Voronoi Diagram Research Articles

Sectional Voronoi tessellations: Characterization and high-dimensional limits

Sectional Voronoi tessellations: Characterization and high-dimensional limits

Subgrid-Scale Topographic Effects on Radiation for Global Weather Forecast Models

The incoming solar radiation arriving the Earth’s surface is strongly influenced by surface terrain. Conventional global weather forecast models, with grid scales of about 10 km, lack the resolution to accurately capture terrain-induced variations. We devised a new parameterization method to incorporate high-resolution subgrid-scale terrain data into grid-scale radiative flux calculations without averaging or smoothing topographic features. Utilizing a 15″ digital elevation model from the Shuttle Radar Topography Mission, we computed subgrid-scale data and transformed them onto the Korean Integrated Model’s cubed sphere grid using a Voronoi diagram to maintain geographical accuracy. The new scheme was initially evaluated through offline ideal tests and case studies. The results demonstrated that the scheme accurately captured the variations in downward shortwave flux, keeping the mean flux on a global scale nearly constant. The global mean flux difference in all skies was less than 0.01%. Statistical analyses demonstrated improved temperature and geopotential height predictions compared to reanalysis data. The anomaly correlation coefficient for East Asia at 850 hPa increased by 0.036 at 240 forecast hours. Overall, the anomaly correlation coefficient and root mean square error of geopotential height and temperature showed enhancements, particularly in the Northern Hemisphere and tropics. Importantly, the scheme introduces negligible additional memory and CPU requirements, making it suitable for both regional and global models. Only a 0.58% increase in CPU time was observed for the 10-day forecast.

Self-organising phenomena in 2D complex plasma simulations withnon-mono dispersed dust size distributions

Complex plasma with a variety of continuous and discrete dust grain size distributions are simulated in 2D with molecular dynamics simulations with radial geometry to determine differences in self-organizing phenomena to more realistically represent the actual in situ variations in dust-size. The standard deviation of particle size σ(a) strongly correlates with phase separation and coupling parameter Γ for all distribution types. We observe local differences in bond order parameters and Voronoi diagrams for different size distributions, and our results suggest that phase transition is affected by continuous size distributions, particularly in the binary distribution case. Simulations with discrete size result in artifacts and discontinuities that are not found in the continuous distributions. The use of continuous distributions is observed to be beneficial both for more realistic approximation of complex plasma experiments and to study systems of strongly coupled particles in general.

Translating Words to Worlds: Zero-Shot Synthesis of 3D Terrain from Textual Descriptions Using Large Language Models

The current research on text-guided 3D synthesis predominantly utilizes complex diffusion models, posing significant challenges in tasks like terrain generation. This study ventures into the direct synthesis of text-to-3D terrain in a zero-shot fashion, circumventing the need for diffusion models. By exploiting the large language model’s inherent spatial awareness, we innovatively formulate a method to update existing 3D models through text, thereby enhancing their accuracy. Specifically, we introduce a Gaussian–Voronoi map data structure that converts simplistic map summaries into detailed terrain heightmaps. Employing a chain-of-thought behavior tree approach, which combines action chains and thought trees, the model is guided to analyze a variety of textual inputs and extract relevant terrain data, effectively bridging the gap between textual descriptions and 3D models. Furthermore, we develop a text–terrain re-editing technique utilizing multiagent reasoning, allowing for the dynamic update of the terrain’s representational structure. Our experimental results indicate that this method proficiently interprets the spatial information embedded in the text and generates controllable 3D terrains with superior visual quality.

Characterization of the Coordination and Solvation Dynamics of Solvated Systems─Implications for the Analysis of Molecular Interactions in Solutions and Pure H2O.

