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Abstract This paper is concerned with bird-strike numerical simulations using the Smoothed Particle Hydrodynamics method to represent the bird model. A comparison between bird models with classical mesh-based particle distributions and bird models with initial particle distributions generated using a technique based on the Weighted Voronoi Tessellation algorithm is presented. The adopted iteration technique to fill the bird model with particles is described. Particle distributions generated using this new technique are assessed in comparison with reference bird models commonly used in the literature. Results of generic bird-strike simulations on a flat target structure indicate the superiority of the proposed bird models over the bird models with classical mesh-based particle distributions in terms of flow behavior, conservation of total energy, normal forces, pressures, and computational efficiency. [ABSTRACT FROM AUTHOR]

The use of Bayesian trans‐dimensional sampling in 2‐D and 3‐D imaging problems has recently become widespread in geophysical inversion. Its benefits include its spatial adaptability to the level of information present in the data and the ability to produce uncertainty estimates. The most used parameterization in Bayesian trans‐dimensional inversions is Voronoi cells. Here we introduce a general software, TransTessellate2D, that allows 2‐D trans‐dimensional inference with Voronoi cells and two alternative underlying parameterizations, Delaunay triangulation with linear interpolation and Clough‐Tocher interpolation, which utilize the same algorithm but result in either C0 or C1 continuity. We demonstrate that these alternatives are better suited to the recovery of smooth models, and show that the posterior probability solution is less susceptible to multimodalities which can complicate the interpretation of model parameter uncertainties. Key Points: We present a new software for trans‐dimensional surface reconstruction incorporating hierarchical error estimation, Hamiltonian Monte Carlo, and parallel temperingWe propose two alternative parameterizations to the ubiquitous Voronoi cellsThese alternate parameterizations may open up the application of trans‐dimensional inversion to a wider variety of geophysical problems [ABSTRACT FROM AUTHOR]

Currently, grid and glass methods are the two most popular choices to generate uniform particle distributions (i.e. pre-initial conditions) for cosmological N -body simulations. In this article, we introduce an alternative method called the capacity constrained Voronoi tessellation (CCVT), which originates from computer graphics. As a geometrical equilibrium state, a CCVT particle configuration satisfies two constraints: (i) the volume of the Voronoi cell associated with each particle is equal; (ii) every particle is in the centre-of-mass position of its Voronoi cell. We show that the CCVT configuration is uniform and isotropic, follows perfectly the minimal power spectrum, P (k) ∝ k 4, and is quite stable under gravitational interactions. It is natural to incorporate periodic boundary conditions during CCVT making, therefore, we can obtain a larger CCVT by tiling with a small periodic CCVT. When applying the CCVT pre-initial condition to cosmological N -body simulations, we show that it plays as good as grid and glass schemes. The CCVT method will be helpful in studying the numerical convergence of pre-initial conditions in cosmological simulations. It can also be used to set up pre-initial conditions in smoothed-particle hydrodynamics simulations. [ABSTRACT FROM AUTHOR]

Highlights • Envelope theorem is applied to optimize the shapes of contact components in toroidal CVT. • After derive an envelope of a family of straight lines, we propose an inner cone CVT and an outer cone CVT. • Spin ratios of the two proposed CVTs are calculated. The results show that the proposed CVTs can transmit power without spin motion. • The comparisons show that durability properties of the inner cone and the outer cone CVTs are both improved. Abstract The efficiency of toroidal continuously variable transmission (CVT) is limited by the spin loss caused by different speed distributions of the contact areas between discs and rollers. Although two types of zero-spin CVTs are offered, a demerit in the form of difficult speed ratio variation is observed simultaneously. The core idea of this study is the realisation of a method based on the envelope theorem to optimise the shapes of discs and rollers. After the envelopes are calculated, two zero-spin CVTs (i.e. inner cone and outer cone CVTs) are proposed. The calculation of the spin ratio shows that the two proposed CVTs can both transmit power without the spin motion. The total efficiency of the proposed CVTs can therefore be improved, as evidenced by a widely accepted computational model. A comparison of the proposed CVTs and the conventional CVTs is conducted, and the results show that the durability properties of the proposed CVTs are both improved. Although it is hard to manufacture, the inner cone CVT surpassed the demerit of the control difficulty which remains observable in conventional zero-spin CVTs and the outer cone CVT. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

To achieve highly dynamic jumps with legged robots, it is essential to control the rotational dynamics of the robot. In this paper, we aim to improve the jumping performance by proposing a unified model for planning highly dynamic jumps that can approximately model the centroidal inertia. This model abstracts the robot as a single rigid body for the base and point masses for the legs. The model is called the Lump Leg Single Rigid Body Model (LL-SRBM) and can be used to plan motions for both bipedal and quadrupedal robots. By taking the effects of leg dynamics into account, LL-SRBM provides a computationally efficient way for the motion planner to change the centroidal inertia of the robot with various leg configurations. Concurrently, we propose a novel contact detection method by using the norm of the average spatial velocity. After the contact is detected, the controller is switched to force control to achieve a soft landing. Twisting jump and forward jump experiments on the bipedal robot SLIDER and quadrupedal robot ANYmal demonstrate the improved jump performance by actively changing the centroidal inertia. These experiments also show the generalization and the robustness of the integrated planning and control framework. [ABSTRACT FROM AUTHOR]

Conventional site investigation schemes typically use an empirical sampling strategy, which involves equal sampling spacing with regular grid patterns. However, this approach assigns equal importance to the entire site and does not account for subsurface stratigraphic variations and site constraints. In this study, a data-driven multi-stage sampling strategy is proposed to adaptively optimize the borehole locations for a three-dimensional (3D) geotechnical site, considering the subsurface stratigraphic uncertainties and irregular site geometries. The initial sampling plan is determined based on weighted centroidal Voronoi tessellation, which assigns various sampling densities to zones depending on their importance. Measurements obtained in the previous sampling stage are combined with prior geological knowledge to establish and update a 3D geological domain using a physics-informed geological modelling method. The next optimal location for sampling is adaptively determined with the objective of maximizing the reduction in the stratigraphic uncertainty. The proposed method represents the first data-driven 3D site planning method that explicitly considers 3D subsurface stratigraphic variations. The performance of the proposed multi-stage sampling strategy is illustrated using a simulation study. The results indicate that the proposed method efficiently identifies the optimal sampling locations while comprehensively considering the 3D subsurface geological uncertainties and irregular site geometries. • A data-driven sampling strategy is proposed to optimize borehole locations. • The method takes 3D stratigraphic variations and site geometries into consideration. • The method relies on Voronoi tessellation and information entropy for optimization. [ABSTRACT FROM AUTHOR]

