively, more than 10 times greater than those reported in the literature for 3D-printed analogues. This work establishes a versatile and generalizable conceptual strategy for engineering multilevel, hierarchical architectures with programmable functionalities, advancing the design of energy-efficient soft actuators and reconfigurable/adaptive material systems.
- Research Article
- 10.1016/j.crfs.2026.101451
- May 22, 2026
- Current Research in Food Science
- Mengke Li + 7 more
Structured bigel-based foams with tailored textural properties: a bigel-based strategy for cream replacement
- Research Article
- 10.3390/ma19102123
- May 18, 2026
- Materials
- Wei Qiu + 5 more
This study examined the foaming characteristics of asphalt and their effects on the performance of cold recycled mixtures. The expansion ratio and half-life were used to evaluate effects of asphalt type, foaming temperature, and water content. The influence of asphalt content, gradation, cement content, curing time, and mixing water on mechanical properties and water stability was analyzed. The results indicate that asphalt type is the key factor affecting foaming performance. CNOOA asphalt showed optimal foaming at 160 °C with 2% water, achieving an expansion ratio of 27 and a half-life over 30 s. Optimal asphalt contents for gradations A and B are 3.5% and 2.5%, respectively. A 1.5% cement content provides the best performance balance. Dry and wet indirect tensile strengths increased by 91.18% and 205.56% after 3-day curing. The optimal mixing water ranges are 60–90% and 70–80% of optimum moisture content for gradations A and B. Curing time has the most significant influence on performance, followed by cement and asphalt content. This study provides a theoretical basis for optimizing foamed asphalt cold recycling.
- Research Article
- 10.1007/s00417-026-07271-8
- May 9, 2026
- Graefe's archive for clinical and experimental ophthalmology = Albrecht von Graefes Archiv fur klinische und experimentelle Ophthalmologie
- Junya Nagata + 8 more
To determine whether the expansion ratio of the bony nasolacrimal duct on computed tomography (CT) can differentiate malignant lacrimal tumors from benign lesions and primary acquired nasolacrimal duct obstruction (PANDO). The study retrospectively analyzed 19 patients with malignant lacrimal tumors and 195 with unilateral PANDO who visited the Kyushu University Hospital and underwent CT-dacryocystography between April 2018 and March 2023. Of the 195 PANDO cases, 14 that developed a lacrimal sac mass associated with chronic dacryocystitis were defined as the benign mass group. Clinical data including age, sex, tumor location and histopathology, and CT findings of the bony nasolacrimal duct were obtained via medical records. The malignant tumor group included 12 males and 7 females, and the mean age was 54.7 years. The benign mass group included 7 males and 7 females, and the mean age was 67.5 years. The PANDO group included 39 males and 142 females, and the mean age was 70.3 years. Tumor locations in patients with malignant tumors, including overlapping sites, were the lacrimal sac in 17 cases, the nasolacrimal duct in 9, the canaliculus in 2, and the nasal cavity in 1. Histopathological diagnoses were squamous cell carcinoma in 8 cases, malignant lymphoma in 4, adenoid cystic carcinoma in 2, and 1 case each of sebaceous carcinoma, mucoepidermoid carcinoma, apocrine adenocarcinoma, rhabdomyosarcoma, and Langerhans cell histiocytosis. Tumor locations in patients with benign masses were the lacrimal sac in 11 cases, the nasolacrimal duct in 2, and the nasal cavity in 1. Histopathological diagnoses were inflammatory granulation tissue in 11 cases and cyst in 3. Median expansion ratios of the bony nasolacrimal duct (affected side/unaffected side) on axial CT were 167.5% in the malignant tumor group, 123.3% in the benign mass group, and 106.8% in the PANDO group. Malignant lacrimal tumors showed considerably greater expansion of the bony nasolacrimal duct on CT. An expansion ratio of ≥ 150% may be a useful adjunctive marker for distinguishing malignant lacrimal tumors in clinical practice.
- Research Article
- 10.1016/j.carbpol.2026.124996
- May 1, 2026
- Carbohydrate polymers
- Congpei Wu + 5 more
Development of a double-network gel foam based on sodium carboxymethyl cellulose with enhanced extinguishing and re-ignition resistance performance for tank fires.