The characterization of solvation shells of atoms, ions, and molecules in solution is essential to relate solvation properties to chemical phenomena such as complex formation and reactivity. Different definitions of the first-shell coordination sphere from simulation data can lead to potentially conflicting data on the structural properties and associated ligand exchange dynamics. The definition of a solvation shell is typically based on a given threshold distance determined from the respective solute-solvent pair distribution function g(r) (i.e., GC). Alternatively, a nearest neighbor (NN) assignment based on geometric properties of the coordination complex without the need for a predetermined cutoff criterion, such as the relative angular distance (RAD) or the modified Voronoi (MV) tessellation, can be applied. In this study, the effect of different NN algorithms on the coordination number and ligand exchange dynamics evaluated for a series of monatomic ions in aqueous solution, carbon dioxide in aqueous and dichloromethane solutions, and pure liquid water has been investigated. In the case of the monatomic ions, the RAD approach is superior in achieving a well separated definition of the first solvation layer. In contrast, the MV algorithm provides a better separation of the NNs from a molecular point of view, leading to better results in the case of solvated CO2. When analyzing the coordination environment in pure water, the cutoff-based GC framework was found to be the most reliable approach. By comparison of the number of ligand exchange reactions and the associated mean ligand residence times (MRTs) with the properties of the coordination number autocorrelation functions, it is shown that although the average coordination numbers are sensitive to the different definitions of the first solvation shell, highly consistent estimates for the associated MRT of the solvated system are obtained in the majority of cases.

Crystal plasticity modeling fatigue behavior in bimodal Ti–6Al–4V: Effects of microdefect and lamellar orientation

AbstractInvestigating fatigue failure in titanium alloys is crucial for material design and engineering. Fatigue behavior in dual‐phase titanium alloys is strongly correlated with microstructural features and microdefects. This work formulates an improved modeling method to investigate fatigue behavior of bimodal Ti–6Al–4V, emphasizing the effects of lamellar orientation and microdefects. Using an improved Voronoi tessellation method, we establish representative volume element (RVE) models with various grain size distributions. Crystal plasticity finite element modeling (CPFEM) is used to analyze fatigue deformation in bimodal Ti–6Al–4V, considering microdefects and lamellar orientation. Fatigue indicator parameters are then incorporated into CPFEM to predict fatigue life and verified with experimental data. Numerical results highlight the significant influence of lamellar orientation and microdefects on fatigue behavior, with predicted life within the 3‐error band. This method efficiently overcomes challenges in quantitatively characterizing microstructural lamellae that experiments are short of, paving the way for designing fatigue‐resistant alloy materials with similar microstructures.

Reactor field reconstruction from sparse and movable sensors using Voronoi tessellation-assisted convolutional neural networks

The aging of operational reactors leads to increased mechanical vibrations in the reactor interior. The vibration of the in-core sensors near their nominal locations is a new problem for neutronic field reconstruction. Current field-reconstruction methods fail to handle spatially moving sensors. In this study, we propose a Voronoi tessellation technique in combination with convolutional neural networks to handle this challenge. Observations from movable in-core sensors were projected onto the same global field structure using Voronoi tessellation, holding the magnitude and location information of the sensors. General convolutional neural networks were used to learn maps from observations to the global field. The proposed method reconstructed multi-physics fields (including fast flux, thermal flux, and power rate) using observations from a single field (such as thermal flux). Numerical tests based on the IAEA benchmark demonstrated the potential of the proposed method in practical engineering applications, particularly within an amplitude of 5 cm around the nominal locations, which led to average relative errors below 5% and 10% in the L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_2$$\\end{document} and L∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_{\\infty }$$\\end{document} norms, respectively.

Scaling Landscape Fire History: Wildfires Not Historically Frequent in the Main Population of Threatened Gunnison Sage-Grouse

