Voronoi Diagram Research Articles

Navigation of a Quadrotor Based on Voronoi Division Calculated from Local Information

This study applies a successful collision-avoidance method using buffered Voronoi cells (BVC) to control quadrotors. In particular, we consider the case of dealing with stationary obstacles using only the local information obtained from sensors, which has not been discussed in previous studies. In this study, we assume an unknown environment with grid-shaped obstacles. We demonstrate that four quadrotors can compute the information required for the BVC-based collision avoidance algorithm and move in the same environment without communicating with each other or receiving information from a central controller, using the local information obtained from the mounted 3D LiDAR. Simulations indicate that the system can handle static obstacles using point-cloud data obtained using 3D LiDAR as Voronoi seeds. We also demonstrate that the BVC-based collision avoidance algorithm can be applied to quadrotors controlled by a simple PD position controller without any modification to the controller. These findings show that the BVC-based collision avoidance can be easily implemented using existing commercial drones.

Short and medium range order in the rapidly solidified metallic liquid Ta: Atomic packing, connection modes, and pressure effect

In this study, molecular dynamics (MD) simulations were utilized to explore the Short and Medium-Range Order (MRO) in the rapidly solidified metallic liquid tantalum (Ta). Radial distribution function (RDF) and Voronoi tessellation analysis (VTA) techniques were employed to thoroughly explore the effect of pressure on the connectivity and structural properties at the Short-Range Order (SRO) and MRO levels. Our findings indicate that, at a quenching rate of 1013 K s-1, glassy states are achieved at or below 20 GPa, while crystalline phases emerge at 25 GPa. VTA analysis indicates a significant alteration in the local structure of glassy Ta with increasing pressure. Specifically, the fraction of icosahedral-like clusters decreases while the fraction of crystal-like clusters rises notably.Furthermore, we highlight that icosahedral-like clusters strongly tend to form 3-atom connection mode, while crystal-like clusters prefer 2-atom and 4-atom connection modes. Notably, icosahedral-like clusters are identified as the primary contributors to the emergence of the left sub-peak in the second peak of the RDF. In contrast, all cluster types contribute to the appearance of the right sub-peak.

High-traversability and efficient path optimization for deep-sea mining vehicles considering complex seabed environmental factors

In cobalt-rich crust regions, rapid and safe pathfinding is critical for the operation of Deep-Sea Mining Vehicles (DSMVs). However, existing pathfinding solutions rarely account for traversability predictions in complex mining environments and extensive map data often results in computational inefficiencies. This paper proposes a High-Traversability and Efficient Path Optimization (HTEPO) strategy designed to ensure safe navigation and rapid decision-making accounting for complex seabed environmental factors. Initially, we develop a traversability assessment model combining the Analytic Hierarchy Process (AHP) with the Fuzzy Comprehensive Evaluation (FCE) method. This model assigns traversability scores to map out high-risk and impassable areas effectively. We then introduce a novel map model that integrates these scores with Voronoi diagrams to reduce search space and improve computing efficiency, ensuring safer route selections. Further, based on traversability index and map model, an enhanced A∗ algorithm equipped with adaptive heuristic weights is utilized to swiftly identify high-traversability paths for the DSMVs. Finally, three case studies with different seabed mining environments validate the excellent performance of the proposed method over other major existing methods in terms of path safety and computational efficiency.

Rift Gaps in Chemical-Wave Network Systems.

We carry out experiments in diffusion-precipitation systems in a framework with multiple diffusion sources. The advancing precipitation fronts reach a point where they stop, leaving a rift or gap between the precipitate zones. In a similar setting, fractal metal deposits emerging from various reduction centers were synthesized. They were shown to meander in the medium, but fail to meet or overlap, thus also leaving a gap or rift just like in the precipitation system. The obtained patterns were analyzed by calculating entropy and front velocity for the former system, and fractal dimension for the latter. The observed structures represent chemical analogs of Voronoi diagrams.

