Voronoi Diagram Research Articles

A Hybrid Method Combining Voronoi Diagrams and the Random Walk Algorithm for Generating the Mesostructure of Concrete.

The modeling of the concrete matrix serves as a foundation for mesoscale analysis of concrete, which provides a crucial avenue for investigating the crack propagation and strength characteristics of concrete. However, the primary prerequisite for conducting such analyses is the generation of aggregate models. By combining the advantages of Voronoi diagrams and the random walk algorithm (RWA), a Voronoi-random walk algorithm is proposed in this paper. The algorithm overcomes the limitations of traditional methods, including constraints on aggregate volume fraction, low computational efficiency, and insufficient randomness in aggregate distribution. The meso-structure of a concrete block was modeled by the proposed method, and then its failure behavior under uniaxial compression was simulated using the finite element method. The numerical results agreed well with the experimental observations, indicating the effectiveness and accuracy of the proposed approach.

Topology of Intermetallic Crystals: Classification, Uniformity, and Transitions.

We have analyzed the crystal structures of 7551 binary intermetallic compounds, which are deposited in the inorganic crystal structure database, using a combined geometrical-topological approach as implemented in our program package ToposPro. We represented each crystal structure with two models: (i) the topological model of periodic atomic net and (ii) the geometrical model of the Voronoi partition of crystal space. Within the former model, we have classified all intermetallics into 949 topological types, 20 of which cover 57% of the whole sample. Using our recently developed topological network model of reconstructive solid-state transformations, we have described possible mechanisms of displacive transitions between the most abundant topological types and revealed a key role of the body-centered lattice in these transitions. The Voronoi partition model enabled us to introduce the concept of uniformity of the overall structure and the environment of separate atoms; the uniformity is estimated by the second moment of inertia of atomic Voronoi polyhedra. We have shown that the structures with a low uniformity value either contain mistakes in the crystallographic data or have significantly directed interatomic bonds. The proposed uniformity criteria can serve for the estimation of the robustness of an intermetallic structure.

Isotropic Growth on Cartesian Voxel Grids with von Neumann Neighborhoods for Rapid Generation of Synthetic Microstructures

Randomized instantiations of synthetic microstructures are needed to assess the statistical significance of microstructure variability. Algorithms that use Voronoi tessellations of random points produce synthetic polycrystalline microstructures with a less realistic appearance than random packing of spheroidal particles followed by growth-until-impingement. Additionally, Voronoi tessellations offer limited control of morphological parameters and are challenging to implement when the desired volume fraction is less than unity. However, unless additional physics-based constraints are applied, growth on a Cartesian voxel grid utilizing a von Neumann neighborhood element results in anisotropic growth that is generally not observable along the primary axes. The present work describes both analytical and empirically optimized corrections for directional growth rates and a framework for their inclusion in a synthetic microstructure generation algorithm. The presented algorithm can produce synthetic microstructures similar to those produced by random seed Monte Carlo techniques in a fraction of the computational time.

Dynamical system prediction from sparse observations using deep neural networks with Voronoi tessellation and physics constraint

Despite the success of various methods in addressing the issue of spatial reconstruction of dynamical systems with sparse observations, spatio-temporal prediction for sparse fields remains a challenge. Existing Kriging-based frameworks for spatio-temporal sparse field prediction fail to meet the accuracy and inference time required for nonlinear dynamic prediction problems. In this paper, we introduce the Dynamical System Prediction from Sparse Observations using Voronoi Tessellation (DSOVT) framework, an innovative methodology based on Voronoi tessellation which combines convolutional encoder–decoder (CED) and long short-term memory (LSTM) and utilizing Convolutional Long Short-Term Memory (ConvLSTM). By integrating Voronoi tessellations with spatio-temporal deep learning models, DSOVT is adept at predicting dynamical systems with unstructured, sparse, and time-varying observations. CED-LSTM maps Voronoi tessellations into a low-dimensional representation for time series prediction, while ConvLSTM directly uses these tessellations in an end-to-end predictive model. Furthermore, we incorporate physics constraints during the training process for dynamical systems with explicit formulas. Compared to purely data-driven models, our physics-based approach enables the model to learn physical laws within explicitly formulated dynamics, thereby enhancing the robustness and accuracy of rolling forecasts. Numerical experiments on real sea surface data and shallow water systems clearly demonstrate our framework’s accuracy and computational efficiency with sparse and time-varying observations.

