Spatial Tessellations: Concepts and Applications of Voronoi Diagrams

Senechal, Marjorie; Okabe, Atsuyuki; Boots, Barry; Sugihara, Kōkichi

doi:10.2307/2687299

Cited by 92 publications

(71 citation statements)

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“…Two different atomistic models with a simulation box size of 21.9 × 21.9 × 21.2 nm as presented in Figure were developed in this study. The first type represents the polycrystalline ZrB 2 with 12 grains (made with a total of 1 027 538 atoms) where grain sizes and orientations were randomly determined using the 3‐dimensional Voronoi construction method . A Voronoi tessellation or diagram is a cell structure constructed from randomly positioned points, also referred to as Poisson points.…”

Section: Molecular Models and Simulation Proceduresmentioning

confidence: 99%

“…To capture the interfacial interactions between ZrB 2 and ZrC, interaction parameters between Zr ZrB2 ‐Zr ZrC , B ZrB2 ‐Zr ZrC , Zr ZrB2 ‐C ZrC , and B ZrB2 ‐C ZrC atoms are required (subscripts in each atom define the ceramic phase). The parameters for Zr ZrB2 – Zr ZrC and B ZrB2 –Zr ZrC interactions are taken from Tersoff potential used in pure ZrB 2 simulation . The B ZrB2 –C ZrC interaction has been described by the Tersoff type potential proposed by Kınacı et al The parameters for Zr ZrB2 ‐C ZrC and B ZrB2 ‐C ZrC interactions are not readily available.…”

Section: Molecular Models and Simulation Proceduresmentioning

confidence: 99%

“…The first type represents the polycrystalline ZrB 2 with 12 grains (made with a total of 1 027 538 atoms) where grain sizes and orientations were randomly determined using the 3-dimensional Voronoi construction method. 47,48 A Voronoi tessellation or diagram is a cell structure constructed from randomly positioned points, also referred to as Poisson points. For polycrystalline material, we can think of these points as grain nucleation sites where the solidification starts and then uniform outward grain growth occurs in all directions.…”

Section: Simulation Proceduresmentioning

confidence: 99%

“…The parameters for Zr ZrB2 -Zr ZrC and B ZrB2 -Zr ZrC interactions are taken from Tersoff potential used in pure ZrB 2 simulation. 47 The B ZrB2 -C ZrC interaction has been described by the Tersoff type potential proposed by Kınacı et al 50 The parameters for Zr ZrB2 -C ZrC and B ZrB2 -C ZrC interactions are not readily available. As such, parameters for these interactions are estimated from the available interactions between Zr and B as well as B and B, respectively.…”

Section: Simulation Proceduresmentioning

confidence: 99%

See 3 more Smart Citations

Grain boundary driven mechanical properties of ZrB₂ and ZrC‐ZrB₂ nanocomposite: A molecular simulation study

Kayser

Adnan

2018

J Am Ceram Soc

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In this study, we report the grain boundary driven mechanical behavior of 2 polycrystalline ultra‐high‐temperature ceramics (UHTCs), zirconium diboride (ZrB2) and zirconium carbide (ZrC) with zirconium diboride (ZrC‐ZrB2). These nanocomposites were investigated using large‐scale molecular dynamics simulations. First, the atomistic models of the polycrystalline ZrB2 and ZrC‐ZrB2 nanocomposites were subjected to tensile loading to determine their elastic constants and tensile strengths. It was found that the presence of nanoparticles imparts an insignificant effect on the mechanical properties of ZrB2. It has also been observed that the failure mechanisms of both the ZrB2 and ZrC‐ZrB2 nanocomposite are driven by grain boundary deformation. At any instant during the applied load transfer, local tensile stress distribution data indicate that atomic stress becomes much higher near the grain boundaries compared to other locations. The authors performed additional sets of simulations to obtain tensile and shear properties of grain boundary material. When these properties were compared with the adjacent single crystal and overall polycrystalline material properties, it was found that the shear strength and stiffness of the grain boundary materials are significantly lower than the single crystal or polycrystal ZrB2. It is believed that the overall deformation and failure properties of ZrB2 and its composite are controlled by the properties of grain boundary. Hence, the addition of nanoparticles played an insignificant role on the mechanical properties of ZrB2.

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Section: Molecular Models and Simulation Proceduresmentioning

confidence: 99%

Section: Molecular Models and Simulation Proceduresmentioning

confidence: 99%

Section: Simulation Proceduresmentioning

confidence: 99%

Section: Simulation Proceduresmentioning

confidence: 99%

See 2 more Smart Citations

Grain boundary driven mechanical properties of ZrB₂ and ZrC‐ZrB₂ nanocomposite: A molecular simulation study

Kayser

Adnan

2018

J Am Ceram Soc

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“…Voronoi diagrams are widely used to deal with spatial optimization and spatial partitioning problems, especially in delimiting the service area of facilities [13][14][15][16]. Recently, Qiao et al [17] used the Voronoi diagram to create service areas for the charging stations in Shanghai and then identified the one with the highest time cost to locate the new facility.…”