The main population of ~5000 threatened Gunnison sage-grouse (GUSG; Centrocercus minimus) in Colorado depends on sagebrush plants that are killed by wildfires, with recovery taking decades, so frequent fire is a threat, but did it occur historically? Early land surveys showed that the historical (preindustrial) fire rotation (FR), the expected period to burn area equal to a focal land area, was 90–143 years in GUSG ranges, which is not classed as frequent fire (≤25 years). However, recent research, based on fire scars on trees at ten sites near sagebrush, suggested some frequent fire historically in the main population. That study was not spatial, essential to estimate FR, so spatial data were created in GIS with land-survey reconstructions, survey dates, fire-scar sites, mapped sagebrush, and Thiessen polygons around sites. The previous study assumed fires that burned 2+ sites likely burned across sagebrush. Historical FRs were calculated several ways over a common period. A recovery estimate of FR was 90–135 years, a land-survey estimate was 82–131 years, and three spatial scar-based estimates were 93–107 years, showing agreement. However, the comparison found that only 8.8% of the land-survey fire area was detected at fire-scar sites. Detailed analysis showed that 10 fire-scar sites were insufficient to detect historical fire sizes and distributions across the large 168,753 ha sagebrush area. Adequate fire reconstruction could require ~45–60 fire-scar sites, making it feasible to study only ~30,000 ha of sagebrush. Using the two remaining methods, which cross-validate, showed frequent fire did not occur historically in the study area, as historical FRs were 82–135 years.

Topological balance of cell distributions in plane monolayers

Most of normal proliferative epithelia of plants and metazoans are topologically invariant and characterized by similar cell distributions according to the number of cell neighbors (DCNs). Here we study peculiarities of these distributions and explain why the DCN obtained from the location of intercellular boundaries and that based on the Voronoi tessellation with nodes located on cell nuclei may differ from each other. As we demonstrate, special microdomains where four or more intercellular boundaries converge are topologically charged. Using this fact, we deduce a new equation describing the topological balance of the DCNs. The developed theory is applied for a series of microphotographs of non-tumoral epithelial cells of the human cervix (HCerEpiC) to improve the image processing near the edges of microphotographs and reveal the topological invariance of the examined monolayers. Special contact microdomains may be present in epithelia of various natures, however, considering the well-known vertex model of epithelium, we show that such contacts are absent in the usual solid-like state of the model and appear only in the liquid-like cancer state. Also, we discuss a possible biological role of special contacts in context of proliferative epithelium dynamics and tissue morphogenesis.

Microstructure-based prediction of hydrodynamic forces in stationary particle assemblies

In this work, we derive novel hydrodynamic force models to describe the interaction of a flow with particles in an assembly when only an averaged resolution of the flow is available. These force models are able to predict the average drag on the particle assembly, as well as the deviations from the average drag force and the lift force for each individual particle in the assembly. To achieve this, PR-DNS of various particle assemblies and flow regimes are carried out, varying the particle volume fraction up to 0.6, and the mean particle flow Reynolds number up to 300. To characterize the structure of the particles in the assembly, a Voronoi tessellation is carried out, and a number of scalars, vectors and tensors are defined based upon this tessellation. The microstructure informed hydrodynamic force models are based on symbolic regressions of these quantities derived from the Voronoi tessellation, the global particle volume fraction of the particle assembly and the flow regime represented by the Reynolds number, and the forces on the individual particles in the assembly.The resulting hydrodynamic force models are single expressions and can be directly employed in a Lagrangian particle tracking (LPT) or computational fluid dynamics/discrete element model (CFD/DEM) framework. By comparing the results of the newly proposed hydrodynamic force models with an averaged force model, as is usually adopted in Lagrangian particle tracking simulations, we show that, potentially, a significant increase in accuracy can be achieved, with only a relatively small increase in computational cost, compared to the cost of the CFD/DEM simulation.

