Voronoi Diagram Research Articles

A new test of gravity – I. Introduction to the method

ABSTRACT We introduce a new scheme based on the marked correlation function to probe gravity using the large-scale structure of the Universe. We illustrate our approach by applying it to simulations of the metric-variation f(R) modified gravity theory and general relativity (GR). The modifications to the equations in f(R) gravity lead to changes in the environment of large-scale structures that could, in principle, be used to distinguish this model from GR. Applying the Monte Carlo Markov Chain algorithm, we use the observed number density and two-point clustering to fix the halo occupation distribution (HOD) model parameters and build mock galaxy catalogues from both simulations. To generate a mark for galaxies when computing the marked correlation function we estimate the local density using a Voronoi tessellation. Our approach allows us to isolate the contribution to the uncertainty in the predicted marked correlation function that arises from the range of viable HOD model parameters, in addition to the sample variance error for a single set of HOD parameters. This is critical for assessing the discriminatory power of the method. In a companion paper, we apply our new scheme to a current large-scale structure survey.

Unlocking the Thermal Efficiency of Irregular Open-Cell Metal Foams: A Computational Exploration of Flow Dynamics and Heat Transfer Phenomena

An open-cell metal foam has excellent characteristics such as low density, high porosity, high specific surface area, high thermal conductivity, and low mass due to its unique internal three-dimensional network structure. It has gradually become a new material for enhanced heat transfer in industrial equipment, new compact heat exchangers, microelectronic device cooling, etc. This research established a comprehensive three-dimensional structural model of open-cell metal foams utilizing Laguerre–Voronoi tessellations and employed computational fluid dynamics to investigate its flow dynamics and coupled heat transfer performance. By exploring the impact of foam microstructure on flow resistance and heat transfer characteristics, the study provided insights into the overall convective heat transfer performance across a range of foam configurations with varying pore densities and porosities. The findings revealed a direct correlation between convective heat transfer coefficient (h) and pressure drop (ΔP) with increasing Reynolds number (Re), accompanied by notable changes in fluid turbulence kinetic energy (e) and temperature (T), ultimately influencing heat transfer efficiency. Furthermore, the analysis demonstrated that alterations in porosity (ε) and pore density significantly affected unit pressure drop (ΔP/L) and convective heat transfer coefficient (h). This study identified an optimal configuration, highlighting a metal foam with a pore density of 20 PPI and a porosity of 95% as exhibiting superior overall convective heat transfer performance.

Location privacy protection method based on differential privacy in crowdsensing task allocation

With the widespread popularity of smart phones, watches and other devices, mobile crowdsensing (MCS) has gradually entered the public’s field of vision. However, the widespread use of MCS technology is accompanied by an increasing risk of workers’ personal privacy being violated. Typically, workers are required to submit location information in order to participate in task assignments, and the privacy of a worker’s location information is a key factor in determining worker participation. Therefore, in order to solve the problem of workers location privacy leakage in the process of task allocation, this paper proposes a location privacy protection method based on local differential privacy (VLDPP). VLDPP constructs a task map based on Voronoi diagram according to the task location, and each task location is mapped into a task area to hide the task location. A local coordinate system is constructed based on the task area, and all workers in the area have their relative location coordinates recalculated and encoded, and then the encoding is perturbed by local differential privacy, thus ensuring workers location privacy. The worker uploads the perturbed location information to the server, which determines the workers in the task by calculating the worker’s acceptance rate and completes the task allocation. In addition, this paper improves the availability of perturbed worker location information by dividing the task area at a secondary level. This paper uses the internationally recognized World Check-In Gowalla dataset for experimental evaluation, which shows that the proposed method has good performance in terms of data availability and efficiency, providing adequate privacy guarantees.

D4G framework: a novel Voronoi diagram classification for decoding natural geometrics to enhance the built environment

This study enhances designers’ ability to decode natural geometric patterns, simplify their descriptions, and apply them to the built environment using Voronoi diagram (VD). Therefore, VDs are examined using a literature review, establishing the D4G classification of VDs, which consists of five acronyms: dimension, domain, distribution, dominance, and generator. Additionally, we developed an analytical comparison matrix to conclude the VDs’ application benefits at different design scales. Finally, we validate the proposed framework at three integration scales: interior, architectural, and urban design, to decode natural geometric patterns and generate various VDs using Rhino software and Grasshopper plug-in. The study concluded that a limitless number of decoding patterns can be deduced based on the inputs. Nevertheless, the analytical comparison matrix was applied to selected patterns using the D4G classification of VDs, and the D4G classification-based framework was evaluated in only three case studies. Moreover, the expected benefits were determined for each case.