Composite membrane consisting of selective layer and support is the mainstream membrane configuration. Support has drawn increasing attention in recent years. In this work, transport through composite membrane with support pore location distributing randomly was studied based on 2D Voronoi tessellations and the corresponding membrane performance calculation method was developed. For the calculation, firstly, irregular Voronoi regions are transformed into regular polygons with fixed number of edges meanwhile maintaining the region area. Then, the membrane performance can be obtained by combining the computation results of regular support surface pore spatial distribution and random support surface pore spatial distribution formulas. Poisson Voronoi diagrams, one of the most representative Voronoi diagrams, were mainly used to describe the support surface pore spatial distribution. The results indicate the importance of the number of support surface pores, which determines the average area of Voronoi regions. Support surface pores should be as many as possible. Another important conclusion is that a certain randomness of support surface pore structure (size and location) may not exert an influence on the composite membrane performance. That is, when calculating the composite membrane performance, the support surface pore spatial distribution and surface pore size distribution can be considered as being regular. • A novel way to calculate the performance of composite membrane with support pore location distributing randomly based on 2D Voronoi tessellations was developed • Poisson Voronoi diagrams were mainly used to describe the support surface pore spatial distribution. • The number of pores is a key parameter since it determines the average area of Voronoi regions. • A certain randomness of support surface pore structure (size and location) may not affect the composite membrane performance. [ABSTRACT FROM AUTHOR]

Chopped Tape Thermoplastic Composites (CTTCs) offer high formability and performance for complex-shaped components in the aerospace and automotive industries. However, the mesoscopic discontinuity leads to spatial variabilities and correspondingly high scatter in the elastic properties of CTTCs due to the random orientations of chopped tapes and chopped tape-cavity edge interactions. Here we propose a new approach to investigate the effect of mould cavity edges on chopped tape orientation and hence the mechanical properties of CTTCs. Based on this approach, a Set Voronoi tessellation was implemented to represent the variability of local Young's Modulus and chopped tape-cavity edge interactions occurring during the manufacturing process. It was confirmed that the chopped tapes align along the edges, and progressively transition to a random orientation towards the middle of the specimen. The results were validated on moulded specimens and demonstrated the ability to deconvolute the edge interaction. [Display omitted] [ABSTRACT FROM AUTHOR]

The detailed numerical investigation and design of cold-formed S960 steel grade square bird-beak (SBB) T- and X-joints have been presented in this paper. The SBB joint is one of the novel bird-beak tubular joint configurations and obtained by rotating the chord member of a conventional square hollow section (SHS) joint along its centroidal axis by 45°. In this investigation, accurate finite element (FE) models were developed for SBB T- and X-joints using the tests carried out by the authors. The developed FE models successfully replicated the static strengths, load vs deformation curves and failure modes of test specimens. In order to gain an in-depth understanding on the static behaviour of SBB joints, a comprehensive FE parametric study was performed using the verified FE models. The joint failure strengths and joint ultimate capacities of a total of 220 SBB T- and X-joints specimens, including 200 FE specimens investigated in this study, were evaluated against the nominal strengths predicted from the literature and European code. All SBB T- and X-joints test and FE specimens were failed by the chord crown failure (C) mode. It has been shown that the design provisions given in the literature and European code are unsuitable and uneconomical for the design of cold-formed S960 steel grade SBB T- and X-joints investigated in this study. Therefore, accurate and reliable design equations are proposed in this study for predicting the static strengths of the investigated SBB T- and X-joints. • Cold-formed S960 steel grade square bird-beak (SBB) T- and X-joints were numerically investigated. • 200 SBB T- and X-joints FE specimens were analysed in the parametric study. • Chord crown failure (C) was the observed failure mode for all SBB T- and X-joints. • Static strengths were compared with nominal strengths predicted from literature and European code. • Existing design rules are unsuitable for the investigated SBB T- and X-joints. New, accurate and reliable design rules are proposed. [ABSTRACT FROM AUTHOR]

