Average Degree Research Articles

Measuring Entanglement in Physical Networks.

The links of a physical network cannot cross, which often forces the network layout into nonoptimal entangled states. Here we define a network fabric as a two-dimensional projection of a network and propose the average crossing number as a measure of network entanglement. We analytically derive the dependence of the average crossing number on network density, average link length, degree heterogeneity, and community structure and show that the predictions accurately estimate the entanglement of both network models and of real physical networks.

Typical alien invasive aquatic-plant species changed the stability rather than the diversity of plankton community in fresh water

Alien invasive aquatic-plant (AIA) species are severely threatening the aquatic ecosystems worldwide, especially biodiversity. Although plankton have been used to monitor and address biodiversity, some gaps remain in understanding of the relationships between plankton communities and AIA species. Here, the effects of two typical AIA species (Pistia stratiotes and Eichhornia crassipes) on plankton communities in freshwater with a native plant Vallisneria natans were investigated using a 50-d microcosm experiment. Results showed that AIA species significantly decreased water pH and dissolved oxygen while increased oxidation-reduction potential (p < 0.05). AIA species, especially P. stratiotes, significantly inhibited dry biomass accumulation in V. natans by an average rate of 39.0 %, decreased water pH by up to 14.62 %, and increased aboveground lengths and chlorophyll contents of V. natans by up to 36.2 % and 63.7 % (p < 0.05), respectively. These species further modified the growth strategy of V. natans from dry biomass accumulation to aboveground elongation. Although the AIA species did not alter plankton diversity (p > 0.05), but they changed their dominant species, functional communities (e.g., Groups D and TB), and co-occurrence networks. P. stratiotes decreased the average degree of the networks by 12.37–19.02 % and the graph density by 10.53–14.47 %, while E. crassipes decreased the modularity of the networks by 10.24 % compared with the control (without AIA species), respectively. Overall, AIA species inhibited the growth of V. natans and decreased the stability of plankton communities and their resistance to environmental disturbances. These findings enhance our understanding of how AIA species affect the growth of native plants and variations in plankton communities, thereby providing a theoretical basis for improving the ecological function and safety of freshwater.

Physical model case study: treatment effect of soft ground by vacuum preloading combined with liquid bag pressurization method

Vacuum preloading and composite ground reinforcement are commonly used methods for reinforcing soft soil, but there is a lack of integrated design method for vacuum preloading combined with composite ground. This case study introduces an innovative approach that combines vacuum preloading with liquid bag pressurization to achieve the integrated design of consolidation drainage method and composite ground reinforcement, which is different from the reported air bag pressurization. To illustrate the effectiveness of this method. Model tests were carried out to analyze the variation of water discharge, pore water pressure, ground settlement, and average consolidation degree in the process of vacuum consolidation. The study investigated the water content, undrained shear strength, and ground bearing capacity of composite ground after ground treatment. A correlation between average undrained shear strength and characteristic value of ground-bearing capacity was established to evaluate and predict the treatment effect of composite ground. Research shows that compared with traditional vacuum preloading, the undrained shear strength can be increased by 13.78%–65.08%, and the characteristic value of bearing capacity for the composite ground can be enlarged by 2.3–4 times. These results indicate that the vacuum preloading combined with liquid bag pressurization can significantly improve reinforcement effect on soft ground.

Evolution of passing network in the Soccer World Cups 2010–2022

ABSTRACT This study investigates the evolution of passing networks (PN) at both team and player levels in the FIFA World Cups (WC) from 2010 to 2022. Analyzing 256 matches (7328 player observations) using a multiple-camera tracking system across four WCs, we considered six playing positions: goalkeeper (n = 521), central defender (n = 1192), fullback (n = 1223), midfielder (n = 2039), winger (n = 1320), and central forward (n = 1033). We used 17 network metrics and considered contextual variables such as team formation, and team ranking. Linear mixed-effect models analyzed differences in team and player PN parameters by year and team strength. Results showed a shift from possession-play to direct-play from the 2010 to 2018 WCs, with possession-play returning in 2022. Specifically, high- and low-quality teams significantly decreased their density, average degree (AD), modularity, and average path length in 2018 (p < 0.05). High-quality teams showed increased density, AD, and average weighted degree in 2022 (p < 0.05). Midfielders and central forwards exhibited significantly lower centrality parameters, whereas central defenders and goalkeepers showed increased centrality parameters (p < 0.05). This study highlights the evolutionary trends of passing relationships from a network analysis perspective over twelve years, providing insights into the changing dynamics of team interactions and positional prominence in elite soccer.

