Search Results (44)

We investigate the asymptotic maximum value and convergence of the Voronoi Entropy (VE) for a 2D random point process (S = 1.690 ± 0.001) and point sets with long-range order characterized by hyperuniformity. We find that for the number of polygons of about n > 100, the VE range is between S = 0 (ordered set of seed points) and S = 1.69 (random set of seed points). For circular regions with the dimensionless radius R normalized by the average distance between points, we identify two limits: Limit-1 (R = 2.5, 16 ± 6 points) is the minimum radius, for which it is possible to construct a Voronoi diagram, and Limit-2 (R = 5.5, 96 ± 6 points) at which the VE reaches the saturation level. We also discuss examples of seed point patterns for which the values of VE exceed the asymptotic value of S > 1.69. While the VE accounts only for neighboring polygons, covering the 2D plane imposes constraints on the number of polygons and the number of edges in polygons. Consequently, unlike the conventional Shannon Entropy, the VE captures some long-range order properties of the system. We calculate the VE for several hyperuniform sets of points and compare it with the values of exponents of collective density variables characterizing long-range correlations in the system. We show that the VE correlates with the latter up to a certain saturation level, after which the value of the VE falls to S = 0, and we explain this phenomenon. Full article

In large-scale Unmanned Aerial Vehicle (UAV) and task environments—particularly those involving obstacles—dimensional explosion remains a significant challenge in Multi-Robot Task Allocation (MRTA). To this end, a novel heuristic MRTA framework based on Topological Graph Construction (TGC) is proposed. First, the physical map is transformed into a pixel map, from which a Generalized Voronoi Graph (GVG) is generated by extracting clearance points, which is then used to construct the topological graph of the obstacle environment. Next, the affiliations of UAVs and tasks within the topological graph are determined to partition different topological regions, and the task value of each topological node is calculated, followed by the first-phase Task Allocation (TA) on these topological nodes. Finally, UAVs within the same topological region with their allocated tasks perform a local second-phase TA and generate the final TA result. The simulation experiments analyze the influence of different pixel resolutions on the performance of the proposed method. Subsequently, robustness experiments under localization noise, path cost noise, and communication delays demonstrate that the total benefit achieved by the proposed method remains relatively stable, while the computational time is moderately affected. Moreover, comparative experiments and statistical analyses were conducted against k-means clustering-based MRTA methods in different UAV, task, and obstacle scale environments. The results show that the proposed method improves computational speed while maintaining solution quality, with the PI-based method achieving speedups of over 60 times and the CBBA-based method over 10 times compared with the baseline method. Full article

Accurate sea surface temperature (SST) forecasting in coastal upwelling systems requires predictive models capable of representing complex oceanic geometries. This work revisits grid-to-mesh coupling strategies in Graph Neural Networks (GNNs) and analyzes how mesh topology and connectivity influence prediction accuracy and artifact formation. This standard coupling process is a significant source of discretization errors and spurious numerical artifacts that compromise the final forecast’s accuracy. Using daily Copernicus SST and 10 m wind reanalysis data from 2000 to 2020 over the Canary Islands and the Northwest African region, we evaluate four mesh configurations under varying grid-to-mesh connection densities. We analyze two structured meshes and propose two new unstructured meshes for which their nodes are distributed according to the bathymetry of the ocean region. The results show that forecast errors exhibit geometric patterns equivalent to order-k Voronoi tessellations generated by the k-nearest neighbor association rule. Bathymetry-aware meshes with $k=3$ and $k=4$ grid-to-mesh connections significantly reduce polygonal artifacts and improve long-term coherence, achieving up to 30% lower $\mathrm{RMSE}$ relative to structured baselines. These findings reveal that the underlying geometry, rather than node count alone, governs error propagation in autoregressive GNNs. The proposed analysis framework provides a clear understanding of the implications of grid-to-mesh connections and establishes a foundation for artifact-aware, geometry-adaptive learning in operational oceanography. Full article