Capture zone scaling in 2D Ge island nucleation on Si(111)-(7 × 7) at elevated temperatures

Recently we have studied the concentration N2D of 2D Ge island nucleated on large-scale Si(111)-(7 × 7) terraces at 550 − 650 °C as function of the substrate temperature T and Ge deposition rate R [J. Cryst. Growth. 531 (2020) 125347], where we have shown that N2D(R) dependence is characterized by a power law with scaling exponent χ = 1 ± 0.1. However, in the frames of classical Venables rate-equation approach, the obtained range of χ values do not allow one to unambiguously determine the critical nucleus size i, since χ = 1 ± 0.1 can be attributed to both diffusion limited (DL) and attachment limited (AL) growth regimes. In order to determine an exact i size and growth kinetics, in this work, we have investigated the scaled capture-zone distribution (CZD) of nucleated 2D Ge islands on the same Ge/Si(111)-(7 × 7) samples and described it by the generalized Wigner distribution Pβ=aβAβexp-bβA2, where Pβ is the probability density of getting into some region of capture zone values, A is normalized Voronoi cell area for 2D island, β=iχ is scaling parameter directly related to the critical nucleus size i. It has been shown that the kinetics of 2D Ge island nucleation on the wide Si(111)-(7 × 7) terraces at elevated temperatures should procced under AL growth kinetics with i = 3–5 particles.

A novel weight index-based uniform partition technique of multi-dimensional probability space for structural uncertainty quantification

Accurately and efficiently achieving the uncertainty quantification of engineering structures is a challenging issue. The direct probability integral method (DPIM) provides an effective pathway to address this issue. However, the key partition technique via Voronoi cell of DPIM requires a prohibitive computational burden for multi-dimensional probability space. Moreover, due to the distributed nonuniformity of representative points, the accuracy of DPIM with the partition technique via Voronoi cell (DPIM-Voronoi) for obtaining the response probability density function (PDF) of structures with multi-dimensional probability space still needs to be improved. To this end, a novel weight index-based uniform partition technique is proposed in this study. This technique can generate uniformly distributed representative points and calculate their assigned probabilities using the weight indexes of representative regions. This feature ensures that the representative points can fill the probability space in a highly uniform manner, and avoid the resource-consuming calculation process of assigned probability by Monte Carlo simulation in the original partition technique via Voronoi cell. Based on the proposed technique, DPIM with a Weight index-based Uniform partition technique (DPIM-WU) is developed. Compared to DPIM-Voronoi, the advantages of DPIM-WU include: (1) improving the computational accuracy of response PDF for structures with multi-dimensional probability space, especially in the tail region, leading to improved accuracy of the dynamic reliability; (2) remarkably reducing the computational cost, with minimal computer memory required for the partition process of multi-dimensional probability space; (3) enhancing the robustness to the number of representative points. These advantages are verified through the stochastic response and dynamic reliability analyses of four typical examples, including the 5-story buildings, dry friction system, cylinder structure, and adjacent buildings with pounding motion. Notably, in the stochastic pounding response analysis of adjacent buildings, a stochastic P-bifurcation occurs as the coefficient of variation of the structural parameters decreases.

Urban Food Deserts and Cardiovascular Health: Evaluating the Impact of Nutritional Inequities on Elderly Populations in Santiago

This study examines the link between food deserts and cardiovascular health in older adults in Santiago’s Metropolitan Region, Chile. As the population ages and chronic diseases rise, understanding the impact of food accessibility on health is essential. Using multiscale geographically weighted regression, we analyzed data from the Cardiovascular Health Program, socioeconomic indicators, and food desert maps, sourced from the Chilean Ministry of Health and other databases. Spatial analysis, including Voronoi diagrams, assessed the influence of food deserts on health outcomes. Findings show a significant correlation between limited access to healthy foods and higher cardiovascular disease rates, especially in economically disadvantaged areas. The regression model is significant to contribute to the explanation of disease prevalence, emphasizing the impact of food availability on health. This study highlights the importance of considering spatial factors in urban planning and public health policies. By showcasing the role of food environments in health disparities, it advocates for integrated health interventions. Targeted urban planning to address food deserts can enhance access to healthy foods, improving cardiovascular health and well-being among Santiago’s elderly. The findings provide insights for policymakers to create healthier urban environments and stress the need for sustainable food systems to support public health.