AddiVortes: (Bayesian) Additive Voronoi Tessellations

The Additive Voronoi Tessellations (AddiVortes) model is a multivariate regression model that uses Voronoi tessellations to partition the covariate space in an additive ensemble model. Unlike other partition methods, such as decision trees, this has the benefit of allowing the boundaries of the partitions to be non-orthogonal and non-parallel to the covariate axes. The AddiVortes model uses a similar sum-of-tessellations approach and a Bayesian backfitting MCMC algorithm to the BART model. We utilize regularization priors to limit the strength of individual tessellations and accepts new models based on a likelihood. The performance of the AddiVortes model is illustrated through testing on several data sets and comparing the performance to other models along with a simulation study to verify some of the properties of the model. In many cases, the AddiVortes model outperforms random forests, BART and other leading black-box regression models when compared using a range of metrics. Supplementary materials for this article are available online.

Evolution mapping II: describing statistics of the non-linear cosmic velocity field.

Abstract We extend the evolution mapping approach, introduced in the first paper of this series to describe non-linear matter density fluctuations, to statistics of the cosmic velocity field. This framework classifies cosmological parameters into shape parameters, which determine the shape of the linear matter power spectrum, PL(k, z), and evolution parameters, which control its amplitude at any redshift. Evolution mapping leverages the fact that density fluctuations in cosmologies with identical shape parameters but different evolution parameters exhibit similar non-linear evolutions when expressed as a function of clustering amplitude. We analyse a suite of N-body simulations sharing identical shape parameters but spanning a wide range of evolution parameters. Using a method for estimating the volume-weighted velocity field based on the Voronoi tesselation of simulation particles, we study the non-linear evolution of the velocity divergence power spectrum, Pθθ(k), and its cross-power spectrum with the density field, Pδθ(k). We demonstrate that the evolution mapping relation applies accurately to Pθθ(k) and Pδθ(k). While this breaks down in the strongly non-linear regime, deviations can be modelled in terms of differences in the suppression factor, g(a) = D(a)/a, similar to those for the density field. Such modelling describes the differences in Pθθ(k) between models with the same linear clustering amplitude to better than 1percnt accuracy at all scales and redshifts considered. Evolution mapping simplifies the description of the cosmological dependence of non-linear density and velocity statistics, streamlining the sampling of large cosmological parameter spaces for cosmological analysis.

Theoretical Investigation into Polymorphic Transformation between β-HMX and δ-HMX by Finite Temperature String

Polymorphic transformation is important in chemical industries, in particular, in those involving explosive molecular crystals. However, due to simulating challenges in the rare event method and collective variables, understanding the transformation mechanism of molecular crystals with a complex structure at the molecular level is poor. In this work, with the constructed order parameters (OPs) and K-means clustering algorithm, the potential of mean force (PMF) along the minimum free-energy path connecting β-HMX and δ-HMX was calculated by the finite temperature string method in the collective variables (SMCV), the free-energy profile and nucleation kinetics were obtained by Markovian milestoning with Voronoi tessellations, and the temperature effect on nucleation was also clarified. The barriers of transformation were affected by the finite-size effects. The configuration with the lower potential barrier in the PMF corresponded to the critical nucleus. The time and free-energy barrier of the polymorphic transformation were reduced as the temperature increased, which was explained by the pre-exponential factor and nucleation rate. Thus, the polymorphic transformation of HMX could be controlled by the temperatures, as is consistent with previous experimental results. Finally, the HMX polymorph dependency of the impact sensitivity was discussed. This work provides an effective way to reveal the polymorphic transformation of the molecular crystal with a cyclic molecular structure, and further to prepare the desired explosive by controlling the transformation temperature.

An Algorithm for Creating a Synaptic Cleft Digital Phantom Suitable for Further Numerical Modeling

One of the most significant applications of mathematical numerical methods in biology is the theoretical description of the convectional reaction–diffusion of chemical compounds. Initial biological objects must be appropriately mimicked by digital domains that are suitable for further use in computational modeling. In the present study, an algorithm for the creation of a digital phantom describing a local part of nervous tissue—namely, a synaptic contact—is established. All essential elements of the synapse are determined using a set of consistent Boolean operations within the COMSOL Multiphysics software 6.1. The formalization of the algorithm involves a sequence of procedures and logical operations applied to a combination of 3D Voronoi diagrams, an experimentally defined inner synapse area, and a simple ellipsoid under different sets of biological parameters. The obtained digital phantom is universal and may be applied to different types of neuronal synapses. The clear separation of the designed domains reveals that the boundary’s conditions and internal flux dysconnectivity functions can be set up explicitly. Digital domains corresponding to the parts of a synapse are appropriate for further application of the derived numeric meshes, with various capacities of the included elements. Thus, the obtained digital phantom can be effectively used for further modeling of the convectional reaction–diffusion of chemical compounds in nervous tissue.