Remotely sensed data have been instrumental in improving our understanding of the nature of fires within tropical landscapes. However, most studies have depicted fires in a negative light, highlighting how land-use and land-cover changes make forests more vulnerable to fire damage. In contrast to such fires, indigenous peoples utilize fires as a key part of their livelihood practices, and such relationships have not been extensively examined using remotely sensed data. In this paper, we utilize MODIS Active Fire data to examine the spatial and temporal distribution of fires relative to indigenous lands across Guyana. We employed the DBSCAN clustering algorithm and Voronoi polygons to examine the patterns of fire distribution across the Guyanese landscape. We found that while indigenous territories accounted for approximately 15% of Guyana’s terrestrial landscape, 25% of fires occurred within Amerindian lands, and 71% within 16 km of village boundaries. A strong linear distance decay (R² = 0.97) was observed between the occurrence of fires and Amerindian village boundaries. Four previously undefined fire regions emerged for Guyana–Coastal, Forest, Forest Edge North, and Forest Edge South–with the Forest Edge regions hosting the second highest number of fires but the highest indigenous peoples’ presence. The spatial distribution of fires relative to each region suggested that Forest Edge indigenous villages had a strong reliance on fires as a part of their toolkit for maintaining the rich ecological processes characteristically observed around their lands. Full article

Partial Differential Equation (PDE)-based hydrologic models demand extensive preprocessing, creating a bottleneck and slowing down the model setup process. Mesh generation typically lacks integration with hydrological features like river networks. We present GHOST Mesh (GMesh), an automated, watershed-oriented mesh generator built within the Watershed Modeling Framework (WMF), to address this. While primarily designed for the GHOST hydrological model, GMesh’s functionalities can be adapted for other models. GMesh enables rapid mesh generation in Python by incorporating Digital Elevation Models (DEMs), flow direction maps, network topology, and online services. The software creates Voronoi polygons that maintain connectivity between river segments and surrounding hillslopes, ensuring accurate surface–subsurface interaction representation. Key features include customizable mesh generation and variable refinement to target specific watershed areas. We applied GMesh to Iowa’s Bear Creek watershed, generating meshes from 10,000 to 30,000 elements and analyzing their effects on simulated stream flows. Results show that higher mesh resolutions enhance peak flow predictions and reduce response time discrepancies, while local refinements improve model performance with minimal additional computation. GMesh’s open-source nature streamlines mesh generation, offering researchers an efficient solution for hydrological analysis and model configuration testing. Full article

As a discontinuous deformation method, the block element method (BEM) characterizes a material’s elastoplastic behavior through the constitutive relation of thin-layer elements between adjacent blocks. To realistically simulate rock damage paths, this work improves the traditional BEM by using random Voronoi polygonal grids for discrete modeling. This approach mitigates the distortion of damage paths caused by regular grids through the randomness of the Voronoi grids. As the innovation of this work, the iterative algorithm is combined with polygonal geometric features so that the area–perimeter fractal dimension can be introduced to optimize random Voronoi grids. The iterative control index can effectively improve the geometric characteristics of the grid while maintaining the necessary randomness. On this basis, a constitutive relation model that considers both normal and tangential damage is proposed. The entire process from damage initiation to macroscopic fracture failure in rocks is described using two independent damage surfaces and a damage relationship based on geometric mapping relationships. The analysis results are in good agreement with existing experimental data. Furthermore, the sensitivity method is used to analyze the influence of key mechanical parameters in the constitutive model. Full article