Mechanical and Permeability Properties of Radial-Gradient Bone Scaffolds Developed by Voronoi Tessellation for Bone Tissue Engineering

Mechanical and Permeability Properties of Radial-Gradient Bone Scaffolds Developed by Voronoi Tessellation for Bone Tissue Engineering

A B-spline material point method for deformation failure mechanism of soft–hard interbedded rock

Geological hazards related to soft–hard interbedded rock are frequent in rock engineering. The material point method (MPM) is a mesh-free numerical approach specifically designed for analyzing large deformations. Notably, significant grid-crossing errors frequently arise when material points traverse the underlying grid. To investigate the failure mechanism of soft–hard interbedded rock, an enhanced MPM incorporating B-spline basis functions and Voronoi polygon discretization is developed and subsequently validated through comparisons with uniaxial compression test data and other numerical methods. The numerical results of soft–hard interbedded rock specimens associated with different soft layer dips (SLD) and confining pressures indicate that the SLD has a great effect on compressive strength and crack extension at low confining pressure. Rocks from SLD-30° to SLD-75° correspond to the “sliding failure along discontinuities” failure mode and have lower compressive strength than rocks with other SLD angles. It is also demonstrated that the propagation of cracks leads to a significant alteration in the internal stress state of the rock, and that stress concentrations at the crack tip exacerbate the development of failure surface. Furthermore, the failure mode of soft–hard interbedded rock can be categorized into four types: (1) sliding failure across multiple discontinuities, (2) tensile fracture across multiple discontinuities, (3) sliding failure along discontinuities, (4) tensile-split along discontinuities.

Understanding shared bike usages toward metros with fewer physical road separations

Physical road separations are normally considered cyclist-friendly, but whether they are unfriendly to the combination of bike-share (BS) and metros is seldom investigated since they might affect the cycling’s flexibility and convenience to cross streets and reach the destination. Although integrating BS and metro is thought to mitigate traffic congestion, how traffic congestion affects the usage of integration remains unknown. This study, conducted in Suzhou, China, examines new factors (road separation and traffic congestion) alongside well-studied factors influencing BS and metro integration. The survey revealed increased BS usage frequency after a new metro’s opening. Variables such as road separations, traffic congestion information, road network density, and proximity to metros are considered. They are processed in a selected area considering cyclable network and Thiessen Polygon corresponding to the selected metro stations. An ordered probit model is established to investigate significant factors. It is found that as more columns of road separations exist, the cyclists are less likely to use BS towards metros, regardless of whether they are cycling weekends or weekdays. Interestingly, after the new metro opened and a new metro hub was formed, proximity to the new metro hub is associated with lower BS transfer demand. A higher congestion level promotes more cycling toward the metro system on weekdays as well as higher parking fees. This indicates that the combination of BS and metro could attract former motor vehicle users and this finding could be instructive for urban planners and road designers.

Radioactive sources search method based on multi-robot and Voronoi partition

In this paper, it is proposed to locate multiple unknown radioactive sources within a certain time limit through particle filtering and Voronoi partitioning. Firstly, with each robot as a Voronoi centroid, the entire area is partitioned. Then, the robots conduct source search concurrently through particle filtering. When all the robots complete the process of one-particle filtering, the iteration ends and the next one begins until the search for the radioactive source is terminated. Finally, experiment is conducted to demonstrate the efficiency and accuracy of the proposed method.

Evaluation and Division Methods of Coupled Spatial Units between Parks and Living Circles: A Case Study of Four National-Level New Areas

This study, based on the perspective of supply and demand coupling between parks and living circles, divides spatial units by introducing the Thiessen polygon method with urban parks as the core. Simultaneously, the coefficient of variation (CV) was used to evaluate the distribution characteristics of these spatial units. The suitability of the spatial units was comprehensively evaluated through the three indicators of park service support, functional concentration of living circle, and management and development level. The Node–Place (NP) model was used to quantify the coupling relationship between the park and the living circle, and the characteristics of the coupling units were deeply analyzed from the aspects of supply and demand services, coupling configuration relationship, development management, etc. The results are empirically applied to four national-level new areas, thereby providing a new evaluation method and perspective for urban planning and management.