Section: Introductionmentioning

confidence: 99%

Service Area Delimitation of Fire Stations with Fire Risk Analysis: Implementation and Case Study

Chen

et al. 2020

IJERPH

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Under the rapid development of urbanization, fire service becomes one of the biggest contributive factors to personal health and property safety. A reasonable plan of fire services should first address the issue of service area delimitation for fire emergency facilities. Specifically, there are two key factors for fire services including rescue efficiency and load balancing, which are usually handled by the space partitioning methods (e.g., Voronoi diagram). The traditional methods tend to model the space in a homogeneous plane with Euclidean distance, while in reality, the movement of rescuing is constrained by the street network. In addition, the built environment is complex by its variation of fire risk across places. Therefore, we propose a novel constrained Voronoi diagram for fire service area delimitation by adding the datasets of street network and historical fire incidents. Considering the prior knowledge that a fire engine is expected to reach the location of incident within five minutes, which is also called Golden 5 min, we propose a network partitioning algorithm which is able to increase the five-minute coverage of fire stations. Through a case study in Nanjing, China, we demonstrate the practicability of the proposed method in delimitating service areas of fire stations across time.the unbalanced built environment leads to the spatial heterogeneity of service demand. At the same time, the intricate roads have greatly affected the ability of urban services. Therefore, the traditional Voronoi diagram that models the urban space as a homogeneous environment is no longer suitable for delimiting the service areas of current urban facilities.In the literature, many extensions of the Voronoi diagram have been developed to adapt to the complexity of real-world geographic scenes. For example, Okabe et al. [18] formulate six Voronoi diagrams defined on the network, termed generalized network Voronoi diagrams, to precisely represent service areas in urban areas. The extension of the Voronoi diagram to a network space is more in line with the real characteristics of a street network service transmission and more suitable for urban activities, e.g., retail services. With considering the geographic distribution of demands and the socioeconomic context, Wang et al. [19] apply the hexagon-based adaptive crystal growth Voronoi diagrams to delimit middle school service areas. The results indicate that, compared with the raster-based method, the hexagon grid method is more accurate in measuring continuous weighted planes. Furthermore, the weighted Voronoi diagram allows for a more detailed modeling of services by introducing the varied capabilities of a facility. It is widely used in urban planning applications including trade zone design [20], transportation and logistics problems [21-23], political districting [24], substation planning [25,26], and school districting [19,27].However, there are few studies on the service division applied to urban emergency facilities, especially fire stations. As a critical emergenc...

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Voronoi diagrams and Delaunay triangulation for modelling animal territorial behaviour

Guillermo‐Ferreira,

Filippov,

Kovalev

et al. 2024

Ecology and Evolution

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We explore the use of movable automata in numerical modelling of male competition for territory. We used territorial dragonflies as our biological inspiration for the model, assuming two types of competing males: (a) faster and larger males that adopt a face‐off strategy and repulse other males; (b) slower and smaller males that adopt a non‐aggressive strategy. The faster and larger males have higher noise intensity, leading to faster motion and longer conservation of motion direction. The velocity distributions resemble the Maxwell distributions of velocity, expected in Brownian dynamics, with two probable velocities and distribution widths for the two animal subpopulations. The fast animals' trajectories move between visually fixed density folds of the slower animal subpopulation. A correlation is found between individual velocity and individual area distribution, with smaller animals concentrated in a region of small velocities and areas. Attraction between animals results in a modification of the system behaviour, with larger animals spending more time being surrounded by smaller animals and being slowed down by their interaction with the surroundings. Overall, the study provides insights into the dynamics of animal competition for territory and the impact of attraction between animals.

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Spatial Tessellations: Concepts and Applications of Voronoi Diagrams

Cited by 92 publications

References 0 publications

Grain boundary driven mechanical properties of ZrB₂ and ZrC‐ZrB₂ nanocomposite: A molecular simulation study

Grain boundary driven mechanical properties of ZrB₂ and ZrC‐ZrB₂ nanocomposite: A molecular simulation study

Service Area Delimitation of Fire Stations with Fire Risk Analysis: Implementation and Case Study

Voronoi diagrams and Delaunay triangulation for modelling animal territorial behaviour

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Spatial Tessellations: Concepts and Applications of Voronoi Diagrams

Cited by 92 publications

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Grain boundary driven mechanical properties of ZrB2 and ZrC‐ZrB2 nanocomposite: A molecular simulation study

Grain boundary driven mechanical properties of ZrB2 and ZrC‐ZrB2 nanocomposite: A molecular simulation study

Service Area Delimitation of Fire Stations with Fire Risk Analysis: Implementation and Case Study

Voronoi diagrams and Delaunay triangulation for modelling animal territorial behaviour

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Grain boundary driven mechanical properties of ZrB₂ and ZrC‐ZrB₂ nanocomposite: A molecular simulation study

Grain boundary driven mechanical properties of ZrB₂ and ZrC‐ZrB₂ nanocomposite: A molecular simulation study