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We introduce an atomistic classifier based on a combination of spectral graph theory and a Voronoi tessellation method. This classifier allows for the discrimination between structures from different minima of a potential energy surface, making it a useful tool for sorting through large datasets of atomic systems. We incorporate the classifier as a filtering method in the Global Optimization with First-principles Energy Expressions (GOFEE) algorithm. Here, it is used to filter out structures from exploited regions of the potential energy landscape, whereby the risk of stagnation during the searches is lowered. We demonstrate the usefulness of the classifier by solving the global optimization problem of two-dimensional pyroxene, three-dimensional olivine, Au12, and Lennard-Jones LJ55 and LJ75 nanoparticles. [ABSTRACT FROM AUTHOR]

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

To enhance the material utilization rate in hot forging of straight teeth face gears, an optimization model of the process parameters was built. The "protrusion" volume generated during hot forging was used as the optimization objective, while the maximum stress was used as the constraint. And key parameters crucial to the hot forging process, including deformation temperature, friction factor, mold preheating temperature, and forging strike speed, were selected as design variables. To evaluate the "protrusion" volume and maximum stress under different process parameters, the inherited Latinized centroidal Voronoi tessellation (ILCVT) method was used to generate training samples containing initial design points. Subsequently, the hot forging process of spur gears was simulated by using deform-3D software. The Kriging model was introduced to model the implicit relationship between design variables and performance responses. The simulated annealing algorithm was introduced. Moreover, the disturbance model, annealing temperature attenuation method, and temperature variation strategy were improved to enhance the algorithm search efficiency. The optimized forging process parameters were workpiece deformation temperature of 1 049 °C, friction factor of 0.32, mold preheating temperature of 206 °C, and forging strike speed of 249 mm/s. The effectiveness of the optimization results were verified through a combination of simulation and experimental methods. The results show that the optimized process parameters effectively reduces the "protrusion" volume. [ABSTRACT FROM AUTHOR]

This paper presents safe coverage control algorithms for multi-agent systems, integrating Centroidal Voronoi Tessellation (CVT) and control barrier functions (CBFs). This study aims to ensure safety and spatial optimization by combining CVT and CBFs for obstacle avoidance, testing the controller through simulations, and verifying the results with RT mobile robots. This development of safe coverage control algorithms for multi-agent systems achieves a synergy that addresses both safety and spatial optimization, which are crucial for multi-agent systems. The proposed CVT-CBF-based controller has been validated through extensive simulations in the ROS/Gazebo environment and physical experiments with RT robots, demonstrating its effectiveness in achieving collision-free coverage. This study provides a comprehensive understanding of the integration of CVT and CBFs for safe coverage control with obstacle avoidance in multi-agent systems, highlighting both its potential and the necessary considerations for practical deployment. [ABSTRACT FROM AUTHOR]

The simplification operation has always been a challenging research problem in the field of cartography generalization and expression. Continuous tessellation area data of land cover, whose source data come from high-resolution remote sensing satellite sensors, are an important type of remote sensing application data to express the spatial distribution information of natural and artificial objects on Earth's surface. In this paper, a novel and practical simplification method for continuous tessellation area data is proposed. The first step is area discretization, in which a general topological structure containing semantic features is established, and land patches are divided into multiple arcs on the basis of this topological structure. The second step is arc simplification, in which arcs are classified into artificial and natural types according to their semantic and morphological features, and corresponding simplification algorithms are assigned. The final step is area reconstruction, based on the semantic and topological information, and simplified arcs are reconstructed to patch polygons. The geography and national conditions census data of a city in Guizhou Province, China, are used to verify the rationality and effectiveness of the method. Experimental results showed that the method proposed in this article is suitable for the simplification processing of artificial and natural land features. The simplification results can maintain the overall shape of the patches and reduce the complexity of the arcs effectively, and the semantic information of each patch after simplification is also correct. [ABSTRACT FROM AUTHOR]