Exploration on Advanced Intelligent Algorithms of Artificial Intelligence for Verb Recognition in Machine Translation

This article aimed to address the problems of word order confusion, context dependency, and ambiguity in traditional machine translation (MT) methods for verb recognition. By applying advanced intelligent algorithms of artificial intelligence, verb recognition can be better processed and the quality and accuracy of MT can be improved. Based on Neural machine translation (NMT), basic attention mechanisms, historical attention information, dynamically obtain information related to the generated words, and constraint mechanisms were introduced to embed semantic information, represent polysemy, and annotate semantic roles of verbs. This article used the Workshop on MT (WMT), British National Corpus (BNC), Gutenberg, Reuters Corpus, and OpenSubtitles corpus, and enhanced the data in the corpora. The improved NMT model was compared with traditional NMT models, Rule-Based MT (RBMT), and Statistical MT (SMT). The experimental results showed that the average verb semantic matching degree of the improved NMT model in five corpora was 0.85, and the average Bilingual Evaluation Understudy (BLEU) score in five corpora was 0.90. The improved NMT model in this article can effectively improve the accuracy of verb recognition in MT, providing new methods for verb recognition in MT.

Recovering sustainability in the Brazilian Amazon: an analysis of engineering courses from the perspective of innovation and sustainability

Purpose This study aims, from the perspective of the recovery of sustainability, to develop a framework on sustainability and innovation in the formation of engineers in the courses of Engineering in the Brazilian Amazon. Design/methodology/approach For this work, a quantitative approach was adopted in the research process. A survey instrument was developed from the main evidence in the literature, the electronic instrument in Google Forms, was sent in the period from November 2022 to February 2023 to engineering students from public institutions in the Brazilian eastern Amazon, who had 80% of the course completed and graduates. Findings Of the students and graduates who responded to the survey, 58% are male and 42% female, with an average age of 24 years, 72% who have the 8th semester, 28% graduates. As for the practices, they stand out with the highest average degree of agreement in the innovation aspect formation of partnerships and fostering creativity and innovation; in the sustainability aspect the study of sustainability helps to understand the environmental, social and economic challenges and importance of training for sustainability and innovation; in the sustainable recovery aspect, the interaction between university and local community and new research can contribute to the recovery of sustainability and in the SDGs 6 and 8. Originality/value This paper presents the perceptions of engineering students and graduates from the Brazilian Amazon, which is considered one of the most strategic regions for the country and internationally in terms of environmental challenges. The main evidence shows that there is a need to adapt academic curricula, seeking to focus on projects that promote participation and the creation of trends aimed at social problems and the current demands of the society in which they are inserted.

Comparison of Short Uncemented Metaphyseal Stem and Long-Stem Reverse Shoulder Arthroplasty in Proximal Humerus Fractures: Preliminary Study at 2-Year Follow-Up.

Introduction: In the last few years, short metaphyseal-socket prosthetic humeral stems have been introduced for reverse shoulder arthroplasty (RSA). A short stem may have advantages in humeral force distribution, reducing shear stress and preserving bone stock, keeping in mind the need for possible future revision surgery. The main objective of our study was to validate the use of a short stem prosthesis in the surgical treatment of humeral fractures by comparing clinical and radiological outcomes of our studied implant with those obtained with the use of traditional long-stem implants. Methods: In this multicentric, controlled prospective study, 125 patients with proximal three- or four-fragment humerus fractures were selected and treated with RSA. A short stem was used in group A (n = 53, mean age: 75.6 ± 5.6 years old), and a long stem was used in group B (n = 72, mean age: 71.76 ± 3). Active range of motion (ROM), Constant score (CS), Quick DASH, American Shoulder and Elbow Surgeons Shoulder (ASES) score, and Visual Analog Scale (VAS) scores were collected and analyzed at 2 years mean follow-up, as well as humeral and glenoid bone resorption (sum Inoue scores and Sirveaux scores were used). Results: No statistically significant differences were observed between group A and B in ROM, Constant score (51.69 ± 15.8 vs. 53.46 ± 15.96, p > 0.05), Quick DASH (31.5 ± 21.81 vs. 28.79 ± 13.72, p = 0.85), ASES (82.53 ± 17.79 vs. 84.34 ± 15.24, p = 0.57), or the VAS (0.53 ± 1 vs. 0.56 ± 1.07, p = 0.14) at the final follow-up. No statistically significant differences were found in the radiographic parameters between the two groups. No statistically significant differences were found for the average degree of humeral and glenoid bone resorption either. Conclusions: The use of a short metaphyseal-socket stem can be considered a safe, effective, and feasible option in reverse shoulder arthroplasty for treating proximal humerus fractures. Our results are encouraging, with no statistically significant differences identified between the proposed treatment and traditional long stems.