- Research Article
- 10.3390/pr14091367
- Apr 24, 2026
- Processes
- Xingxing Fan + 5 more
Images of wind turbine blades captured by drones often feature complex backgrounds, and small targets such as minor defects or images have low resolution, leading to reduced recognition rates. To address environments with complex feature backgrounds, this paper proposes the PPS-MSDeim model. Based on the lightweight end-to-end detection framework DEIM-N, it introduces three core innovations to tackle the challenge of detecting small, irregular defects on wind turbine blades against complex backgrounds. First, we design an inverted multi-scale deep separable convolutional module (MDSC). After compressing channels via a bottleneck layer, it concurrently processes 3 × 3, 5 × 5, and 7 × 7 inverted deep separable convolutions. By first fusing channel information and then extracting multi-receiver-field spatial features, this approach enhances the ability to characterize morphologically variable defects while reducing computational overhead. The MDSC is then embedded into the backbone network HGNetv2. Second, we construct a Multi-Scale Feature Aggregation and Diffusion Pyramid Network (MFADPN). Through a Multi-Scale Feature Aggregation Module (MSFAM), it directly fuses features from layers P2 to P5, achieving deep integration of high-level semantics and low-level details. Combining dilated convolutions with expansion ratios of 1, 3, and 5 captures multi-level context, and a Sobel edge branch is introduced to enhance defect contours; subsequently, a feature diffusion operation is performed to distribute the enhanced features back to each level, shortening information paths and preventing signal decay; simultaneously, a high-resolution detection head is added to P2 and the P5 head is removed to improve sensitivity for small object detection. Finally, we propose the PPSformer module to replace the original Transformer encoding layer. It uses patch embedding to convert images into sequences and introduces a multi-head probabilistic sparse self-attention mechanism that focuses only on key-value pairs during attention computation. This design efficiently captures irregularly varying feature information and globally detects data anomalies induced by external defects. This study uses real engineering data sets, and the results show that PPS-MSDeim, based on DEIM, increased mAP@0.5 by 6.7%, reaching 95.1%. mAP@0.5–0.95 increased by 12.0%, reaching 70.1%. This indicates that the proposed method has a significant advantage in detecting defects in wind turbine blades.
- Research Article
- 10.1080/10454438.2026.2660103
- Apr 22, 2026
- Journal of Applied Aquaculture
- Sathyaruban Sutharshiny + 5 more
ABSTRACT The ornamental fish industry faces financial challenges due to expensive ingredients. This study aimed to create cost-effective diets for juvenile guppy and swordtail using 15 local ingredients, reducing reliance on imports and lowering costs. Using linear programming, 18 feed formulations were developed, each with seven raw ingredients meeting nutritional needs. The feed costs varied significantly, with soybean-based diets being the most expensive, whereas, alternative protein sources such as Azolla pinnata (Az) and groundnut cake (GNC) emerged as the most economical substitutes. The inclusion of cassava flour (CF) significantly (p < .05) increased the expansion ratio (2.53 ± 0.09) and water absorption index (4.53 ± 0.10) of feed pellets. The Az diets resulted in pellets with lower bulk density (428.60 ± 18.42 kgm−3) and higher floatability (86.67 ± 5.77%hr−1). Alternative protein sources such as Az and GNC, along with the starch source CF, effectively reduced feed costs to less than $12 (USD) while maintaining physical and nutritional quality. Use of cost-effective ingredients (Az, GNC, and CF) not only lowers feed production costs but also satisfies the nutritional needs, thereby offering a sustainable solution for the ornamental fish industry globally.
- Research Article
- 10.3390/ma19081592
- Apr 15, 2026
- Materials (Basel, Switzerland)
- Saurabh Tiwari + 4 more
The hole expansion ratio (HER) is a critical formability metric for advanced high-strength steels (AHSS) in automotive applications; however, its experimental determination is costly and time-consuming. This study presents a machine learning framework for HER prediction using physics-informed synthetic data generation to address data scarcity challenges. A dataset of 300 AHSS conditions was generated based on validated empirical relationships from the literature, incorporating chemical composition, microstructure fractions, and mechanical properties. Multiple machine learning algorithms were evaluated, with the optimized Gradient Boosting model achieving excellent predictive performance on an independent test set (R2 = 0.80, RMSE = 5.81%, MAE = 4.93%). The feature importance analysis revealed physically meaningful rankings, with the ultimate tensile strength dominating (40.9%), followed by the bainite volume fraction (15.1%), martensite volume fraction (14.7%), and strain hardening exponent (12.4%). These rankings align with the established metallurgical understanding, thereby validating our synthetic data approach. The results demonstrate that machine learning models trained on physics-informed synthetic data can accurately predict the HER values with errors comparable to the experimental variability, providing a practical tool for accelerated AHSS design and optimization in automotive applications.