This study aimed to investigate the impact of local canopy environmental characteristics on the regeneration of common tree species in the understory of broadleaved Korean pine forests, thus deepening the understanding of species coexistence and forest growth cycle mechanisms. This study focused on nine tree species found in the Liangshui National Nature Reserve in Heilongjiang Province, China. We stratified trees by height and simulated the LAI distribution of each class using Voronoi polygons. These layers were overlaid to generate an integrated LAI spatial map. All these procedures were integrated into the self-developed R package Broadleaf.Korean.pine.LAI, which was used to calculate individual-level canopy environment indicators, including average local LAI, local LAI standard deviation, canopy percent, vertical distribution tendency degree, local coniferous LAI, and local broadleaf LAI. These indicators were then compared with the average values of uniformly distributed understory sampling points. A principal component analysis (PCA) was conducted to reduce the dimensionality of the local canopy environmental characteristics for both the uniformly distributed points and regeneration habitats of each tree species, resulting in comprehensive canopy environmental characteristics. Wilcoxon rank-sum tests were applied to assess the significance of differences between the regeneration habitats and the understory average, as well as between the regeneration habitats of seedlings and saplings within the same species. Cliff’s delta effect size was used to evaluate the impact of each environmental factor on the transition of regeneration from seedlings to saplings. The results showed that, based on both individual canopy environmental indicators and composite indices derived from principal component analysis, seedlings tended to regenerate in areas with higher canopy coverage, whereas saplings were more commonly established in relatively open habitats. Clear differences exist between the regeneration habitats of coniferous and broadleaf species, with coniferous species tending to regenerate in areas with higher local broadleaf LAIs compared with broadleaf species. The effect size analysis showed that canopy percent, vertical distribution tendency degree, average local LAI, and local coniferous LAI have greater impacts on the transition from seedlings to saplings, while the effect of local broadleaf LAI is relatively small. These findings suggest that strong shade tolerance allows species to establish seedling banks under canopy patches, while interspecific differences in growth response to microhabitats shape their roles in the forest growth cycle. Future research should explore the physiological responses and trait characteristics of tree regeneration under varying canopy patch environments. Long-term monitoring of regeneration processes—including invasion, growth, and mortality—across different canopy patches will help elucidate the mechanisms shaping understory spatial patterns. Full article

To study the effects of rock models with different fractal dimensions on their mechanical properties and fracture behavior, three representative numerical rock models, including the digital texture model, the Voronoi polygon model, and the Weibull distribution model, are established in this paper. These models are used to simulate the structure of multi-mineral rocks and to investigate the influence of fractal dimensions on the mechanical properties and fracture behavior of rocks. Uniaxial compression numerical tests are carried out on 2D and 3D intact rocks under different fractal dimensions using the particle flow simulation method. The relationship between fractal dimensions and uniaxial compression strength and fracture behavior was analyzed. The results show that the fractal dimension of the Weibull distribution model is the largest, followed by the digital texture model, and the fractal dimension of the Voronoi polygon model is the smallest. With the increase in fractal dimension, the uniaxial compressive strength of intact rocks increases significantly, and their relationship is approximately linear. The influence of fractal dimension on rock strength shows a similar trend in both the 2D and 3D models. This study provides a new perspective for the application of fractal dimensions in multi-mineral rock models. Full article

High noise resistance and high boundary fitting accuracy have always been the goals of image classification. However, the two mutually constrain each other, making it extremely difficult to reach equilibrium. To deal with this problem, the unsupervised image classification algorithm based on fully fuzzy Voronoi tessellation is proposed. It extends Voronoi tessellation from hard to fuzzy, and proposes a hierarchical fuzzy membership model, i.e., pixels fuzzily belong to Voronoi polygons and polygons fuzzily belong to clusters. The objective function is established based on the hierarchical fuzzy membership model by fully considering the transitivity of fuzziness between different levels. Then, the optimal classification result can be obtained by the fuzzy comprehensive decision theory under the best parameter solution. The first level retains the flexibility of pixels while modeling spatial constraints. The second level determines which class the polygon belongs to under the constraint of the first level. It provides an effective way of balancing noise resistance and boundary fitting. In addition, the Voronoi tessellation is explicitly expressed in the objective function in the form of the mathematical model, which allows it to obtain the optimal value through analytical solutions instead of the previous random sampling method. It greatly increases the convergence speed of the algorithm. Experiments have been performed on simulated and several remote sensing images with seven comparing algorithms to demonstrate the effectiveness of the proposed algorithm. Full article