When one is attempting to model framed structures and adopts beam-like finite elements formulated with reference to their centroidal axis—which avoids the interaction between axial and flexural effects—one must, in many practical situations, take into account geometrically complex curved-line finite elements. This fact, which can be quite disadvantageous, is typically called for when solving physically nonlinear problems or modeling nonprismatic beams having cross sections varying asymmetrically around their straight centerlines. This paper proposes then a flexibility-type method based on the principle of virtual forces (PVF) to obtain, according to the Timoshenko beam theory (TBT), exact expressions for the structural properties of nonprismatic frame elements described with reference to noncentroidal axes. The main advantage of this method is that it allows, through the use of straight-line segments, the modeling of complex variable-rigidity frame elements. To interpolate the variable sectional rigidities over the elements, one adopts polynomials of different orders. In addition, this new method allows one to obtain the exact Timoshenko's shape functions (TSFs) for nonprismatic frame elements with noncentroidal axes. Such shape functions are needed to evaluate deformation-dependent structural properties, such as geometric stiffness. We validate the robustness of the proposed formulation by solving in-plane tapered beams possessing thin-walled monosymmetric cross sections. Using analytical and highly accurate 3D ANSYS responses, this work determines and compares responses described in terms of displacements, rotations, internal forces, and stresses. • Nonprismatic frame elements. • Noncentroidal axes. • Exact structural-property matrices. • Exact Timoshenko's shape functions. • Thin-walled monosymmetric cross sections. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with distributed coordination of multiple mobile actuators for pollution neutralization in a polluted environment, where a static mesh sensor network is pre-deployed for measuring the concentration of contaminants, and mobile actuators with neutralizing chemicals implement spraying operation at a steady rate to reduce the contaminants continuously. A hazard intensity distribution is introduced to evaluate adverse impact of contaminants on the environment. Autonomous actuators are dynamically deployed to minimize the total hazard intensity. This coordination problem can be formulated as a distributed deployment problem based on centroidal Voronoi tessellation (CVT). Two control strategies with switching motion controllers are proposed to achieve optimal deployment of mobile actuators for unlimited and limited actuating range respectively. To escape local minimum and balance the actuator workload, a novel workload adjustment strategy is designed to change the normalized amount of neutralizer sprayed by mobile actuators, which makes each actuator approach a common workload. Compared with pure CVT and switching motion controller, the total hazard intensity can be further decreased if the workload adjustment strategy is implemented. Simulation examples are provided to validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the molecular dynamics simulations are utilized to study the cooling rate effect and to understand the relationship among the local atomic structure, free volume, and mechanical property in Cu 50 Zr 50 metallic glass. The radial distribution function, bond pair analysis technique, and Voronoi tessellation are performed to characterize the structure evolution and local atomic configurations during the cooling process. The results demonstrate that a faster cooling rate results in a higher glass transition temperature and less amount of icosahedra-like clusters. It has been recognized that the concentration of free volumes presents a strong evidence of upward trends as the cooling rate increases. The analyses for the free volume and Voronoi polyhedron indicate that icosahedral-like clusters show a lower free volumes as compared with the rest clusters, revealing that well-developed icosahedra-like clusters in Cu 50 Zr 50 make the system densely packed and lower free volume structure. In addition, the simulated alloy obtained at a lower cooling rate exhibits a higher yield strength and elastic modulus, all of which may attribute to the structure with more densely icosahedral-like clusters and less free volumes. Highlights • Quantitatively calculate the free volume on the atomic level in Cu 50 Zr 50 metallic glasses. • The free volumes of icosahedral-like, crystal-like, mixed and other type clusters are described quantitatively. • Icosahedral-like cluster is responsible for the densely packed structure and high yield strength. [ABSTRACT FROM AUTHOR]

A key process in the life of any multicellular organism is its development from a single egg into a full grown adult. The first step in this process often consists of forming a tissue layer out of randomly placed cells on the surface of the egg. We present a model for generating such a tissue, based on mechanical interactions between the cells, and find that the resulting cellular pattern corresponds to the Voronoi tessellation of the nuclei of the cells. Experimentally, we obtain the same result in both fruit flies and flour beetles, with a distribution of cell shapes that matches that of the model, without any adjustable parameters. Finally, we show that this pattern is broken when the cells grow at different rates. [ABSTRACT FROM AUTHOR]

Nonuniform distribution of tri-structural-isotropic (TRISO) fuel particles in a spherical fuel element (SFE) may increase the failure probability of the SFE in the high-temperature gas-cooled reactor, leading to the release of fission products. To evaluate the uniformity of the TRISO particles nondestructively, 3-dimensional cone-beam computed tomography is used to image the SFE, and TRISO particles are segmented. After TRISO particle positions are identified, the Voronoi tessellation and Delaunay triangulation are used to extract several geometric metrics. Results indicate that both the Voronoi volume distribution and the nearest neighbor-distance distribution follow the log-normal distributions, which provide strong evidence that the TRISO particles are approximately randomly uniformly distributed. Further study will be focused on validating the conclusion with more SFE data. [ABSTRACT FROM AUTHOR]

The atomic structures, glass forming evolutions, mechanical properties and high pressure behavior of Mg 75 Zn 20 Ca 5 and Mg 60 Zn 35 Ca 5 bulk metallic glasses, which are promising candidates for biomedical implants, have been examined by using ab initio molecular dynamics simulations. The pair-distribution function and coordination number analyses show that increasing Zn content in the alloy results in a decrease in several bond distances and an increase in the total coordination number of each species due to the atomic size difference between Mg and Zn atoms. According to the Voronoi tessellation, bond pair and bond angle distribution analyzes, the fivefold geometrical arrangements (pentagonal-bipyramid) are the most predominant in the first coordination shell, indicating the stability of the amorphous states and their dense atomic packing. The most striking result emerged from the calculations of mechanical properties is that an increase of Zn (≥30%) content in the alloy yields embrittlement in the alloys. Under uniaxial compressions, both compositions undergo structural failure between 6 and 8 GPa. Under hydrostatic pressure, a diminishing in fcc/hcp ordering and an enlargement of the ideal icosahedral ordering may indicate a more disordered structure. In our view, these results represent a good step toward understanding the atomic structures Mg-Zn-Ca bulk metallic glasses. [ABSTRACT FROM AUTHOR]

In this paper, four binary hard sphere crystals were numerically constructed by discrete element method (DEM) through different packing modes under three-dimensional (3D) mechanical vibration. For each crystal, a modified Voronoi tessellation method (called radical tessellation) was utilized to quantitatively investigate the topological and metrical properties of radical polyhedra (RPs). The topological properties such as the number of faces, edges, vertices per RP and the number of edges per RP face as well as the metrical properties such as perimeter, surface area, volume, and relative pore size per RP were systematically characterized and compared. Meanwhile, the mechanism of the binary hard sphere crystallization was also investigated. The results show that the packing sequence and pattern of the large spheres can determine the structure of the binary hard sphere crystal. The RP structures and their metrical and topological properties of the four binary hard sphere crystals (even the packing density of the two crystals is the same) are quite different. Each property can clearly reflect the specific characteristics of the corresponding binary hard sphere crystalline structure. The obtained quantitative results would be useful for the deep understanding of the structure and resultant properties of binary hard sphere crystals. [ABSTRACT FROM AUTHOR]

Motivation Single-molecule localization microscopy (SMLM) can play an important role in integrated structural biology approaches to identify, localize and determine the 3D structure of cellular structures. While many tools exist for the 3D analysis and visualization of crystal or cryo-EM structures little exists for 3D SMLM data, which can provide unique insights but are particularly challenging to analyze in three dimensions especially in a dense cellular context. Results We developed 3DClusterViSu, a method based on 3D Voronoi tessellations that allows local density estimation, segmentation and quantification of 3D SMLM data and visualization of protein clusters within a 3D tool. We show its robust performance on microtubules and histone proteins H2B and CENP-A with distinct spatial distributions. 3DClusterViSu will favor multi-scale and multi-resolution synergies to allow integrating molecular and cellular levels in the analysis of macromolecular complexes. Availability and impementation 3DClusterViSu is available under http://cbi-dev.igbmc.fr/cbi/voronoi3D. Supplementary information Supplementary figures are available at Bioinformatics online. [ABSTRACT FROM AUTHOR]