Microperimetry and Structural Risk Factors on OCT in Intermediate Age-Related Macular Degeneration

PurposeTo determine the relationship between structural biomarkers on optical coherence tomography (OCT) that increases the risk of disease progression and microperimetric retinal sensitivity in patients with intermediate age-related macular degeneration (iAMD) DesignProspective cross-sectional, observational study ParticipantsForty-five eyes of 23 patients with iAMD MethodsPatients underwent OCT and microperimetry. OCT scans were evaluated for the risk factors intraretinal hyperreflective foci (HRF), hyporeflectivity within drusenoid lesions (HRDL), subretinal drusenoid deposits (SDD), double layer sign (DLS) and drusen volume. Microperimetric retinal sensitivity was analyzed with a 33-point grid covering the macula. With a novel method of determining what part of the retina corresponded to each microperimetry point, a Voronoi diagram was constructed, dividing the macula in cells consisting of the region nearer to each point than any other. The Voronoi diagram was superimposed on the OCT making it possible to determine the point-to-point location of the OCT risk factors. Univariable and multivariable linear mixed effects models were used for analysis Main Outcome MeasuresAssociation between microperimetric retinal sensitivity and OCT risk factors at individual measuring points Results1479 points of retinal sensitivity and corresponding structural area on OCT were included in this study. Retinal sensitivity was significantly decreased with presence of the OCT risk factors HRF, HRDL, DLS and drusen volume (all P < 0.001) when analyzed with the univariable linear mixed effects model. The multivariable model showed a significant decrease of retinal sensitivity with presence of HRF (P < 0.001), DLS (P = 0.025) and greater drusen volume (P < 0.001) ConclusionPresence of HRF, DLS, and greater drusen volume, all of which increase the risk of disease progression, are significantly and independently associated with decreased microperimetric retinal sensitivity in patients with iAMD.

ANALYSIS OF EXISTING METHODS FOR DETERMINING INTERMEDIATE GEOTECHNICAL CHARACTERISTICS OF SOILS

This article presents an overview of the main methods for determining the intermediate geotechnical characteristics of soils, emphasizing the importance of strict adherence to the testing regime. Deterministic and stochastic interpolation methods such as Thiessen polygons, inverse distance weighting (IDW), Spline and Kriging are discussed. Special attention is given to the problem of determining strength properties at various points, where only certain areas are to be investigated and intermediate values are obtained by interpolation methods. The analysis of geotechnical reliability using Kriging numerical models and methods of using geographic information systems for processing and presenting geotechnical data are also discussed.

Numerical investigation of the mechanical properties of lattice structures inspired from polycrystalline materials

In this work, polycrystalline-like lattice structures that are inspired by the geometry of polycrystalline materials are designed. They are generated by filling periodic lattice structures into a Voronoi diagram. Then, finite element analyses of two periodic and eight polycrystalline-like lattice structures are performed to compare their mechanical properties. The numerical results show that polycrystalline-like lattice structures consisting of anisotropic rectangular X-type periodic unit cells are isotropic at the macroscale. Moreover, they have a higher specific stiffness and specific strength than periodic lattice structures under compression. Then, the energy absorption capability is investigated. Five energy absorption indicators (energy absorption, energy absorption per unit volume, specific energy absorption per unit mass, crush stress efficiency, and plateau stress) reveal that polycrystalline-like lattice structures are better energy absorption structures. Furthermore, the defect sensitivity of missing struts is discussed. The findings of this work offer a new route for designing novel lattice structures.

Representation of the microstructure of pearlitic steels for DEM simulations of fatigue

The fatigue behavior of pearlitic steels in wheel-rails is correlated to the microstructure. However, existing models do barely take this correlation into account. In this work, we propose a hierarchical meshing to describe the microstructure of pearlitic steels. The mesh includes grain and block/colony boundaries, lamellae orientations, and orientation perpendicular to lamellae. We use the Voronoi Tessellation method to generate elements with the specific area fraction distribution for pearlite colony areas. The colony and block information is obtained from SEM and EBSD measurements of R260 steel to construct the mesh that represents the microstructure. Finally, we obtained the deformed microstructure via simple geometrical shearing. This meshing method is the first step for modeling fatigue crack growth anisotropy due to plastic deformation.