Modulating the rejuvenation in a Al75Mg25 metallic glass by multiple recovery annealing treatment

Rejuvenation presents a promising way to improve the plasticity of metallic glasses. How modulating the degree of rejuvenation of metallic glasses remains a challenging issue. Here, based on the molecular dynamics simulation, we investigate the evolution of the structural and mechanical properties of a binary Al75Mg25 metallic glass and successfully realized the rejuvenation modulation through the multiple recovery annealing treatment. A range of samples with different degrees of rejuvenation were obtained by successive multiple recovery annealing process. According to our calculations, we found that the degree of rejuvenation is highly correlated with the Al-centered clusters. Microstructural analyses show that a higher degree of rejuvenation is concomitant with less 1551 index of Honeycutt-Andersen indices and a lower content of <0,0,12,0 > in terms of Voronoi Tessellation analysis. Moreover, our calculated results demonstrate that the samples with the aging initial state show a higher degree of rejuvenation as compared to the samples with the rejuvenated initial state. This can be attributed to that there are more icosahedral clusters, which are more likely to change to other types of clusters with low local fivefold symmetry in the aged samples during the subsequent high-temperature annealing process. Our work confirms that proper multiple (no more than three times) recovery annealing treatment can increase the degree of rejuvenation of metallic glasses and can offer a better understanding of the effect of rejuvenation on the microstructures and mechanical properties of metallic glasses.

Energy-based characterisation of large-scale coherent structures in turbulent pipe flows

Large-scale coherent structures in incompressible turbulent pipe flow are studied for a wide range of Reynolds numbers ( $Re_\tau =180, 550, 1000, 2000$ and $5200$ ). Employing the Karhunen–Loève decomposition and a novel approach based on the Voronoi diagram, we identify and classify statistically coherent structures based on their location, dimensions and $Re_{\tau }$ . With increasing $Re_{\tau }$ , two distinct classes of structures become more energetic, namely wall-attached and detached eddies. The Voronoi methodology is shown to delineate these two classes without the need for specific criteria or thresholds. At the highest $Re_{\tau }$ , the attached eddies scale linearly with the wall-normal distance with a slope of approximately $l_y\sim 1.2y/R$ , while the detached eddies remain constant at the size of $l_y \approx 0.26R$ , with a progressive shift towards the pipe centre. We extract these two classes of structures and describe their spatial characteristics, including radial size, helix angle and azimuthal self-similarity. The spatial distribution could help explain the differences in mean velocity between pipe and channel flows, as well as in modelling large and very-large-scale motions (LSM and VLSM). In addition, a comprehensive description is provided for both wall-attached and detached structures in terms of LSM and VLSM.

Local classification of crystalline structures in complex plasmas using a PointNet

Abstract In complex plasmas, microparticles can form ordered crystalline structures under specific conditions. Accurately identifying these structures, such as face-centered cubic, hexagonal close-packed, and body-centered cubic, is a common task in physics. Previous methods rely on detecting symmetries in the spatial arrangement of particles, often requiring extensive calculations. This study presents a novel approach by utilizing a PointNet-based deep learning algorithm, called WignerNet, to classify these structures directly from three-dimensional reconstructions of their Voronoi cells. The model was trained exclusively on artificial and labeled data, incorporating various noise levels, and subsequently tested on real experimental data. The results demonstrate that our method effectively classifies structures, reducing computational complexity and improving accuracy compared to conventional techniques. This advancement opens up new possibilities for real-time analysis of complex plasma systems in various research.