This paper presents a novel technique for resampling point clouds of a smooth surface. The key contribution of this paper is the generalization of centroidal Voronoi tessellation (CVT) to point cloud datasets to make point resampling practical and efficient. In particular, the CVT on a point cloud is efficiently computed by restricting the Voronoi cells to the underlying surface, which is locally approximated by a set of best-fitting planes. We also develop an efficient method to progressively improve the resampling quality by interleaving optimization of resampling points and update of the fitting planes. Our versatile framework is capable of generating high-quality resampling results with isotropic or anisotropic distributions from a given point cloud. We conduct extensive experiments to demonstrate the efficacy and robustness of our resampling method. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel method for generating cell complexes with anisotropy conforming to the Hessian of an arbitrary given function. This is done by variationally optimizing the discontinuous piecewise linear approximation of the given functions over power diagrams. The resulting cell complexes corresponding to the approximations are referred to as Optimal Power Diagram (OPD). A hybrid optimization technique, coupling a modified Monte Carlo method with a local search strategy, is tailored for effectively solving the specific optimization task. In contrast to the Optimal Voronoi Tessellation (OVT) method (Budninskiy et al., 2016), our OPD method does not restrict the target functions to be convex, providing more diverse classes of tessellations of the domain. Furthermore, our OPD method generally yields smaller approximation errors than the OVT method, which uses underlaid approximants. We conduct several experiments to demonstrate the efficacy of our optimization algorithm in finding good local minima and generating high-quality anisotropic polytopal meshes. [ABSTRACT FROM AUTHOR]

A new spatially balanced sampling design for environmental surveys is introduced, called Halton iterative partitioning (HIP). The design draws sample locations that are well spread over the study area. Spatially balanced designs are known to be efficient when surveying natural resources because nearby locations tend to be similar. The HIP design uses structural properties of the Halton sequence to partition a resource into nested boxes. Sample locations are then drawn from specific boxes in the partition to ensure spatial diversity. The method is conceptually simple and computationally efficient, draws spatially balanced samples in two or more dimensions and uses standard design-based estimators. Furthermore, HIP samples have an implicit ordering that can be used to define spatially balanced over-samples. This feature is particularly useful when sampling natural resources because we can dynamically add spatially balanced units from the over-sample to the sample as non-target or inaccessible units are discovered. We use several populations to show that HIP sampling draws spatially balanced samples and gives precise estimates of population totals. [ABSTRACT FROM AUTHOR]

Centroidal Voronoi tessellation (CVT)-based mesh generation is a very effective technique for creating high-quality Voronoi meshes and their dual Delaunay triangulations that often play a crucial role in applications, including ocean and atmospheric simulations using finite volume schemes. In the next generation climate models, the spacing scales change dramatically across the whole sphere and require ultra-high resolution and smooth transitions from coarse to fine grid regions. Thus fast and robust spherical CVT (SCVT) meshing algorithms become highly desirable. In this paper, we first propose a Lloyd-preconditioned limited-memory BFGS method for constructing SCVTs that is also applicable to the construction of CVTs of general domains. This method is then parallelized based on overlapping domain decomposition, enabling excellent scalability on distributed systems. Results of several computational experiments show that the new method could incur computational time costs one order of magnitude smaller compared with some existing methods for generating large-scale highly variable-resolution meshes, while also providing significant improvements in mesh quality. [ABSTRACT FROM AUTHOR]

Highlights • A Voronoi tessellation algorithm is incorporated to model the rock microstructure. • A modified contact model is adopted to simulate the intergranular cracking. • Numerical simulations are carried out to verify this new approach. • Grain-size effects on micro-mechanical parameters and REV size are studied. Abstract In this study, a two-dimensional Voronoi element based-numerical manifold method (VE-NMM) was developed as a new approach to investigate the micro- and macro- mechanical properties of intact rocks. The Voronoi technique was used to generate a polygonal grain assemblage to approximate the microstructure of sandstone samples from Gubei colliery of Huainan mining area in China. A modified contact model incorporating cohesion and tensile strength was adopted to interpret the interactions between rock grains. A series of laboratory tests, i.e. scanning electron microscope tests, uniaxial compression and Brazilian tests were carried out to obtain the microstructural information and macro-mechanical properties of the sandstone samples. To verify the proposed VE-NMM, simulations of Brazilian tensile splitting and uniaxial compressive tests were carried out and the results, in terms of strength, elastic constant and crack distribution, were compared to those of the laboratory tests. To investigate the effects of grain size on the micro-mechanical parameters and the representative elementary volume (REV) size, numerical uniaxial compression tests with different grain sizes (2mm, 3 mm and 4 mm) were conducted using the developed VE-NMM approach. Simulation results indicate that both the micro-mechanical parameters and the representative elementary volume size are heavily dependent on grain size. [ABSTRACT FROM AUTHOR]

Voronoi tessellation, and its dual the Delaunay triangulation, provide a cohesive framework for the study and interpretation of phenomena of geographical space in two and three dimensions. The planar and spherical solutions introduce errors in the positional accuracy of both Voronoi vertices and Voronoi edges due to errors in distance computations and the path connecting two locations with planar lines or great circle arcs instead of geodesics. For most geospatial applications the introduction of the above errors is insignificant or tolerable. However, for applications where the accuracy is of utmost importance, the ellipsoidal model of the Earth must be used. Characteristically, the introduction of any positional error in the delimitation of maritime zones and boundaries results in increased maritime space for one state at the expense of another. This is a situation that may, among others, have a serious impact on the financial activities and the relations of the states concerned. In the context of previous work on maritime delimitation we show that the Voronoi diagram constitutes the ideal solution for the development of an automated methodology addressing the problem in its entirety. Due to lack of a vector methodology for the generation of Voronoi diagram on the ellipsoid, the aforementioned solution was constrained by the accuracy of existing approaches. In order to fill this gap, in this paper we deal with the inherent attributes of the ellipsoidal model of the Earth, e.g. the fact that geodesics are open lines, and we elaborate on a methodology for the generation of the Voronoi diagram on the ellipsoid for a set of points in vector format. The resulting Voronoi diagram consists of vertices with positional accuracy that is only bounded by the user needs and edges that are comprised of geodesics densified with vertices equidistant to their generators. Finally, we present the implementation of the proposed algorithm in the Python programming language and the results of two case studies, one on the formation of closest service areas and one on maritime boundaries delimitation, with the positional accuracy set to 1 cm. [ABSTRACT FROM AUTHOR]