A typhoon-induced storm surge numerical model with GPU acceleration based on an unstructured spherical centroidal Voronoi tessellation grid

A typhoon-induced storm surge numerical model with GPU acceleration based on an unstructured spherical centroidal Voronoi tessellation grid

Voronoi cells in metric algebraic geometry of plane curves

Voronoi cells of varieties encode many features of their metric geometry. We prove that each Voronoi or Delaunay cell of a plane curve appears as the limit of a sequence of cells obtained from point samples of the curve. We use this result to study metric features of plane curves, including the medial axis, curvature, evolute, bottlenecks, and reach. In each case, we provide algebraic equations defining the object and, where possible, give formulas for the degrees of these algebraic varieties. We show how to identify the desired metric feature from Voronoi or Delaunay cells, and therefore how to approximate it by a finite point sample from the variety.

Novel Skin-Reinforcement Design by Cross–Longitudinal Layout Inspired by Dragonfly Wing

The objective of this study is to develop a novel aircraft design approach using biomimetics as an alternative to traditional airframes. This approach is primarily inspired by the dragonfly wing, which possesses reinforcement structures composed of cross veins and longitudinal veins. These structures are assumed to regulate deformation and enhance stiffness, respectively. The cross veins were replicated using weighted centroidal Voronoi tessellation (WCVT) based on the out-of-plane displacement of the skin. In contrast, the longitudinal veins were replicated by extracting a centerline from the topology optimization (TO) results on the skin, achieved through image analysis techniques such as binarization and skeletonization. The longitudinal layout effectively reduces compliance by distributing internal loads, utilizing only essential reinforcements on the skin without increasing its mass. The WCVT layout significantly enhances the buckling resistance of the reinforced skin. As a result, the skin reinforced using both cross–longitudinal layouts from TO and WCVT exhibited a buckling load 2.7 times greater while maintaining a lower mass compared to conventional layouts.

An Adaptive Sampling Strategy for Real-Time Anomaly Detection with Unmanned Sensing Vehicles

Unmanned sensing vehicles (USVs) have been widely used for real-time anomaly detection in various applications, including environmental monitoring, precision agriculture, and military surveillance. The USVs collecting data can only provide partial information about the space being monitored. Thus, it is critical to decide where to deploy the USVs at each point in time to maximize the change detection capability, while minimizing deployment costs. This article proposes an adaptive sampling strategy for real-time anomaly detection with USVs. First, a novel spatio-temporal sequential tensor decomposition algorithm is developed to decompose the high-dimensional data collected by the USVs into three components, a spatial component, a temporal component, and a sparse component, that captures the locations suspicious of change. The spatial and temporal components are used for one-step prediction to guide the adaptive sampling strategy. The strategy is designed to maximize the detection power and control the deployment costs. The main idea is to balance exploration and exploitation by designing a sampling distribution function to decide where to collect data at each acquisition time. The movement of the USVs is controlled by using Voronoi tessellations on the sampling distribution function. The performance of the proposed framework is demonstrated through simulations and case studies.

Role of cluster structure on the deformation behavior of Zr58Cu36Al6 metallic glass

Molecular dynamics simulations were used to simulate the process of tensile and compressive deformation of Zr58Cu36Al6 metallic glass (MG), and the variations of various cluster structures during the deformation were analyzed by the Voronoi tessellation method. The prepared Zr58Cu36Al6 alloy was found to be amorphous and the glass transition temperature obtained was about 753 K. In the deformation processes, the icosahedral-like clusters with the biggest quantity percentage decreased significantly and eventually, the damaged icosahedral-like clusters tended to be destroyed into "fragmented" clusters. Icosahedral-like clusters were more stable due to their lower average strain and shear stress compared to other clusters. The higher strain and shear stress of the clusters led to an earlier stress drop of Zr58Cu36Al6 MG during compression. However, the higher connectivity of the icosahedral network remained in Zr58Cu36Al6 MG making the overshoot stress and flow stress larger but lower plasticity in compression than those in tension.