Vertex models have become essential tools for understanding tissue morphogenesis by simulating the mechanical and geometric properties of cells in various biological systems. These models represent cells as polygons or polyhedra, capturing cellular interactions such as adhesion, tension, and force generation. This review explores the ongoing evolution of computational vertex models, highlighting their application to complex tissue dynamics, including organoid development, wound healing, and cancer metastasis. We examine different energy formulations used in vertex models, which account for mechanical forces such as surface tension, volume conservation, and intercellular adhesion. Additionally, this review discusses the challenges of expanding traditional 2D models to 3D structures, which require the inclusion of factors like mechanical polarisation and topological transitions. We also introduce recent advancements in modelling techniques that allow for more flexible and dynamic cell shapes, addressing limitations in earlier frameworks. Mechanochemical feedback and its role in tissue behaviour are explored, along with cutting-edge approaches like self-propelled Voronoi models. Finally, the review highlights the importance of parameter inference in these models, particularly through Bayesian methods, to improve accuracy and predictive power. By integrating these new insights, vertex models continue to provide powerful frameworks for exploring the complexities of tissue morphogenesis. Full article

Assessing the quality of maize seedlings is crucial for field management and germplasm evaluation. Traditional methods for evaluating seedling quality mainly rely on manual field surveys, which are not only inefficient but also highly subjective, while large-scale satellite detection often lacks sufficient accuracy. To address these issues, this study proposes an innovative approach that combines the YOLO v8 object detection algorithm with Voronoi spatial analysis to rapidly evaluate maize seedling quality based on high-resolution drone imagery. The YOLO v8 model provides the maize coordinates, which are then used for Voronoi segmentation of the field after applying the Convex Hull difference method. From the generated Voronoi diagram, three key indicators are extracted: Voronoi Polygon Uniformity Index (VPUI), missing seedling rate, and repeated seedling rate to comprehensively evaluate maize seedling quality. The results show that this method effectively extracts the VPUI, missing seedling rate, and repeated seedling rate of maize in the target area. Compared to the traditional plant spacing variation coefficient, VPUI performs better in representing seedling uniformity. Additionally, the R² for the estimated missing seedling rate and replanting rate based on the Voronoi method were 0.773 and 0.940, respectively. Compared to using the plant spacing method, the R² increased by 0.09 and 0.544, respectively. The maize seedling quality evaluation method proposed in this study provides technical support for precision maize planting management and is of great significance for improving agricultural production efficiency and reducing labor costs. Full article

A mathematical procedure enabling the transformation of an arbitrary tessellation of a surface into a bi-colored, complete graph is introduced. Polygons constituting the tessellation are represented by vertices of the graphs. Vertices of the graphs are connected by two kinds of links/edges, namely, by a green link, when polygons have the same number of sides, and by a red link, when the polygons have a different number of sides. This procedure gives rise to a semi-transitive, complete, bi-colored Ramsey graph. The Ramsey semi-transitive number was established as $R_{trans}\left(3,3\right)=5$ Shannon entropies of the tessellation and graphs are introduced. Ramsey graphs emerging from random Voronoi and Poisson Line tessellations were investigated. The limits $\zeta =\underset{N\to \infty }{\lim }{\displaystyle \frac{N_g}{N_r}}$, where N is the total number of green and red seeds, $N_g$ and $N_r$, were found $\zeta =$ 0.272 ± 0.001 (Voronoi) and $\zeta =$ 0.47 ± 0.02 (Poisson Line). The Shannon Entropy for the random Voronoi tessellation was calculated as $S=$ 1.690 ± 0.001 and for the Poisson line tessellation as S = 1.265 ± 0.015. The main contribution of the paper is the calculation of the Shannon entropy of the random point process and the establishment of the new bi-colored Ramsey graph on top of the tessellations. Full article