The recently introduced multidimensional archive of phenotypic elites (MAP-Elites) is an evolutionary algorithm capable of producing a large archive of diverse, high-performing solutions in a single run. It works by discretizing a continuous feature space into unique regions according to the desired discretization per dimension. While simple, this algorithm has a main drawback: it cannot scale to high-dimensional feature spaces since the number of regions increase exponentially with the number of dimensions. In this paper, we address this limitation by introducing a simple extension of MAP-Elites that has a constant, predefined number of regions irrespective of the dimensionality of the feature space. Our main insight is that methods from computational geometry could partition a high-dimensional space into well-spread geometric regions. In particular, our algorithm uses a centroidal Voronoi tessellation (CVT) to divide the feature space into a desired number of regions; it then places every generated individual in its closest region, replacing a less fit one if the region is already occupied. We demonstrate the effectiveness of the new “CVT-MAP-Elites” algorithm in high-dimensional feature spaces through comparisons against MAP-Elites in maze navigation and hexapod locomotion tasks. [ABSTRACT FROM AUTHOR]

Accurate characterization of random heterogeneity in a material microstructure is essential to the accurate characterization of complex fracture patterns that result from random crack nucleation and propagation. It is also important to characterize microstructural behavior at intermediate scales, between the length scale of material heterogeneity and the scale of a Representative Volume Element (RVE). The availability of material property data at multiple scales will ultimately allow adjustment of computational cost and level of accuracy with respect to resolution of complex fracture patterns. Statistical Volume Elements (SVE) may be generated at the mesoscale by partitioning an RVE. SVE provide a probabilistic characterization of material heterogeneity, while also presenting a continuum representation of apparent properties. Appropriate definition of an SVE requires modeling choices, such as partitioning methods and size. An essential modeling assumption is the choice of loading condition used to approximate SVE apparent behavior, since the constitutive properties of an SVE are not necessarily invariant with respect to the boundary condition applied. This work develops a Voronoi tessellation based partitioning scheme applied at various length scales, for heterogeneous materials with various contrast ratios. Results show the variability of failure strength for a given SVE as a function of loading direction. Results of the mesoscale material property analysis are implemented in an asynchronous spacetime discontinuous Galerkin (aSDG) finite element based fracture model. [ABSTRACT FROM AUTHOR]

The Geographic Profiling (GP) is a data analysis tool that has great potential. Presently, it is used only minimally, and is almost always used “as it is”, independently on other analysis or data processing methods. GP was initially created as a forensic tool, to find the origin of a series of events (crimes) done by a single actor. However, using this method in integration with others, it is possible to enlarge the opportunities of geographical data analysis. The promising results of this method in integration with others, even if some of them are quite well known methods since many years-and thus well tested-show a number of further possible applications. Here we treat data clustering and partitioning with Kmeans and Dbscan methods; space partitioning (Voronoi tessellation) and a method to assign weights to the events constituting the data set. The software used in this review was written in Python, was released under GPL license and is available on Bitbucket (https://bitbucket.org/ugosnt/al_and_ugo/). [ABSTRACT FROM AUTHOR]

This study considers a remapping algorithm between irregularly distributed observations and grid points based on Voronoi diagrams and examines its potential for verification of precipitation forecasts. We propose a new remapping method using Voronoi diagrams to apply conservative area-weighted remapping on grid data to station points, describing a representative area for each station point. Conservative remapping is applied to interpolate daily precipitation data between grid and station points over South Korea. The proposed method shows significant differences from bilinear interpolation, which has been widely used in modeling communities, for local maximum and mean in a given domain. It is also shown that different interpolation methods have an impact on verification results of precipitation forecast from a numerical weather prediction model against station observations. It is suggested that the proposed method has potential to be used for verifying precipitation forecasts at in situ observation points, with its conservativeness and capability to be applied in any remapping direction between grids and stations. [ABSTRACT FROM AUTHOR]

This paper advances the previous theoretical work of authors by conducting experiments on a generalized coverage optimization algorithm using a team of heterogeneous mobile robots. A scalar measure (herein called the density) of the environment defines a nonuniform coverage metric of the area. Mobile robots are spatially configured such that their asymptotic placements in an area maximize the nonuniform coverage metric. Over the last fifteen years, a large body of research work has been conducted in solving the area coverage optimization problem where the focus was mainly on theoretical results followed by mostly numerical simulations. In some cases, the coverage optimization algorithms were validated with experimental results, but the implementation platforms were suitable to specific homogeneous robot platforms. Here, the emphasis is on the real-time implementation of the authors’ previously published theoretical results on area coverage optimization problems using a team of heterogeneous mobile robots. The robots are heterogeneous in the sense that they have different actuator limits, physical dimensions, and processing capabilities. The modularity of the algorithm stems from the fact that the additional hardware/software architecture is open-source and can be applied to different robots regardless of their internal electromechanical system architectures. The algorithm is implemented using the emerging robot operating system in a multithreaded manner. A commercial robot simulator was used to validate the coverage performance followed by a set of experiments conducted in an indoor environment. [ABSTRACT FROM PUBLISHER]

The discrete element method with dilated polyhedral elements is developed to simulate the interaction between ice floes and the floating structure. The 2D-Voronoi tessellation algorithm is adopted to generate polyhedral ice floes with a given ice thickness in broken ice field. According to the Minkowski sum theory, the dilated polyhedron is constructed via sweeping a sphere on the surface of a basic polyhedron. The Hertzian contact model and its simplified form are then adopted to determine the contact force between dilated elements due to the round profile of the element. Meanwhile, the buoyancy and buoyancy moment, the drag force and drag moment on ice floes are calculated by meshing every polyhedral element as tetrahedrons. The floating structure Kulluk , which operates in the Arctic, is modeled as a rigid body restricted by mooring lines with the linear stiffness. The structure motion is calculated with six degrees of freedom in terms of the ice contact force, the buoyancy, the drag force of current, and the mooring force. Under different ice thickness and concentration, the ice load on the floating structure is reasonably compared with the field data. General influences of different ice conditions are analyzed to provide operational principles in engineering. [ABSTRACT FROM AUTHOR]