Comparative Performance Evaluation of ANN and Hybrid ANN-HBA Models for Temporal and Spatial Modeling of Precipitation in East Azarbaijan Province of Iran

In this study, temporal and spatial modeling of precipitation was performed in East Azarbaijan province of Iran using 27-year (1996-2022) data by employing two neural network models, i.e., stand-alone artificial neural network (ANN) and hybrid ANNHoney badger optimization algorithm (ANN-HBA). In temporal modeling, one-month and two-month precipitation delay steps were used as input parameters, and monthly precipitation was considered as output parameter. On the other hand, in spatial modeling, longitude, latitude, and altitude were used as input parameters and average monthly precipitation was considered as output parameter. Comparative performance of both the employed models was evaluated using three statistical criteria, i.e., root mean square error (RMSE), correlation coefficient (R) and Nash- Sutcliffe efficiency (NSE). In addition, precipitation in ungauged areas was estimated based on rainfall data of the nearby rain gauges through spatial interpolation methods such as isohyet and Thiessen polygon. Results of the temporal precipitation modeling revealed better performance of the hybrid ANN-HBA model over the stand-alone ANN model. Furthermore, the hybrid ANN-HBA model, during testing phase of the temporal modeling, could resemble the precipitation most accurately at Maraghe station (with values of R as 0.95, RMSE as 1 mm, and NSE as 0.85). Similarly, the hybrid ANN-HBA model during testing phase (with values of R as 0.95, RMSE as 1 mm, and NSE as 0.96) outperformed the stand-alone ANN model in depicting the precipitation adequately at spatial scale.

Prediction of the Hydrological Drought Index (HDI) based on Rain Simulation Data using an Artificial Neural Network (ANN) in the Randugunting Watershed, Rembang Regency

Randugunting Watershed, with the main river Randugunting River, originates from the North Limestone Mountains of Rembang Regency. Because of its cyclical nature, the river flow discharge is continually subject to change. The discharge rises during rainy weather and falls during dry weather. Due to this issue, Rembang will likely experience drought throughout the dry season. The objectives of this study are to: (1) determine the drought index and its sharpness based on the Hydrological Drought Index Method (HDI) and (2) make drought predictions using the HDI based on discharge for the years 2023–2026 using simulated rain data with Artificial Neural Networks (ANN). Calculation of regional rainfall using the Thiessen Polygon Method. To find simulated rain and drought prediction based on the ANN with Backpropagation algorithm using Mathlab software. From the analysis indicate that the number of months that would experience wet conditions are decreasing from 7 months in 2023 and 2024 to 6 months in 2025 and only 3 months in 2026. In the anticipated drought from 2023 to 2026, there will be 14 dry months, 8 very dry months, and 3 extremely dry months. The examination of the hydrological drought’s duration revealed that the typical drought period fell between May and November.

Shallow crustal deformation in the Yunnan-Myanmar and surrounding areas by regionally weighted interpolation of GPS measurements data

Yunnan-Myanmar and its surrounding areas are the areas directly affected by the collision of the Eurasian Plate and the Indian Plate. In view of the uneven distribution of GPS stations in Yunnan and Myanmar, this paper employs the method of regionally weighted interpolation. In areas with a high concentration of GPS stations, a combination of Voronoi cell weighting function and Gaussian function weighting is utilized, while in regions with sparse GPS coverage, a combination of Voronoi cell weighting function and quadratic function weighting is employed. Utilizing the rigid-body movement uniform strain model, we calculate the horizontal strain rates of the crust in Yunnan-Myanmar and adjacent areas, followed by an in-depth analysis of model performance and the activity of primary faults. The results show that: (1) We found that Yunnan Myanmar strain has obvious boundary characteristics. (2) Upon scrutinizing the model, it was ascertained that the model delineated in this study possesses an expansive search range, enabling it to yield more precise outcomes, particularly in regions characterized by the disparate distribution of GPS stations; (3) Through the analysis of the profiles of horizontal GPS velocity field and maximum shear strain rates of the main faults in the study area, we found that the direction of the maximum shear strain rate is consistent with the direction of the main faults in the study area, and that the slip and maximum shear strain rate of the major faults increase and decrease along the tectonic direction.