A study on the sound scattering characteristics in random structure using Voronoi Tessellation

In room acoustic design, the use of acoustic diffusers is an effective method for achieving a uniform sound field and controlling reverberation. A common approach is to use periodic diffusers that control reflection directions based on the wavelength of sound. In this study, we explore the utilization of random and nonperiodic structures as acoustic diffusers, taking inspiration from the amorphous structures in nature. The irregularities in random structures are expected to enable the broad diffusion of a wide range of frequencies in various directions. We utilized Voronoi tessellation in both two and three dimensions to create 2D Voronoi diffusers with irregular aperture shapes and 3D Voronoi diffusers with irregular aperture shapes and slopes. Then, the acoustic diffusion characteristics of the 2D and 3D Voronoi diffusers were compared with a periodic-type structure through the finite element analysis and experiments. On the basis of these results, the irregularities in the openings and slopes of Voronoi diffusers broaden the scattering frequencies and enhance the scattering coefficients. This suggests that amorphous structures utilizing Voronoi tessellation can be effective as acoustic diffusers.

Research on mobile energy storage scheduling strategy for emergency power supply protection of post-disaster isolated loads

Aiming at the problem of insufficient power supply capacity of isolated loads in oceanic islands, a concept based on mobile energy storage and power conservation is proposed in this paper. Firstly, the energy flow and traffic flow characteristics of mobile energy storage are quantitatively analyzed, and an accurate mathematical model is established. Furthermore, the time-space distribution characteristics of load are carefully considered, and the Voronoi diagram and Tyson polygon method are introduced to determine cell differentiation. On this basis, combined with the power demand of load nodes and the energy storage characteristics of mobile energy storage vehicles, the evaluation indicators of cell energy and relative surplus energy of cells are designed, and the agent-cellular automata algorithm is used to schedule the mobile energy storage. The simulation results show that the power supply mode based on mobile energy storage can effectively improve the reliability of isolated loads. This paper provides a new perspective for solving the reliable power supply problem of isolated loads.

The dual problem of space: Relative player positioning determines attacking success in elite men’s football

ABSTRACT The concept of space has been successfully modelled in football using spatiotemporal player data and Voronoi diagrams. Current approaches, however, are narrow in scope by focusing on an inter-team allocation of space to measure space control. The present work extends this widespread perspective with an intra-team application of the Voronoi diagram and its dual Delaunay triangulation to measure space management. Both models are leveraged to derive novel performance metrics, which assess how teams use triangular positioning and how players tie up defenders during attacks. The outcome of N = 128,187 attacking sequences from 306 elite men’s football matches is analysed using linear mixed-effects models to validate the proposed performance metrics. Results show that attacking success is characterized by player positioning which promotes forming of large triangles especially in ball proximity, whereas the overall number of triangles is of no relevance. Furthermore, players tie up more defenders and thus create free teammates more often during successful attacks. The results demonstrate that a new perspective on space is helpful to better quantify and understand the effect of space management and player positioning on attacking performance in football.

TCDM: Transformational Complexity Based Distortion Metric for Perceptual Point Cloud Quality Assessment.

The goal of objective point cloud quality assessment (PCQA) research is to develop quantitative metrics that measure point cloud quality in a perceptually consistent manner. Merging the research of cognitive science and intuition of the human visual system (HVS), in this article, we evaluate the point cloud quality by measuring the complexity of transforming the distorted point cloud back to its reference, which in practice can be approximated by the code length of one point cloud when the other is given. For this purpose, we first make space segmentation for the reference and distorted point clouds based on a 3D Voronoi diagram to obtain a series of local patch pairs. Next, inspired by the predictive coding theory, we utilize a space-aware vector autoregressive (SA-VAR) model to encode the geometry and color channels of each reference patch with and without the distorted patch, respectively. Assuming that the residual errors follow the multi-variate Gaussian distributions, the self-complexity of the reference and transformational complexity between the reference and distorted samples are computed using covariance matrices. Additionally, the prediction terms generated by SA-VAR are introduced as one auxiliary feature to promote the final quality prediction. The effectiveness of the proposed transformational complexity based distortion metric (TCDM) is evaluated through extensive experiments conducted on five public point cloud quality assessment databases. The results demonstrate that TCDM achieves state-of-the-art (SOTA) performance, and further analysis confirms its robustness in various scenarios.