Dynamics of a susceptible-infected-recovered model on complex networks with interregional migration.

We present a susceptible-infected-recovered model based on a dynamic flow network that describes the epidemic process on complex metapopulation networks. This model views population regions as interconnected nodes and describes the evolution of each region using a system of differential equations. The next-generation matrix method is used to derive the global basic reproduction number for three cases: a general network with homogeneous infection rates in all regions, a fully connected network, and a star network with heterogeneous infection and recovery rates. For the homogeneous case, we show that this global basic reproduction number is independent of the migration rates between regions. However, the rate of convergence of each region to an equilibrium state exhibits a much larger variance in random (Erdős-Rényi) networks compared to small-scale (Barabási-Albert) networks. For the general heterogeneous case, we report interesting results, namely that the global basic reproduction number decays exponentially with respect to the smallest nonzero Laplacian eigenvalue (algebraic connectivity). Furthermore, we demonstrate both analytically and numerically that as the network's algebraic connectivity increases, either by increasing the average node degree of each region or the global migration rate, the global basic reproduction number decreases and converges to the ratio of the average local infection rate to the average local recovery rate, meaning that the lower bound of the global basic reproduction rate does not equal the mean of local basic reproduction rates.

One‐dimensional consolidation analysis of layered soil with exponential flow under continuous drainage boundary

AbstractTo comprehensively consider the influence of boundary conditions, non‐Darcy flow, load forms, and soil stratification on soil consolidation, a one‐dimensional soil consolidation equation is established. By subdividing the soil layer and employing time discretization, the nonlinear consolidation equation is linearized, resulting in an analytical solution for layered soil foundation at any given time. Subsequently, an iterative approach for time solution is employed to obtain a semi‐analytical solution. The correctness of the solution is verified by comparison with solutions based on Darcy's flow and the semi‐analytical method under traditional drainage boundary conditions. Subsequently, the influence of interface parameters, loading conditions, flow index, and other factors on consolidation characteristics is analyzed. The results indicate that higher interface parameter values for continuous drainage boundaries correspond to faster average consolidation rates for stratified soil foundations, while these parameters have little effect on the time required for complete consolidation of the soil layers. Improved boundary drainage performance amplifies the influence of exponential flow on pore water pressure and average consolidation degree. Conversely, poor boundary drainage performance diminishes the impact of exponential flow on soil consolidation, rendering it negligible. Moreover, faster loading rates accentuate the influence of the flow index on the average consolidation degree defined by pore pressure.

Superiority of native soil core microbiomes in supporting plant growth

Native core microbiomes represent a unique opportunity to support food provision and plant-based industries. Yet, these microbiomes are often neglected when developing synthetic communities (SynComs) to support plant health and growth. Here, we study the contribution of native core, native non-core and non-native microorganisms to support plant production. We construct four alternative SynComs based on the excellent growth promoting ability of individual stain and paired non-antagonistic action. One of microbiome based SynCom (SC2) shows a high niche breadth and low average variation degree in-vitro interaction. The promoting-growth effect of SC2 can be transferred to non-sterile environment, attributing to the colonization of native core microorganisms and the improvement of rhizosphere promoting-growth function including nitrogen fixation, IAA production, and dissolved phosphorus. Further, microbial fertilizer based on SC2 and composite carrier (rapeseed cake fertilizer + rice husk carbon) increase the net biomass of plant by 129%. Our results highlight the fundamental importance of native core microorganisms to boost plant production.