- Research Article
- 10.1007/s00894-026-06692-w
- Apr 6, 2026
- Journal of molecular modeling
- Outhman Abbassi + 4 more
The discovery of semiconductor materials for photovoltaic and optoelectronic applications is limited by the computational cost of DFT calculations and the requirement for complete 3D crystal structures. Existing deep learning approaches, including graph neural networks (CGCNN, MEGNet, ALIGNN) and transformer architectures (Matformer, CrysCo), require structural information, limiting their applicability to hypothetical materials of which only the composition is known. We developed MGPP-DL (Materials Graph Property Prediction via Deep Learning), a structure-agnostic approach that predicts the band gap and formation energy directly from the chemical composition of the material structure. Evaluated on 389,000 materials from the Materials Project, MGPP-DL achieves unprecedented accuracy with mean absolute errors of 0.0178 eV/atom for formation energy and 0.0619 eV for band gap, representing a 67% improvement over state-of-the-art models. The model demonstrates a robust generalization (R = 0.9869 and 0.9182, respectively) and provides an acceleration of 10,000 par rapport à la DFT, allowing the high-throughput screening of millions of hypothetical compositions. Chemical compositions are represented as graphs of completely connected elements with nodes encoding 33 elementary properties extracted via Pymatgen, including electronegativity, atomic radius, and stoichiometric coefficients. Three GNN layers with message passing refine the embeddings of elements (64-dimensional) by multi-scale aggregation. GNN output is processed by two EfficientNet blocks (dimension 128, expansion ratio 4) with squeeze-and-excitation attention mechanisms (reduction ratio 0.25). The training employed the optimizer Adam (learning rate 0.001), MSE loss, dropout (0.3), and batch standardization over 40 epochs (batch size 32). The Materials Project dataset (DFT-GGA, functional PBE) has been divided by scaffold methodology (70/15/15) to ensure structural diversity. Python 3.10.12, TensorFlow 2.12.0/Keras (CUDA 11.8), trained on NVIDIA RTX 3080 GPU (10 GB VRAM), with Pymatgen 2023.8.10, NumPy 1.24.3, Pandas 2.0.3, Scikit-learn 1.3.0, Matplotlib 3.7.2, and Seaborn 0.12.2.
- Research Article
- 10.1093/ejo/cjag014
- Apr 3, 2026
- European journal of orthodontics
- Gustavo Hauber Gameiro + 2 more
Long-term neuromuscular effects of rapid maxillary expansion (RME) for functional posterior crossbite (FPCB) remain unclear. This prospective longitudinal study evaluated RME effects on masticatory muscle electromyographic (EMG) activity and transverse skeletal/dental dimensions in children with FPCB. Seventeen FPCB patients (mean age 8.8 years) treated with Hyrax expanders and 15 age-matched controls with normal occlusion were evaluated. Surface EMG activity, dental casts, and posteroanterior cephalograms were recorded at baseline (T1) and at the final evaluation (T2), with a mean interval of 10.6 months between assessments, encompassing the active expansion phase followed by 6 months of removable retention. EMG analysis showed significantly increased masseter and temporalis activity after RME, indicating improved neuromuscular function. Cephalometric measurements revealed significant increases in maxillary skeletal width and maxillo-mandibular skeletal ratio without mandibular changes. Skeletal expansion (2.97 mm) represented 51% of the total maxillary intermolar width increase (5.86 mm), demonstrating favorable skeletal contribution. The maxillary-to-mandibular intermolar ratio normalized compared with controls. Small sample size, single-center design, and 10-month follow-up duration may limit generalizability and long-term stability assessment. RME significantly improves maxillary transverse dimensions and masticatory muscle activity in young FPCB patients. Early treatment optimizes skeletal-to-dental expansion ratio and promotes favorable stomatognathic system development.
- Research Article
- 10.1063/5.0314282
- Apr 1, 2026
- Physics of Fluids
- Yuki Yamahata + 2 more
This study experimentally investigates the relationship between the pressure change (ΔPe) at a sudden expansion and the Reynolds number for liquid flows in rectangular microchannels with different expansion ratios. In the experiments, water and an aqueous glycerol solution with various mass concentrations were used as test liquids, and detailed pressure distributions near the sudden expansion section were measured to determine the ΔPe under laminar to turbulent flow conditions. The experimental results showed that ΔPe increases with Reynolds number; however, the increasing trend is affected by the flow conditions both upstream and downstream of the expansion as well as by the reattachment length of the recirculation region formed downstream of the expansion. The Borda–Carnot equation was found to underestimate ΔPe, particularly in the laminar flow regime. To address this, a prediction model for ΔPe was developed by considering both the velocity distribution and the reattachment length effects. The model parameters were determined by applying the least-squares method, with supporting findings from previous studies for the momentum correction factor, Darcy friction factor, and the reattachment length. The proposed model successfully predicted ΔPe within ±12% on average over a wide Reynolds number range from laminar to turbulent flow regimes. These results demonstrate that the model provides a reliable basis for evaluating expansion losses in microchannels and has potential applicability to the design of microfluidic and microreactor systems.