In this work, we employed molecular dynamics (MD) simulations to study Ti-Al metallic glasses (MGs) using the embedded atom method (EAM) potential to model the atomic interaction with different compositions. The results showed evidence of the metallic glass formation induced by the split occurring in the second peak of the radial distribution function (RDF) curves implying both Ti and Al atoms. The common neighbor analysis (CNA) method confirmed the presence of the icosahedral clusters with a maximum amount observed for an alloy with 75 pct of Al. Analysis of coordination numbers (CNs) indicated that the total CNs are nearly unchanged in these systems. Finally, Voronoi tessellation analyses (VTA) showed a higher value of the number of icosahedral units at Ti25Al75 composition. This specific composition represents a nearby peritectic point localized at a low melting point in the Ti-Al binary phase diagram. The glass forming ability (GFA) becomes important when the fraction of Al increases by forming and connecting “icosahedral-like” clusters (12-coordinated 〈0, 0, 12, 0〉 and 13-coordinated 〈0, 1, 10, 2〉) and by playing a main role in the structure stability of the Ti-Al MGs. [ABSTRACT FROM AUTHOR]

Generating realistic non-uniformly distributed three-dimensional representative volume element (RVE) for modeling the response of high fiber volume fraction composites is challenging. A novel rapid approach employing a random event-driven molecular dynamics simulation (EDMD) was proposed in this study for this purpose. Distributions of continuous unidirectional fibers in the RVEs were assessed using two approaches, namely Voronoi tessellations and radial distribution functions. The developed method was highly efficient in generating RVEs with realistic fiber dispersions. Furthermore, applying the corresponding periodic boundary conditions (PBCs) for finite element modeling is also arduous. A technique was developed within the commercial finite element software ABAQUS to rapidly produce required matching mesh patterns on opposite surfaces of the RVE, and to apply the corresponding PBCs using custom scripts. By coupling the EDMD approach and custom scripts within ABAQUS to rapidly generate and mesh RVEs with high fiber volume fractions, evaluation of the RVE response was greatly simplified. In- and out-of-plane elastic properties of unidirectional glass/epoxy composite in a range of 10–80% fiber volume fractions were determined and compared with analytical models, and available experimental data, with good correlation. [ABSTRACT FROM AUTHOR]

The large deformation response of Ti-6Al-4V structures made through shaped metal deposition is heavily affected by the prior-beta grain structure induced by the manufacturing process. Based on more than 25 tension and shear experiments on individual prior-beta grains, the statistical distribution of the isotropic hardening response of prior-beta grains is identified. In close analogy with Crystal Plasticity Finite Element (CPFE) analysis, Voronoi tesselation is used to generate finite element models of additively-manufactured structures containing multiple prior-beta grains. For each prior-beta grain, a different hardening curve is assigned using a random pull from the truncated Gaussian distribution of Hockett-Sherby type of hardening curves. Similarly, the parameters of the Hosford-Coulomb fracture initiation model are assigned. The comparison of the CPFE simulation results with the experimental results on tension specimens containing multiple prior-beta grains, shows good qualitative and quantitative agreement with regards to the force-displacement response, the surface strain fields, and fracture occurrences. The results demonstrate that the failure of additively-manufactured Ti-6Al-4V components through ductile fracture requires a heterogeneous random medium modeling approach. While the present study focuses on strength and hardening variations, it is noted that further improvements are expected when considering the known texture mismatch between prior-beta grains along with detailed models of the prior-beta grain boundaries. [ABSTRACT FROM AUTHOR]

The microstructure of a highly laminated Lower Bowland Shale sample is characterized at the micron-to millimeter scale, to investigate how such characterization can be utilized for microstructure-based modelling of the shale's geomechanical behavior. A mosaic of scanning electron microscope (SEM) back-scattered electron (BSE) images was studied. Mineral and organic content and their anisotropy vary between laminae, with a high variability in fracturing and multi-micrometer aggregates of feldspars, carbonates, quartz and organics. The different microstructural interface types and heterogeneities were located and quantified, demonstrating the microstructural complexity of the Bowland Shale, and defining possible pathways for fracture propagation. A combination of counting-box, dispersion, covariance and 2D mapping approaches were used to determine that the total surface of each lamina is 3 to 11 times larger than the scale of heterogeneities relative to mineral proportion and size. The dispersion approach seems to be the preferential technique for determining the representative elementary area (REA) of phase area fraction for these highly heterogeneous large samples, supported by 2D quantitative mapping of the same parameter. Representative microstructural models were developed using Voronoï tessellation using these characteristic scales. These models encapsulate the microstructural features required to simulate fluid flow through these porous Bowland Shales at the mesoscale. [ABSTRACT FROM AUTHOR]

Voronoi tessellation theory is applied to model the cells and ligaments in the open aluminum foam material. The cores of the cells are first generated by packing random spheres into the specified spatial domain. Weighted Voronoi tessellation is then applied to make the cellular structure of the foam material. For the open cell foam, the ligaments are created from the edges in the multiple polyhedron geometry. Hypervelocity impact simulation is conducted with the smoothed particle hydrodynamics method in LS-dyna. The finite element reconstruction technique is applied based on the particle output for the fragmentation analysis. The modeling and simulation techniques are verified by comparing the simulation results with testing results. The failure shown in the numerical prediction is consistent to the test result. The stress wave propagation in the foam material, which is extracted from the simulation output, is very different from that in the homogeneous material. The stress wave can only propagate inside the ligaments, and is diffused by the cellular structure. The important tensile failure pattern in the homogeneous material, which is generated by the reflection of the compressive wave on the free surface, is not observed in the foam material. The diffusion of the stress wave spreads the impact effect to a large area, leading to the enhanced dissipation of the impact energy, which increases the ballistic limit of the foam panel. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach that integrates geometric modeling and visual analysis of grain structures in an open source CAD system, aimed at educational purposes. An intuitive and simple automated modeling method produces valid polygonal representations of grain structures, by adopting a novel physics-based particle packing procedure with Voronoi-based tessellation. Models are structured to facilitate the development of interactive visualization prototypes in 3D interactive engines. Microstructural fidelity was pursued for the synthetic models to be accepted as representations of real materials. Meaningful sample’s parameters such as mean number of neighbors and mean number of edges per face were replicated with acceptable precision, when compared to values obtained from 3D reconstruction of an alpha-iron sample. Domain-specific interactive experimental tools informed by learning and cognitive research sought to enhance spatial cognition of grain structures and support learning their fundamental features. [ABSTRACT FROM AUTHOR]