Investigating on thermal insulation in concrete partition wall with insulation-material-infilled Voronoi sections: Feature impact analysis and efficient assessment approach

Reducing energy consumption in building operations, occupying 27 % of total carbon emissions, is crucial for decarbonization. Concrete partition walls with insulation-filled hollow sections, offer high thermal resistance, reducing air conditioning needs. Voronoi pattern represent a space being subdivided into polygonal regions and can be incorporated as the cavity pattern of the hollow section. However, the existing studies on Voronoi sections focus on porosity and pore quantity, with limited research on other feature metrics. This research addresses this gap by quantifying additional feature metrics of Voronoi sections using Bayesian inference, determining their collective influence on insulation. Findings reveal that feature metrics like cavity distribution and standard deviation of cavity areas affect insulation. Additionally, to improve time-consuming simulations, we proposed a model using Graph Neural Networks (GNNs) for accurate and rapid thermal assessments of complex Voronoi sections. Our GNN model, which uses graph-structured data rather than design parameters as training inputs, outperforms another four widely used models, achieving over 85 % prediction accuracy. In this research, two novel approaches are introduced: a Bayesian-based statistical model to understand the relationship between multiple feature metrics and insulation, pinpointing the most promising search space affiliated with certain values ranges of various feature metrics, and a rapid and accurate GNN-based model that uses graph representations of Voronoi sections in building components, preserving detailed geometric information for insulation prediction. Both approaches collectively improve the design process for building components with material-filled Voronoi sections by narrowing the search space and enhancing evaluation efficiency, respectively.

Disruptive atomic jumps induce grain boundary stagnation

Grain growth in polycrystalline materials can be impeded by grain boundary (GB) stagnation. Using atomistic simulations, we observed that during GB migration, the disruptive jumps of a few GB atoms can disturb the original ordered collective movement of GB atoms, leading to the stagnation of the entire GB. These disruptive atomic jumps can be activated by both high driving forces and high temperatures, with even jumps of a few atoms capable of causing the stagnation of an entire GB. This mechanism also explains the non-Arrhenius behavior observed in some GBs. Additionally, a large model size could increase the rate of disruptive atomic jumps, and a clear transition in thermal behavior is observed with the increase of the GB size in GBs exhibiting clear thermally activated stagnation. Our further investigation shows that the disruptive atoms involved in these jumps do not differ from other GB atoms in terms of atomic energy, volume, density, local entropy, or Voronoi tessellation, and no “jam transition” was observed in the energy barrier spectra. This fact makes those disruptive jumps challenging to detect. To address this issue, we propose a displacement vector analysis method that effectively identifies these subtle disruptive jumps.

On the optimality of voronoi‐based column selection

AbstractWhile there exists a rich array of matrix column subset selection problem (CSSP) algorithms for use with interpolative and CUR‐type decompositions, their use can often become prohibitive as the size of the input matrix increases. In an effort to address these issues, in earlier work we developed a general framework that pairs a column‐partitioning routine with a column‐selection algorithm. Two of the four algorithms presented in that work paired the Centroidal Voronoi Orthogonal Decomposition (CVOD; Centroidal Voronoi Tessellation Based Proper Orthogonal Decomposition Analysis, 2003, 137–150) and an adaptive variant (adaptCVOD) with the Discrete Empirical Interpolation Method (DEIM; SIAM J. Sci. Computer. 38 (2016), no. 3, A1454–A1482). In this work, we extend this framework and pair the CVOD‐type algorithms with any CSSP algorithm that returns linearly independent columns. Our results include detailed error bounds for the solutions provided by these paired algorithms, as well as expressions that explicitly characterize how the quality of the selected column partition affects the resulting CSSP solution. In addition to examples involving matrix approximation, we test several of our partition‐based constructions on tasks commonly encountered in model order reduction (MOR).

Converting Tessellations into Graphs: From Voronoi Tessellations to Complete Graphs

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 Rtrans(3,3)=5 Shannon entropies of the tessellation and graphs are introduced. Ramsey graphs emerging from random Voronoi and Poisson Line tessellations were investigated. The limits ζ=limN→∞NgNr, where N is the total number of green and red seeds, Ng and Nr, were found ζ= 0.272 ± 0.001 (Voronoi) and ζ= 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.