Soft rocks are prone to softening upon contact with water, and their rapid deterioration in mechanical properties is a significant cause of instability and failure soft rock masses. Besides, the macroscopic mechanical response of rocks is closely related to the mineral composition and microstructure. The purpose of this research is to consider the heterogeneity factors and softening effects, and systematically investigate the influence of confining pressure and softening time on the damage and failure characteristics of soft rocks. The Voronoi polygons generated using a built-in Voronoi diagram algorithm and contact elements (the substances with cementing capacity) of UDEC discrete element method are employed to represent the clastic grains and interfacial cemented bonding (ICB) structures in soft rock. Based on the Voronoi probabilistic method, the grain-based discrete element model (GB-DEM) considering the softening effect is established by introducing a meso-scale softening damage factor, along with a detailed calibration method for meso-scale parameters. The damage parameters such as the crack initiation threshold, the crack damage threshold, the damage degree, and the tensile and shear crack ratio are then analyzed. The study results indicate that the simulated strengths of the heterogeneous models under different water immersion time are in good agreement with the experimental results. The thresholds for crack initiation and damage, the proportions of tensile and shear cracks, and the degree of damage are positively correlated with the confining pressure. The attenuation patterns of the crack initiation threshold and damage threshold in the heterogeneous models with water immersion time are highly consistent with the meso-scale softening damage factor. The damage parameters show a trend of increasing first and then decreasing with the extension of water immersion time. The cement–cement contact elements are the main locations for crack initiation and propagation. The research outcomes have significant theoretical and practical implications for understanding and predicting the mechanical behavior of soft rocks under a water–rock interaction. Full article

The nacre has excellent impact resistance performance, and it is attracting attention in the field of aerospace composite research. Inspired by the layered structure from nacre, semi-cylindrical nacre-like composite shells of brittle silicon carbide ceramic (SiC) and aluminum (AA5083-H116) were established. Two types of tablet arrangements (regular hexagonal and Voronoi polygons) of the composites were designed, and the same size of ceramic and aluminum shell were established for the impact resistance analyzed numerically. In order to better compare the resistance performance of the four types of structures under different impact velocity, the following parameters were analyzed including energy variation, damage characteristic, bullet residual velocity, and semi-cylindrical shell displacement. The results show that the semi-cylindrical ceramic shells have higher rigidity and ballistic limit, but the severe vibration after impact causes penetrating cracks, and the whole structure failure occurred eventually. The nacre-like composites have higher ballistic limits than semi-cylindrical aluminum shells, and the impact of bullets only causes local failure. In the same conditions, the impact resistance of regular hexagons is better than Voronoi polygons. The research analyzes the resistance characteristic of nacre-like composites and single materials, and provides a reference for the design of nacre-like structures. Full article

The unique structural characteristics and special symmetry of columnar jointed rock mass result in its complex mechanical properties and strong anisotropy, which seriously affects the safety of engineering construction. To better simulate natural columnar jointed rock mass, a geometric model reconstruction method based on a single-random movement Voronoi diagram of uniform seed points using the feasible geological parameters of horizontal polygon density, irregular factor, dip angle, strike angle, transverse joint spacing, and transverse joint penetration rate is proposed in this paper. Based on this method, numerical simulation of CJRM models with varying strike angles, dip angles, and irregular factors under uniaxial compression were conducted. The results show that the uniaxial compression strengths versus strike angle and dip angle both decrease with the increase in the irregular factor, showing a U-shape and a gentle W-shape, respectively. The strength anisotropy of the strike angle decreases from 1.1057 to 1.0395 with the increase in the irregular factor, indicating relatively isotropy. With the increase int the irregular factor, the strength anisotropy of the dip angle increases from 4.3381 to 6.7953, indicating an increasing strong anisotropy at a high degree, and the effect of the irregular factor on strength behavior has the strongest and weakest impact at the dip angles of 60° and 90°, respectively. Full article