An effective numerical method is proposed in this paper to generate a meso-scale composite model of reinforcement concrete (RC) which contains aggregates with random size and shape based on Voronoi tessellation method. Besides the randomly distributed aggregates, the present model takes into account the reinforcement, compared with other conventional methods in finite element modeling of concrete. The shrinking algorithm with random shrinking factors is employed to generate graded aggregates. A simple and effective intersection detection is used for aggregate-reinforcement to prevent the aggregates from overlapping with preset reinforcements, but it is unnecessary for aggregate-aggregate due to the characteristic of Voronoi technique. The artificial layer with random offset distance is adopted to simulate the minimum gap between two adjacent aggregates, and the high-volume fraction model is obtained by the sinking process. In order to verify the reliability of the RC model, the numerical results of penetration are compared with the referenced experimental data, and good agreements are obtained. It is indicated that the proposed model can simulate and explain qualitatively the effects of the meso-scale structural properties on the macroscopic dynamic response of RC. Furthermore, this method has great significance in performance analysis, structural optimization and material design for RC composites. [ABSTRACT FROM AUTHOR]

Superpixels are perceptually meaningful atomic regions that can effectively capture image features. Among various methods for computing uniform superpixels, simple linear iterative clustering (SLIC) is popular due to its simplicity and high performance. In this paper, we extend SLIC to compute content-sensitive superpixels, i.e., small superpixels in content-dense regions with high intensity or colour variation and large superpixels in content-sparse regions. Rather than using the conventional SLIC method that clusters pixels in \mathbb R^5 , we map the input image I to a 2-dimensional manifold \mathcal {M}\subset \mathbb {R}^5 , whose area elements are a good measure of the content density in I . We propose a simple method, called intrinsic manifold SLIC (IMSLIC), for computing a geodesic centroidal Voronoi tessellation (GCVT)—a uniform tessellation—on \mathcal M , which induces the content-sensitive superpixels in I . In contrast to the existing algorithms, IMSLIC characterizes the content sensitivity by measuring areas of Voronoi cells on \mathcal M . Using a simple and fast approximation to a closed-form solution, the method can compute the GCVT at a very low cost and guarantees that all Voronoi cells are simply connected. We thoroughly evaluate IMSLIC and compare it with eleven representative methods on the BSDS500 dataset and seven representative methods on the NYUV2 dataset. Computational results show that IMSLIC outperforms existing methods in terms of commonly used quality measures pertaining to superpixels such as compactness, adherence to boundaries, and achievable segmentation accuracy. We also evaluate IMSLIC and seven representative methods in an image contour closure application, and the results on two datasets, WHD and WSD, show that IMSLIC achieves the best foreground segmentation performance. [ABSTRACT FROM AUTHOR]

The initial stages of metal film growth were studied by computer experiment. The structures were generated by an atomistic model combining the molecular dynamics and Monte Carlo approaches and the analysis of obtained structures was performed by image processing algorithms. Film morphology was tested by several methods and it was found that especially Voronoi tessellation and Quadrat Counts methods are best suited for a description of spatial distribution of objects. The same morphological analysis was applied to experimental data – to micrographs of discontinuous films of Ag, Au and In grown on dielectric or graphite substrates. It was found that for small evaporation rates the atomistic model is in a good agreement with experiments. However, when increasing the evaporation rates the effect of secondary nucleation starts to be pronounced and a discrepancy between modelled and experimentally derived morphological results occurs. This effect was demonstrated for indium films with intensive secondary nucleation. [ABSTRACT FROM AUTHOR]

Spinodal decomposition and voronoi tessellation are combined for the generation of nanocrystalline nanoporous model with grain size corresponding to ligament diameter and randomly distributed crystal orientations. A series of large-scale molecular dynamics (MD) simulations were performed and utilized to research on the mechanical behaviors of nanocrystalline nanoporous platinum (nc-NPPt) undergoing uniaxial tension. The relation between relative density and mechanical properties, together with related atomistic deforming mechanisms of as-generated nc-NPPt were analyzed. It is found that the existence of nanocrystals and substantial surface may lead to decreased tensile strength and increased plasticity of nc-NPPt, and the plastic deformation scheme of nc-NPPt is dominated by grain boundary movements. The present results will provide atomistic insights for understanding deformation mechanisms of nanocrystalline nanoporous metals as well as future mechanical optimization of nanoporous metals. [ABSTRACT FROM AUTHOR]

We present the first weak lensing calibration of μ⋆, a new galaxy cluster mass proxy corresponding to the total stellar mass of red and blue members, in two cluster samples selected from the SDSS Stripe 82 data: 230 red-sequence Matched-filter Probabilistic Percolation (redMaPPer) clusters at redshift 0.1 ≤ z < 0.33 and 136 Voronoi Tessellation (VT) clusters at 0.1 ≤ z < 0.6. We use the CS82 shear catalogue and stack the clusters in μ⋆ bins to measure a mass-observable power-law relation. For redMaPPer clusters we obtain M0 = (1.77 ± 0.36) × 1014 h-1M⊙, α = 1.74 ± 0.62. For VT clusters, we find M0 = (4.31 ± 0.89) × 1014 h-1M⊙, α = 0.59 ± 0.54 and M0 = (3.67 ± 0.56) × 1014 h-1M⊙, α = 0.68 ± 0.49 for a low and a high redshift bin, respectively. Our results are consistent, internally and with the literature, indicating that our method can be applied to any cluster-finding algorithm. In particular, we recommend that μ⋆ be used as the mass proxy for VT clusters. Catalogues including μ⋆ measurements will enable its use in studies of galaxy evolution in clusters and cluster cosmology. [ABSTRACT FROM AUTHOR]