Local environment interaction-based machine learning framework for predicting molecular adsorption energy

Machine learning (ML) models in materials science are mainly developed for predicting global properties, such as formation energy, band gap, and elastic modulus. Thus, these models usually fall short in describing local characteristics, such as molecular adsorption on surfaces. Here, we introduce a local environment interaction-based ML framework that contains a modified graph-based Voronoi tessellation geometrical representation, improved fingerprint feature engineering, and traditional ML and advanced deep learning (DL) algorithms. The precise characterization can be extracted using this framework for representing local information of adsorption of molecules on a surface. Using both traditional ML and advanced DL algorithms, we demonstrate remarkable prediction accuracy and robustness on 0D, two-dimensional (2D), and three-dimensional (3D) catalysts. Furthermore, it is found that the employment of this approach reduces data requirements and augments computational speed, specifically for DL algorithms. This work provides an effective and universal ML framework for various applications of molecular adsorption from catalysis, sensors, carbon capture, and energy storage to drug delivery, signifying a novel and promising avenue in the field of materials informatics. The implementation code in this work is available at https://github.com/mpeshel/LEI-framework LERN .

Second-order texton feature extraction and pattern recognition of building polygon cluster using CNN network

The cluster patterns of features in map space represent a comprehensive reflection of individual feature geometric attributes and their spatial adjacency relationships. These patterns also embody spatial cognition results under the Gestalt principle. Describing non-linear spatial cluster patterns as effective regular structures is one of the fundamental tasks in deep learning for recognizing feature cluster patterns. In this study, based on the concept of texture co-occurrence matrices from regular gray-scale images, we utilized Voronoi diagrams to construct the tessellation structure of building polygons. Built upon the foundation of first-order texton co-occurrence matrices, we established three-dimensional texton co-occurrence matrices for building polygons, considered five attributes of building size, shape, orientation, and density, and encompassed 64 different combinations of second-order neighboring directions. This matrix concretizes the latent Gestalt spatial characteristics of building polygon clusters into a three-dimensional sparse matrix. It is then used as an input vector to construct a deep convolutional neural network for recognizing building polygon cluster patterns. Through adjustments and optimizations of neural network structure and strategies, along with validation through practical case studies and comparisons with other models, we have demonstrated the effectiveness of the second-order texton co-occurrence matrix in describing the characteristics of building polygon clusters.

Innovative Cellular Insulation Barrier on the Basis of Voronoi Tessellation-Influence of Internal Structure Optimization on Thermal Performance.

The optimization of structure and thermal properties in 3D-printed insulation materials remains an underexplored area in the literature. This study aims to address this gap by investigating the impact of 3D printing on the thermal properties of manufactured cellular composites. The materials studied were closed-cell foams with a complex cell structure based on the Voronoi cell model, manufactured using incremental technology (3D printing). The influence of the cellular structure of the composite, the type of material used, and the number of layers in the composite structure on its thermal properties, i.e., thermal conductivity coefficient, thermal resistance, and coefficient of heat transfer, was analyzed. Samples of different types of thermosetting resins, characterized by different values of emissivity coefficient, were analyzed. It was shown that both the type of material, the number of layers of the composite, and the number of pores in its structure significantly affect its thermal insulating properties. Thermal conductivity and permeability depended on the number of layers and decreased up to 30% as the number of layers increased from one to four, while thermal resistance increased to 35%. The results indicate that material structure is key in regulating thermal conduction. Controlling the number of cells in a given volume of composite (and thus the size of the air cells) and the number of layers in the composite can be an effective tool in designing materials with high insulation performance. Among the prototype composites produced, the best thermal performance was that of the metalized four-layer cellular composites (λ = 0.035 ± 0.002 W/m·K, Rc = 1.15 ± 0.02 K·m2/W, U = 0.76 ± 0.01 W/m2·K).