Numerical analysis on the effect of graded porosity in closed-cell metal foams/PCM composites

The porous metal foams are potential to integrate phase change materials (PCMs) to form the shape-stabilized composited PCMs for the applications of thermal energy management and temperature regulation. However, the effect of porosity distribution of foam keeps challenging in designing such PCM-based composites. In this work, the closed-cell graded porosity foams (GPFs) involving various gradient directions and gradient differences of porosity are engineered by shrinking Voronoi tessellations to achieve precisely tunable microstructure. Then the GPF/PW composite is formed by integrating paraffin wax (PW) in each pore and its melting performance is investigated by the computational model, which is validated by the melting experiment of a specific sample. The investigations on the gradient configurations of foams reveal that the gradient direction and gradient difference of porosity have significant influences on the pore-scale melting behavior, liquid fraction variation in time and overall energy storage efficiency of PW. The positive gradient variation along the direction of heating source and the moderate gradient difference, i.e. 20% or 30%, are beneficial to improve the melting behavior of graded models. In contrast to the uniform model, the complete melting time of the graded models can maximum shorten by 5.6%, 3.8% and 3.7% for the bottom, lateral and top heating modes, respectively.

Energy Efficient Localization Technique Using Multilateration for Reduction of Spatially and Temporally Correlated Data in RFID System

RFID plays a vital role in data communication in multidimensional WSNs as it collects vast amounts of redundant data. The physical phenomena constitute the correlated observations in the space domain and generate spatial correlation. Periodic observations of sensor nodes result in a temporal correlation in the data. Reducing these spatio-temporal correlations in RFID surveillance data is necessary for the smooth functioning of the network. This paper proposes a Voronoi diagram-based spatio-temporal data redundancy elimination approach for RFID systems having multiple readers so only one reader will read every RFID tag depending on the distance between the tag and the center of the Minimum Enclosing Circle of the Voronoi cell to which the reader belongs. This approach eliminates spatial redundancy in the gathered data. Reading the RFID tags at regular time intervals larger than a chosen threshold value minimized temporal redundancy. In contrast to existing methods, the proposed technique is free from any false positive and false negative errors, with no loss of data and every tag being read by only one reader. Simulation of the proposed approach also established its superiority to the existing techniques in terms of these performance parameters.

Hot Spots of Gun Violence in the Era of Focused Deterrence: A Space-Time Analysis of Shootings in South Philadelphia

Gun and street group violence remains a serious problem in cities across the United States and the focused deterrence strategy has been a widely applied law enforcement intervention to reduce it. Although two meta-analytical studies concluded that the intervention had a significant effect on violence, questions remain about how violence changes across space and time during and after the intervention. This study applies novel geospatial analyses to assess spatiotemporal changes in gun violence before, during, and after the implementation of Philadelphia Focused Deterrence. Emerging hot spot analysis employing Space-Time cubes of ten annual time bins (2009–2018) at the Thiessen polygon level was used to detect and categorize patterns. The analyses revealed a non-significant decreasing trend across the ten-year period. Furthermore, there were ninety-three statistically significant hot spots categorized into four hot spot patterns: fourteen new hot spots; twenty-three consecutive; one persistent; and fifty-three sporadic. There was no evidence showing statistically significant hot spots for the “diminishing” pattern. Knowledge of these patterns that emerge across micro-locations can be used by law enforcement practitioners to complement data-driven problem solving and fine tune these strategies and other place-based programming. Policymakers can use findings to prioritize resources when developing complementary prevention and intervention efforts by tailoring those efforts to the different emergent patterns.

Impacts of anemometer changes, site relocations and processing methods on wind speed trends in China

Abstract. In situ surface wind observation is a critical meteorological data source for various research fields. However, data quality is affected by factors such as surface friction changes, station relocations and anemometer updates. Previous methods to address discontinuities have been insufficient, and processing methods have not always adhered to World Meteorological Organization (WMO) World Climate Programme guidelines. We analyzed data discontinuity caused by anemometer changes and station relocations in China's daily in situ near-surface (∼ 10 m) wind speed observations and the impact of the processing methods on wind speed trends. By comparing the wind speed discontinuities with the recorded location changes, we identified 90 stations that showed abnormally increasing wind speeds due to relocation. After removing those stations, we followed a standard quality control method recommended by the World Meteorological Organization to improve the data reliability and applied Thiessen polygons to calculate the area-weighted average wind speed. The result shows that China's recent reversal of wind speed was reduced by 41 % after removing the problematic stations, with an increasing trend of 0.017 m s−1 yr−1 (R2 = 0.64, P &lt; 0.05), emphasizing the importance of robust quality control and homogenization protocols in wind trend assessments.