- Research Article
- 10.28991/esj-2026-010-02-021
- Apr 1, 2026
- Emerging Science Journal
- Qandeel Fatima Gillani + 3 more
This study presents the development of a low-toxicity, high-performance intumescent fire-retardant coating (IFRC) through a hybrid epoxy binder doped with Mg, Si, Al, and P particles. The objective was to improve thermal stability and char cohesion and reduce the toxic aromatic emissions typically released from bisphenol-A epoxy systems during combustion. Modified epoxy resins were prepared by dispersing Mg(OH)₂ and incorporating hydroxyl-terminated PDMS, followed by formulation with APP, melamine, expandable graphite, PER, and nano-alumina. Comprehensive analyses using FTIR, ¹³C NMR, DSC, TGA, SEM–EDS, TEM, XRD, and GC–MS, along with ISO-834 furnace and ASTM E-119 flame tests, were employed to evaluate chemical structure, thermal behavior, char morphology, and fire performance. The optimized formulation produced a dense Mg–Al–silicate–phosphate char network, achieved a 6.1× expansion ratio, limited backside steel temperature to 227°C, and retained 36% char at 800°C, which significantly outperformed the unmodified epoxy system. GC–MS confirmed a substantial (≈53%) reduction in toxic volatile emissions. A machine-learning model further validated char compactness with >94% classification accuracy. Collectively, the results demonstrate that synergistic inorganic–siloxane modification offers a scalable, halogen-free pathway to next-generation epoxy-based IFRCs with enhanced fire resistance and markedly lower toxicity.
- Research Article
- 10.1088/1361-665x/ae509b
- Apr 1, 2026
- Smart Materials and Structures
- Z J Dai + 2 more
Abstract Metamaterials with thermal contraction and auxetic effect can effectively prevent irreversible damage caused by thermal stress and impact in engineering applications, playing a crucial role in aerospace and other fields. Therefore, we propose a novel double-negative metamaterial structure by combining triangular arrowhead structures and triangular thermal metamaterial structures, which can achieve thermal expansion coefficient over a wide range from -167×10-6 to 162×10-6 K-1, and Poisson's ratios range from -1.7 to 1.95. Furthermore, we study the impact of the geometric parameters of the designed structures on the coefficient of thermal expansion (CTE), elastic modulus, and Poisson's ratio of the metamaterial by using the stiffness matrix method (SMM). Results show that changing the included angle of the re-entrant triangle of the structure can change the sign of thermal expansion coefficient and Poisson's ratio. This paper provides new ideas and methods for designing mechanical metamaterials with anisotropic adjustable thermal expansion coefficients and Poisson's ratios.
- Research Article
- 10.1016/j.ijhydene.2026.154408
- Apr 1, 2026
- International Journal of Hydrogen Energy
- Hiroaki Ono + 1 more
A data-driven decision support system for high-pressure hydrogen-induced rubber volume expansion testing: Part I. A classification model for predicting test validity
- Research Article
- 10.47176/jafm.19.4.3912
- Apr 1, 2026
- Journal of Applied Fluid Mechanics
- Z X Liu + 5 more
Variable nozzle turbine can enhance the transient response of engine through the regulation of nozzle opening. Under the operating condition characterized by high expansion ratio and small nozzle opening, strong unsteady shock waves tend to develop at the trailing edge of the nozzle blades. These shock waves introduce significant periodic loadings, which can result in high-cycle fatigue and eventual fracture of the rotor blades. This study investigates the unsteady flow characteristics within a representative variable nozzle turbine, with particular focus on the temporal and spatial evolutions of shock waves and their dynamic coupling with the rotor-stator system. It is found that both the intensity and the spatial structure of the shock waves exhibit periodic variation in response to rotor-induced disturbances. The pressure disturbance with a frequency of 10 kHz induces significant blade loading at 50% span of the rotor blade leading edge, whose maximum root mean square (RMS) amplitude is 17.45 kPa. It substantially increases the probability of high-cycle fatigue for the rotor blade leading edge. These findings can offer meaningful guidance for optimizing and controlling shock waves in variable nozzle turbines.