A Comprehensive Deep Learning–Based Approach to Field Reconstruction in Reactor Cores

The aging process or flow-induced vibration of reactor cores may lead to increased mechanical vibrations, affecting the reliability of in-core sensors and necessitating a robust solution for robust field reconstruction. This work tackles the challenges of reconstructing multiphysics fields from sparse and movable measurements by introducing an advanced framework that integrates various machine learning models with Voronoi tessellation. Our approach, building upon the Voronoi tessellation-assisted Convolutional Neural Network (VCNN), expands the capabilities to include a wider array of neural network architectures such as Convolutional Neural Networks (CNNs), Fourier Neural Operator (FNO), Dilated ResNet Encode-Process-Decode (DilResNet), Dilated Convolution Neural Operator (DCNO), Galerkin Transformer (GT), U-shaped Neural Operator (UNO), and Multiwavelet-based Operator (MWT). The effectiveness of these models is evaluated and validated through numerical tests based on the International Atomic Energy Agency benchmark, particularly noting average relative errors below 5% and 10% in the L 2 norm and L ∞ norm, respectively, within a 5-cm amplitude around sensor nominal locations. The developed software toolkit encapsulates these architectures, providing a versatile option for nuclear engineers to reconstruct different types of physical fields efficiently.

Correlation-Based Predictions of Gas Solute Diffusivity in Ionic Liquid Solvents Based on Solvent-Accessible Surface Area.

In our prior study [Olowookere, F. V.; Turner, C. H. J. Phys. Chem. B 2023, 127(42), 9144-9154], we introduced a new scaling relationship to predict gas solute diffusion at challenging conditions, focusing on CO2 and SO2 diffusion in multivalent ionic liquid (IL) solvents. This work extends our initial exploratory study into a much broader array of systems, encompassing additional solutes (N2, CH4, C2H6, C3H8, C3H8O, and H2O) and a variety of different ionic liquid species ([Bzmim3]3+, [Bzmim4]4+, [BMIM]+, [EMIM]+, [HMIM]+, [NapO2]2-, [BzO3]3-, [BF4]-, [Tf2N]-, and [PF6]-). Our study demonstrates a remarkably robust logarithmic correlation between solute diffusion and solvent accessible surface area (SA) across 20 different additional systems. We perform comprehensive analyses of the underlying molecular phenomena responsible for this correlation, including solute lifetime distributions, void space dynamics, and Voronoi tessellation, in order to elucidate a stronger mechanistic understanding of this behavior. Our findings highlight a direct link between the solvent accessible SA and the size of the void domains. Overall, our scaling approach provides an efficient and reliable approach for predicting diffusion from analyses of short simulations at higher temperatures.

DelaunayTriangulation.jl: A Julia package for Delaunay triangulations and Voronoi tessellations in the plane

DelaunayTriangulation.jl: A Julia package for Delaunay triangulations and Voronoi tessellations in the plane

Optimizing large-scale CO2 pipeline networks using a geospatial splitting approach

CO2 transport infrastructure is the backbone of carbon capture and storage (CCS) technology for the mitigation of carbon emissions and project deployment viability. In conventional large-scale CO2 pipeline network designs, the storage sites are generally assumed as the centroids of the major geologic basins, however, this approach might provide suboptimal solutions since the large extension of some storage formations significantly increases the length of the CO2 transportation networks. To address this situation and obtain optimal pipeline routes, we present a novel geospatial splitting framework that partitions large basins into multiple sub-sinks. In our approach, we used a large number of reservoir models varying petrophysical properties and CO2 injection rates to compute pressure plumes through numerical simulations, leading to the calculation of the number of subregions for each basin as a function of the extension of pressure interference areas and boundaries. Finally, we applied K-means clustering and Voronoi polygon algorithms to partition large basins into subregions and obtain their sink coordinates. To demonstrate the capability of the developed workflow, we investigated two CO2 pipeline network modeling case studies using our splitting approach: one regional case study focusing on the Intermountain West (I-West) region and one nationwide case study covering the lower 48 states in the U.S. In both case studies, we compared the optimal pipeline routes using the original and new storage locations and examined the major differences. The use of the developed geospatial approach resulted in both cases in a shortening of the total pipeline network length by 13% and 10%, compared to the pipeline modeling with the original basins, leading to cost reductions of 25% and 17%, respectively, demonstrating that the location of point sinks has a critical impact on the length and expenses of pipelines to efficiently transport CO2 to distant storage sites. Therefore, the workflow presented here contributes to the proper and realistic modeling of case studies that support decision-making in CCS deployment.

The Detection of Maize Seedling Quality from UAV Images Based on Deep Learning and Voronoi Diagram Algorithms

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.