Plastic particles and fluorescent brightener co-modify Chlorella pyrenoidosa photosynthesis and a machine learning approach predict algae growth

Global release of plastics exerts various impacts on the ecological cycle, particularly on primary photosynthesis, while the impacts of plastic additives are unknown. As a carrier of fluorescent brightener, plastic particles co-modify Chlorella pyrenoidosa (C. pyrenoidosa) growth and its photosynthetic parameters. In general, adding to the oxidative damage induced by polystyrene, fluorescent brightener-doped polystyrene produces stronger visible light and the amount of negative charge is more likely to cause photodamage in C. pyrenoidosa leading to higher energy dissipation through conditioning than in the control group with a date of ETR (II) inhibition rate of 33 %, Fv/Fm inhibition rate of 8.3 % and Pm inhibition rate of 48.8 %. To elucidate the ecological effect of fluorescent brightener doping in plastic particles, a machine learning method is performed to establish a Gradient Boosting Machine model for predicting the impact of environmental factors on algal growth. Upon validation, the model achieved an average fitting degree of 88 %. Relative concentration of plastic particles and algae claimed the most significant factor by interpretability analysis of the machine learning. Additionally, both Gradient Boosting Machine prediction and experimental results indicate a matching result that plastic additives have an inhibitive effect on algal growth.

The coupled awareness-epidemic dynamics with individualized self-initiated awareness in multiplex networks

The outbreak of an epidemic often stimulates the generation of public awareness about epidemic prevention. This heightened awareness encourages individuals to take proactive protective measures, thereby curbing the transmission of the epidemic. Previous research commonly adopts an assumption that each individual has the same probability of awakening self-protection awareness after infection. However, in the real-world process, different individuals may generate varying awareness responses due to the differences in the amount of information received. Therefore, in this study, we first propose a coupled awareness-epidemic spreading model, where the self-initiated awareness of each individual can be influenced by the number of aware neighbors. Subsequently, we develop a Micro Markov Chain Approach to analyze the proposed model and explore the effects of different dynamic and structural parameters on the coupled dynamics. Findings indicate that individual awareness awakening can effectively promote awareness diffusion within the proposed coupled dynamics and inhibit epidemic transmission. Moreover, the influence of awareness diffusion on epidemic transmission exhibits a metacritical point, from which the epidemic threshold increases with the increase in the awareness diffusion probability. The research findings also suggest that the increase in the average degree of virtual-contact networks can reduce the value of the metacritical point, while the change in the average degree of the physical-contact networks does not affect the metacritical point. Finally, we conduct extensive experiments on four real networks and obtain results consistent with the above conclusions. The systematic research findings of this study provide new insights for exploring the interaction between individual awareness and epidemic transmission in the real world.

Ultrasoft state of microquasar Cygnus X-3: X-ray polarimetry reveals the geometry of the astronomical puzzle

Cygnus X-3 is an enigmatic X-ray binary that is both an exceptional accreting system and a cornerstone for population synthesis studies. Prominent X-ray and radio properties follow a well-defined pattern, and yet the physical reasons for the state changes observed in this system are not known. Recently, the presence of an optically thick envelope around the central source in the hard state was revealed using the X-ray polarization data obtained with the Imaging X-ray Polarimetry Explorer (IXPE). In this work we analyse IXPE data obtained in the ultrasoft (radio quenched) state of the source. The average polarization degree (PD) of 11.9 ± 0.5% at a polarization angle (PA) of 94° ±1° is inconsistent with the simple geometry of the accretion disc viewed at an intermediate inclination. The high PD, the blackbody-like spectrum, and the weakness of fluorescent iron line imply that the central source is hidden behind the optically thick outflow, similar to the hard-state geometry, and its beamed radiation is scattered, by the matter located along the funnel axis, towards our line of sight. In this picture the observed PD is directly related to the source inclination, which we conservatively determine to lie in the range 26° &lt; i &lt; 28°. Using the new polarimetric properties, we propose a scenario that can be responsible for the cyclic behaviour of the state changes in the binary.

Information Inputs and Outputs of Quality Planning Processes and the Possibilities of Their Improvement through Digital Transformation

Purpose: The article aims to identify the key information inputs of quality planning processes, analyse their availability in the company practice, and propose framework measures for their effective digital transformation. Methodology/Approach: The quality planning process was divided into 10 sub-processes, and a total of 90 information inputs and outputs were identified. Based on the importance evaluation 20 most important information inputs of quality planning were determined. The average digitalisation degree and maturity of the used storage systems were analysed in company practice for these information inputs. The average degree of availability of these inputs was then evaluated, leading to framework proposals for improvement. Findings: The analysis revealed that many key information inputs of quality planning processes are not sufficiently available in practice. Consequently, framework measures to improve the availability of information for quality planning processes were proposed. Research Limitation/Implication: This article provides valuable insights for companies aiming to enhance competitiveness through more effective quality planning in accordance with Industry 4.0 principles. Originality/Value of paper: The paper identifies the information inputs and outputs of quality planning processes and offers framework suggestions for effectively incorporating digital transformation into these processes.