Calibration of agent based models for monophasic and biphasic tumour growth using approximate Bayesian computation

Agent-based models (ABMs) are readily used to capture the stochasticity in tumour evolution; however, these models are often challenging to validate with experimental measurements due to model complexity. The Voronoi cell-based model (VCBM) is an off-lattice agent-based model that captures individual cell shapes using a Voronoi tessellation and mimics the evolution of cancer cell proliferation and movement. Evidence suggests tumours can exhibit biphasic growth in vivo. To account for this phenomena, we extend the VCBM to capture the existence of two distinct growth phases. Prior work primarily focused on point estimation for the parameters without consideration of estimating uncertainty. In this paper, approximate Bayesian computation is employed to calibrate the model to in vivo measurements of breast, ovarian and pancreatic cancer. Our approach involves estimating the distribution of parameters that govern cancer cell proliferation and recovering outputs that match the experimental data. Our results show that the VCBM, and its biphasic extension, provides insight into tumour growth and quantifies uncertainty in the switching time between the two phases of the biphasic growth model. We find this approach enables precise estimates for the time taken for a daughter cell to become a mature cell. This allows us to propose future refinements to the model to improve accuracy, whilst also making conclusions about the differences in cancer cell characteristics.

Understanding melting of Ti crystals with spherical voids from molecular dynamics simulations

Titanium (Ti) is one of the most important metals used in several industrial applications, and the presence of spherical defect reduces its strength and stability. We simulate the melting of Ti crystals with a spherical void of radii 0.6, 0.8, 1.0, and 1.5 nm and also of the crystal without it. Ti is modeled using embedded atom method ,and all crystals are heated at 1 atm from 300 to 2200 K till it melts completely. All molecular dynamics trajectories are analyzed using radial distribution functions, bond-orientational order parameters, Voronoi tessellation, and velocity auto-correlation functions. The results show that 0.6, 0.8, 1.0, and 1.5 nm voids fill before the crystals melt and they fill immediately within few picoseconds; thereafter, atoms rearrange/order to crystal like arrangements, wherein overall crystallinity remains hcp for crystals with 0.6 and 0.8 nm void and changes to bcc for the crystals with 1.0 and 1.5 nm voids. For all crystals with and without void, melting takes place with the loss of both long- and short-range orders and not from liquid like nuclei as proposed by classical nucleation theory.

Intra- and interspecies infectious neighbourhoods as determinant parameters for Mycobacterium bovis infection among badgers in southwestern France

The epidemiological system for Mycobacterium bovis in France involves cattle and, in some areas, wildlife species (mainly badgers and wild boar). This multi-host aspect complicates the control and eradication prospects for bovine tuberculosis in endemic areas, despite the surveillance and control measures implemented for decades in this officially tuberculosis-free European country. To improve control measures, and to manage spillback transmission from badgers to cattle, it is necessary to clarify the transmission mechanisms of M. bovis in these epidemiological systems. We modelled a badger population from a southwestern endemic area by a Dirichlet tessellation based on a sett census conducted by local hunters and trappers between 2013 and 2015. We then used a logistic regression model to test the association between the infection status of setts and computed variables depicting three types of transmission (intraspecific, interspecific and landscape-associated). The apparent prevalence of infected setts was of 40.5%. Two variables were significantly associated with the probability for a sett to be infected: the proportion of neighbouring setts that were infected (OR: 3.19 [2.04–5.17]95%) and the presence of nearby pastures belonging to an infected farm (OR: 2.33 [1.13–4.89]95%]. While badger culling measures have been implemented according to the national TB control plan in the study area since 2012 (in the vicinity of infected farms and their pastures), our results clearly highlight the need to reinforce measures aimed at reducing both intraspecific and interspecific infection pressure. For this purpose, the promising prospect of badger vaccination could be considered, along with biosecurity measures.