Warm Rydberg atom-based quadrature amplitude-modulated receiver

Rydberg atoms exhibit both remarkable sensitivity to electromagnetic fields making them promising candidates for revolutionizing field sensors and, unlike conventional antennas, they neither disturb the measured field nor necessitate extensive calibration procedures. In this study, we propose a receiver design for data-modulated signal reception near the 2.4 GHz Wi-Fi frequency band, harnessing the capabilities of warm Rydberg atoms. Our focus lies on exploring various quadrature amplitude modulations and transmission frequencies through heterodyne detection. We offer a comprehensive characterization of our setup, encompassing the atomic response frequency range, attainable electric field amplitudes, and sensitivity, which we estimate to be equal to 0.50 µV cm−1 Hz−0.5. Additionally, we delve into analyzing communication errors using Voronoi diagrams and evaluating the communication channel capacity across different modulation schemes. We find that the maximum achievable capacity for a single communication channel equals 19.3 Mbps and can be achieved using the QAM4 scheme.

An autonomous centreless approach to chunk-wise data partitioning

AbstractIn this paper, a novel autonomous centreless algorithm is proposed for data partitioning. The proposed algorithm firstly constructs the nearest neighbour affinity graph and identifies the local peaks of data density to build micro-clusters. Unlike the vast majority of partitional clustering algorithms, the proposed algorithm does not rely on singleton prototypes, namely, centres or medoids of the micro-clusters to partition the data space. Instead, these micro-clusters are directly utilised to attract nearby data samples to form shape-free Voronoi tessellations, hence, being centreless and robust to noisy data. A fusion scheme is further implemented to fuse these data clouds with higher intra-cluster similarity together to attain a more compact partitioning of data. The proposed algorithm is able to perform data partitioning on a chunk-wise basis and is highly computationally efficient with the default distance measure. Therefore, it is suitable for both static data partitioning in offline scenarios and streaming data partitioning in online scenarios. Numerical examples on a variety of benchmark datasets demonstrate the efficacy of the proposed algorithm.

Fluid flow zones along fracture corridors inferred from collapse dolines in carbonates of the Irecê Basin, Brazil

AbstractDolines are a widespread karst landform, and understanding their genesis can provide critical information about the evolution of subsurface karstification and groundwater flow zones. Swarms of collapse dolines characterise the karst in the southern portion of the Irecê Basin, northeastern Brazil. The basin comprises Neoproterozoic carbonate rocks approximately 100 m thick, bounded by less soluble older quartzites. The distribution of dolines is not uniform, as they cluster along NW‐SE axes and are aligned with cave systems and permeability (fracture) corridors mostly associated with the Almas and Água de Rega ephemeral rivers. Detailed analysis of sectors with a higher density of dolines was performed using LiDAR and unmanned aerial vehicle (UAV) imagery at two different scales to obtain morphometric and orientation patterns. As expected, scale dependency is observed, with an increase in density and circularity index at a higher resolution scale, but a decrease in mean area and perimeter. However, Voronoi polygon indices are similar at both scales (6.86 ± 1); the departure from the more stable number of six due to the clustering of dolines associated with NW‐SE oriented structural trends. Doline density trends closely follow the orientation of caves, but they are not always spatially connected, since doline evolution may either occlude the caves or be related to a non‐identified void. The Irecê Basin karst system displays a continuum of landforms evolving initially from high‐density fracture zones (fracture corridors), which work as favourable dissolution zones, grading into more integrated flow routes, cave systems and eventually clusters of collapse dolines. Collapse dolines are widespread karst landforms worldwide, and their genesis requires the presence of dissolution voids at depth, which may pass undetected from the surface. In some sectors of Irecê Basin, the existence of doline alignments but the absence of known caves indicates the potential of collapse dolines to be used as proxies for subsurface karstification. Such an approach may allow the prediction of the location and orientation of subsurface zones of enhanced dissolution that can potentially represent productive aquifers or favourable zones for geofluids.

Non-hyperuniformity of Gibbs point processes with short-range interactions

Abstract We investigate the hyperuniformity of marked Gibbs point processes that have weak dependencies among distant points whilst the interactions of close points are kept arbitrary. Various stability and range assumptions are imposed on the Papangelou intensity in order to prove that the resulting point process is not hyperuniform. The scope of our results covers many frequently used models, including Gibbs point processes with a superstable, lower-regular, integrable pair potential, as well as the Widom–Rowlinson model with random radii and Gibbs point processes with interactions based on Voronoi tessellations and nearest-neighbour graphs.