An Analysis of The Agribusiness Communication Structure of Dairy Cattle Farmers: The Case Study of The Tegal Mandiri Farmer Group

Problems in dairy cattle agribusiness require attention not only from the farmers themselves but also from farmer organizations. To understand the communication patterns among group members in the agribusiness sector, including the exchange of information related to cattle production, animal health, and wholesale prices, it is essential to analyze the communication network of the dairy cattle farmer group. This network is significant because it serves as the hub of organizational communication, both internally and externally. This research seeks to analyze the communication structure of the dairy cattle farmer group and investigate the relationship between the respondent characteristics and the communication networks within the Tegal Mandiri farmer group in Bogor Regency. The Social Network Analysis (SNA) method and a quantitative approach were used to conduct the research, with the Tegal Mandiri farmer group members in Bogor Regency as the unit of analysis. The group communication structure was analyzed using degree and closeness centrality, and the relationship between respondent characteristics and the communication network was analyzed using Spearman rank correlation. IBM SPSS Statistics 26 and UCINET 6 were the tools used for analysis. The study revealed that 1) the average degree centrality of the group was between 1.00 and 2.20, and the average closeness centrality was between 400.00 and 558.10. 2) The respondents' characteristics of farmers were significantly related to the communication networks within the group. The study found that the communication structure of the Tegal Mandiri farmer group exhibited low connectivity and an ineffective coordination forum

Depth-dependent responses of soil bacterial communities to salinity in an arid region

Soil salinization adversely affects soil fertility and plant growth in arid region worldwide. However, as the drivers of nutrient cycling, the response of microbial communities to soil salinization is poorly understood. This study characterized bacterial communities in different soil layers along a natural salinity gradient in the Karayulgun River Basin, located northwest of the Taklimakan desert in China, using the 16S rRNA Miseq-sequencing technique. The results revealed a significant filtering effect of salinity on the bacterial community in the topsoil. Only the α-diversity (Shannon index) in the topsoil (0–10 cm) significantly decreased with increasing salinity levels, and community dissimilarity in the topsoil was enhanced with increasing salinity, while there was no significant relationship in the subsoil. BugBase predictions revealed that aerobic, facultatively anaerobic, gram-positive, and stress-tolerant bacterial phenotypes in the topsoil was negatively related to salinity. The average degree and number of modules of the bacterial co-occurrence network in the topsoil were lower under higher salinity levels, which contrasted with the trends in the subsoil, suggesting an unstable bacterial network in the topsoil caused by higher salinity. The average path length among bacterial species increased in both soil layers under high salinity conditions. Plant diversity and available nitrogen were the main drivers affecting community composition in the topsoil, while available potassium largely shaped community composition in the subsoil. This study provides solid evidence that bacterial communities adapt to salinity through the adjustment of microbial composition based on soil depth. This information will contribute to the sustainable management of drylands and improved predictions and responses to changes in ecosystems caused by climate change.

Potassium persulfate enhances humification of chicken manure and straw composting: The perspective of rare and abundant microbial community structure and ecological interactions

Improper disposal of organic solid waste results in serious environmental pollution. Aerobic composting provides an environmentally friendly treatment method, but improving humification of raw materials remains a challenge. This study revealed the effect of different concentrations of potassium persulfate (PP) on humification of chicken manure and straw aerobic composting and the underlying microbial mechanisms. The results showed that when 0.6 % PP was added (PPH group), humus and the degree of polymerization were 80.77 mg/g and 2.52, respectively, which were significantly higher than those in 0.3 % PP (PPL group). As the concentration of PP was increased, the composition of rare taxa (RT) changed and improved in evenness, while abundant taxa (AT) was unaffected. Additionally, the density (0.037), edges (3278), and average degree (15.21) in the co-occurrence network decreased compared to PPL, while the average path (4.021) and modularity increased in PPH. This resulted in facilitating the turnover of matter, information, and energy among the microbes. Interestingly, cooperative behavior between microorganisms during the maturation period (24–60 d) occurred in PPH, but competitive relationships dominated in PPL. Cooperative behavior was positively correlated with humus (p < 0.05). Because the indices, such as higher degree, betweenness centrality, eigenvector centrality, and closeness centrality of the AT, were located in the microbial network center compared to RT, they were unaffected by the concentration of PP. The abundance of carbohydrate and amino acid metabolic pathways, which play an important role in humification, were higher in PPH. These findings contribute to understanding the relative importance of composition, interactions, and metabolic functionality of RT and AT on humification during chicken manure and straw aerobic composting under different concentrations of PP, as well as provide a basic reference for use of various conditioning agents to promote humification of organic solid waste.