Numerical simulation study of PDC cutter rock breaking based on CT scanning to construct a rock model and apply a cohesive element to construct a discretization element

To more accurately simulate the interaction between a polycrystalline diamond compact (PDC) cutter and rock, the structural characteristics of basalt were analysed using computed tomography (CT), and a hard particle–matrix–pore three-phase rock model was established due to its structural characteristics. Three-dimensional models of the interaction between PDC cutters and rock were established by using the finite–discrete element method (FDEM). Using Voronoi diagrams to randomize the grid structure and optimize the propagation of cracks. This study revealed that a broken zone near the cutters will form during the rock breaking process, resulting in the affected area being larger than the area in contact with the formation rock. The rock breaking ability of circular cutters is stronger than that of conical cutters. When a conical cutter breaks hard particles, they are mainly striped or forced away from the rock, but circular cutters can divide hard particles into small pieces. The numerical model used in the research institute can effectively calculation results of the process of interaction between PDC cutter and rock, this proves that the application of the cohesive method to simulate rock breaking by PDC cutters is reliable.

Test Center Location Problem: A Bi-Objective Model and Algorithms

The optimal placement of healthcare facilities, including the placement of diagnostic test centers, plays a pivotal role in ensuring efficient and equitable access to healthcare services. However, the emergence of unique complexities in the context of a pandemic, exemplified by the COVID-19 crisis, has necessitated the development of customized solutions. This paper introduces a bi-objective integer linear programming model designed to achieve two key objectives: minimizing average travel time for individuals visiting testing centers and maximizing an equitable workload distribution among testing centers. This problem is NP-hard and we propose a customized local search algorithm based on the Voronoi diagram. Additionally, we employ an ϵ-constraint approach, which leverages the Gurobi solver. We rigorously examine the effectiveness of the model and the algorithms through numerical experiments and demonstrate their capability to identify Pareto-optimal solutions. We show that while the Gurobi performs efficiently in small-size instances, our proposed algorithm outperforms it in large-size instances of the problem.

Discrete element simulation study on effects of grain preferred orientation on micro-cracking and macro-mechanical behavior of crystalline rocks

Abstract Grain-preferred orientation significantly influences the brittle fracture mechanism and failure mode of crystalline rocks. However, current grain-based models (GBMs) based on particle flow code (PFC) software are mostly proposed on the basis of the Voronoi tessellation method for grain boundary generation, which is difficult to simulate the heterogeneity of microstructure such as shape and orientation of rock minerals. To study the effect of grain-preferred orientation on macroscopic mechanical properties and microscopic characteristics of crystalline rocks, a novel grain-based microstructure transformation method (MTM) is proposed. Based on the MTM, a GBM with a target aspect ratio and crystal orientation is obtained by transforming the Voronoi crystal geometry through a planar coordinate mapping. Specifically, embedded FISH language is used to control random mineral seed size and distribution pattern to generate Tyson polygons. A polygon geometry that satisfies the rock texture is obtained as a grain boundary by spatially transforming the vertex of the Tyson polygon. The transformed complex geometry is taken as the crystal structure of the GBM, and the Lac du Bonnet granite models with different aspect ratios and crystal orientations were developed in PFC2D. Finally, a series of unconfined compressive strength tests are performed in PFC2D to verify the proposed modeling methods for the geometric variation of the crystals and to study the effects of the preferred orientation of the grains on the macroscopic mechanical properties and microscopic fracture mechanisms of the crystalline rocks from different perspectives.

Simulation of interfacial debonding in hollow particle reinforced composites with VCFEM

The addition of hollow glass microsphere into composites is a method to improve mechanical properties. However, the interfacial debonding of hollow microsphere inevitably causes a decrease in the mechanical properties of the material, which ultimately leads to the failure of the composites. In the numerical simulation of such hollow particle-reinforced composites, the ordinary displacement finite element requires a large number of meshes, which undoubtedly greatly increases the computational cost. In this paper, a new VCFEM is proposed to solve this problem by establishing a two-dimensional Voronoi cell finite element model, deriving the residual energy generalized function of hollow particle-reinforced composites, and calculating the interface debonding. The simulation results are compared with the commercial software MARC, ABAQUS to verify the effectiveness of this VCFEM. The results show that this VCFEM greatly improves the computational efficiency while ensuring the accuracy. Based on this model, this paper also investigates the effect of the generation of interfacial debonding on the overall structure and the effect of different wall thickness of hollow particles on the damage of element debonding.