We introduce a two-step method to perform spatio-temporal balanced sampling in a design-based approach. For populations with spatio-temporal trends and with anisotropic effects in the variable of interest, the prediction can be further improved by selecting samples that are well spread over the entire population in space and time. We control the spread of the sample over the population by using the volume of the corresponding three-dimensional Voronoi tessellation. Indeed, spatio-temporal design-based balanced sampling is even more efficient under the presence of a trend and anisotropic effects. We present an intensive simulation study comparing our method to other available methods for spatio-temporal sampling. Finally, we analyze real data by sampling from a population of temperature stations over six European countries. [ABSTRACT FROM AUTHOR]

A numerical study was performed to develop a framework for estimating the confined strength of rock blocks considering scale effects and in-situ heterogeneity (i.e. intensity of structural microdefects and degree of weathering). Grain boundary models using the Voronoi tessellation scheme within UDEC have been used to simulate the results of small (lab) and large (field) scale compression (unconfined and triaxial) and indirect tensile (Brazilian) tests on a series of progressively larger in size and degrading in quality numerical specimens. Accordingly, relationships that link rock block strength with its volume and in-situ condition were developed for the preliminary estimation of scaled Mohr-Coulomb and Hoek-Brown parameters. The results from the scaling analysis generally suggest that cohesion decreases with both increasing scale and degrading sample condition in a manner similar to the scale/condition dependant reduction of uniaxial compression strength (UCS), while the friction angle shows only minor variation with no apparent trend. The measured peak confined strength values were also fitted to the Generalized Hoek-Brown criterion and a new block-scale Geological Strength Index parameter is introduced named micro GSI (mGSI) which was also linked to the scale/condition dependant reduction of UCS. By using the proposed linear and non-linear approaches, once the UCS reduction due to scaling effects is known, the confined strength of rock blocks could be then defined and can be used to carry out preliminary rock engineering calculations and to run discontinuum numerical models in which rock blocks are simulated explicitly. [ABSTRACT FROM AUTHOR]

Properly drawing clustered networks significantly improves the visual readability of the meaningful structures hidden behind the associated abstract relationships. Nonetheless, we often degrade the visual quality of such clustered graphs when we try to annotate the network nodes with text labels due to their unwanted mutual overlap. In this paper, we present an approach for aesthetically sparing labeling space around nodes of clustered networks by introducing a space partitioning technique. The key idea of our approach is to adaptively blend an aesthetic network layout based on conventional criteria with that obtained through centroidal Voronoi tessellation. Our technical contribution lies in choosing a specific distance metric in order to respect the aspect ratios of rectangular labels, together with a new scheme for adaptively exploring the proper balance between the two network layouts around each node. Centrality-based clustering is also incorporated into our approach in order to elucidate the underlying hierarchical structure embedded in the given network data, which also allows for the manual design of its overall layout according to visual requirements and preferences. The accompanying experimental results demonstrate that our approach can effectively mitigate visual clutter caused by the label overlaps in several important types of networks. [ABSTRACT FROM AUTHOR]

Homogenization of a representative volume element (RVE) is often used as the basis for defining the effective properties of a composite material. Although this is a powerful and useful approach for predicting global response, it does not capture the inherent variability of the material. Homogenization of statistical volume elements (SVEs), which are partitions of the RVE, provide a population of apparent properties that can be used to statistically characterize this local variability. The challenge to using these models lies in choosing a partitioning scheme and appropriate mesoscale to define the SVEs. In this work, two partitioning schemes are examined, a traditional square grid and polygon cells generated using Voronoi tessellation. Each scheme is used with a range of mesolength scales, i.e., partition sizes, and applied to composites with varied phase contrast ratios and differing microstructures. The resulting distributions of properties, described by probability density functions and generated using the principle of maximum entropy, are used to compare partitioning schemes. The results show consistent advantages to using Voronoi tessellation. This method reduces the impact of contrast ratio on property bounds, makes the choice of partition size less critical to a mesoscale model, and is able to better distinguish between subtle microstructural differences. [ABSTRACT FROM AUTHOR]

In cellular networks, users are grouped into different cells and served by different access points (base stations) that provide wireless access to services and applications. In general, the service demand is very heterogeneous, non-uniformly distributed, and dynamic. Consequently, radio access networks create very irregular topologies with more access points, where service demand is concentrated. While this dynamism requires networks with the ability to adapt to time-varying conditions, the non-uniformity of the service demand makes the planning, analysis, and optimization difficult. In order to help with these tasks, a framework based on canonical domains and spatial mappings (e.g., conformal mapping) have recently been proposed. The idea is to carry out part of the planning in a canonical (perfectly symmetric) domain that is connected to the physical one (real-scenario) by means of a spatial transformation designed to map the access points consistently with the service demand. This paper continues the research in that direction by introducing additional tools and possibilities to that framework, namely the use of centroidal Voronoi algorithms and non-conformal composite mappings. Moreover, power optimization is also introduced to the framework. The results show the usability and effectiveness of the proposed method and its promising research perspectives. [ABSTRACT FROM AUTHOR]

In this paper, we present an efficient method to eliminate the obtuse triangles for high quality 2D mesh generation. Given an initialization (e.g., from Centroidal Voronoi Tessellation—CVT), a limited number of point insertions and removals are performed to eliminate obtuse or small angle triangles. A mesh smoothing and optimization step is then applied. These steps are repeated till a desired good quality mesh is reached. We tested our algorithm on various 2D polygonal domains and verified that our algorithm always converges after inserting a few number of new points, and generates high quality triangulation with no obtuse triangles. [ABSTRACT FROM AUTHOR]

The Delaunay tessellation of a locally finite subset of the hyperbolic space ℍn is constructed via convex hulls in ℝn+1. For finite and lattice-invariant sets it is proven to be a polyhedral decomposition, and versions (necessarily modified from the Euclidean setting) of the empty circumspheres condition and geometric duality with the Voronoi tessellation are proved. Some pathological examples of infinite, non lattice-invariant sets are exhibited. [ABSTRACT FROM PUBLISHER]