Lattice-Cluster-Theory-Informed Cross-Fractionation Chromatography Revealing Degree of Crystallinity of Single Macromolecular Species.

The relationship between macromolecular architecture and crystallization properties is a relevant research topic in polymer science and technology. The average degree of crystallinity of disperse polymers is a well-studied quantity and is accessible by various experimental methods. However, how the different macromolecular species contribute to the degree of crystallinity and, in particular, the relationship between a certain macromolecular architecture and the degree of crystallinity are not accessible today, neither experimentally nor theoretically. Therefore, in this work, a lattice cluster theory (LCT)-informed cross-fractionation chromatography (CFC) approach is developed to access the degree of crystallinity of single and nonlinear macromolecular species crystallizing from solution. The method entangles high-throughput experimental data from CFC with the LCT for semicrystalline polymers to predict the degree of crystallinity of polymer species with different molecular weights and branching. The approach is applied to a linear low-density polyethylene (ethylene/1-octene copolymer) and a high-density polyethylene, which have specific and different bivariate distributions. The degree of crystallinity of individual macromolecular species of these polymer samples is calculated, and the predicted average degree of crystallinity is compared with experimental measurements, thus successfully validating the approach. Furthermore, the average segment length between branches is introduced as a characteristic molecular feature of branched polyethylene, and its relationship with the degree of crystallinity of certain species is established.

Probability Distribution of Arithmetic Average of China Aviation Network Edge Vertices Nearest Neighbor Average Degree Value and Its Evolutionary Trace Based on Complex Network

Probability Distribution of Arithmetic Average of China Aviation Network Edge Vertices Nearest Neighbor Average Degree Value and Its Evolutionary Trace Based on Complex Network

Experimental study on granule trajectory tracking for the EPB shield tunneling in sandy cobble stratum

An investigation into the movement characteristics of granules during Earth Pressure Balance (EPB) shield tunneling contributes significantly to understanding the interaction between the shield machine and the soil. This understanding also enables researchers to gain deeper insights into the cutting and guiding effects of the shield cutterhead on the soil, thus providing a scientific basis for optimizing shield tunneling parameters and cutterhead designs. To achieve this, indoor model shield tunneling experiments were conducted using independently developed shield tunneling equipment and spatial positioning devices developed by our research group. The research investigated the spatial movement trajectories, radial diffusion, and axial movement characteristics of granules at the face subjected to the action of a spoke-type cutterhead. Furthermore, the study proposes the use of average diffusion degree and movement rates of granules as metrics for evaluating the cutting and steering performance of the cutterhead. The influence of cutterhead rotational speed and advance rate on the movement characteristics of granules was further explored based on these two indicators. The study’s findings reveal the following: (1) Granules at the face predominantly exhibit a spiral movement trajectory when the EPB shield tunneling machine operates in a dynamic equilibrium state. (2) The cutting and steering performance of the cutterhead’s various areas is enhanced progressively from the center to the outer edge, as evidenced by a gradual decrease in the average diffusion degree of granules and an increase in the average axial movement rate (AMR). (3) The AMR and average diffusion degree of granules are influenced by both the rotational speed of the cutterhead and the advance rate of the shield machine. Optimal matching of the rotational speed and advance rate maximizes the average AMR of granules, minimizes the average diffusion degree, reduces the torque on the cutterhead to its lowest point, and consequently, optimizes the efficiency of shield tunneling. This research presents a novel perspective and methodology for understanding the movement characteristics of granules during shield tunneling operations. The outcomes of this study provide valuable insights for the structural design of shield machine cutterheads and the optimization of tunneling parameters.