Processes of random tessellations of the Euclidean space $\mathbb{R}^d$ , $d\geq 1$ , are considered that are generated by subsequent division of their cells. Such processes are characterized by the laws of the life times of the cells until their division and by the laws for the random hyperplanes that divide the cells at the end of their life times. The STIT (STable with respect to ITerations) tessellation processes are a reference model. In the present paper a generalization concerning the life time distributions is introduced, a sufficient condition for the existence of such cell division tessellation processes is provided, and a construction is described. In particular, for the case that the random dividing hyperplanes have a Mondrian distribution—which means that all cells of the tessellations are cuboids—it is shown that the intrinsic volumes, except the Euler characteristic, can be used as the parameter for the exponential life time distribution of the cells. [ABSTRACT FROM AUTHOR]

Hyperbolic lattices are a new type of synthetic materials based on regular tessellations in non-Euclidean spaces with constant negative curvature. While so far, there has been several theoretical investigations of hyperbolic topological media, experimental work has been limited to time-reversal invariant systems made of coupled discrete resonances, leaving the more interesting case of robust, unidirectional edge wave transport completely unobserved. Here, we report a non-reciprocal hyperbolic network that exhibits both Chern and anomalous chiral edge modes, and implement it on a planar microwave platform. We experimentally evidence the unidirectional character of the topological edge modes by direct field mapping. We demonstrate the topological origin of these hyperbolic chiral edge modes by an explicit topological invariant measurement, performed from external probes. Our work extends the reach of topological wave physics by allowing for backscattering-immune transport in materials with synthetic non-Euclidean behavior. Here the authors experimentally demonstrate the anomalous and Chern topological phases in a hyperbolic non-reciprocal scattering network, establishing unidirectional channels to induce new and exciting wave transport properties in curved spaces. [ABSTRACT FROM AUTHOR]

Voronoi treemaps are widely used for hierarchical data visualization. Existing methods calculate the visualization layouts of hierarchical data by combining the proportion optimization of weights and Lloyd's method of sites. However, this may not only produce results with large area errors but also require more time consumption. Besides, the relative visualization position of the same data element between adjacent frames in dynamic hierarchical data may be changed abruptly, resulting in unclear visual results. To this end, we propose an efficient and topological structure preserved visualization approach, called PowerHierarchy, for visualizing hierarchical data. Firstly, an improved version of the power diagram computing algorithm is introduced to generate the visualization layouts of each data element in the hierarchy. Unlike random initialization, we construct a centroidal Voronoi tessellation as input and then use a Breadth-First traversing strategy to adapt the depth information to produce visual layouts of static hierarchical data. Based on this, an updating scheme is presented for visualizing dynamic hierarchical data, where previous results are iteratively fed as inputs to initialize current layouts. Besides, the external boundary sites and their subsites are projected onto the visual boundary and then moved into the visual region with the relative position preserved. Experimental results on several datasets demonstrate the efficiency, accuracy, and topology preservation advantage of our proposed visualization approach. [ABSTRACT FROM AUTHOR]

A compact and tractable two-dimensional model to generate the topological network structure of domain walls in BiFeO3 thin films is presented in this study. Our method combines the stochastic geometry parametric model of the centroidal Voronoi tessellation optimized using the von Neumann entropy, a novel information-theoretic tool for networks. The former permits the generation of image-based stochastic artificial samples of domain wall networks, from which the network structure is subsequently extracted and converted to the graph-based representation. The von Neumann entropy, which reflects information diffusion across multiple spatiotemporal scales in heterogeneous networks, plays a central role in defining a fitness function. It allows the use of the network as a whole rather than using a subset of network descriptors to search for optimal model parameters. The optimization of the parameters is carried out by a genetic algorithm through the maximization of the fitness function and results in the desired graph-based network connectivity structure. Ground truth empirical networks are defined, and a dataset of network connectivity structures of domain walls in BiFeO3 thin films is undertaken through manual annotation. Both a versatile tool for manual network annotation of noisy images and a new automatic network extraction method for highquality images are developed. [ABSTRACT FROM AUTHOR]

Polycrystalline silicon has a wide range of applications in the semiconductor industry. Instead of components whose dimensions are of the same order of magnitude in all three spatial directions, thin slices are primarily used there. Deviating mechanical properties have been noticed among such thin configurations. In this work, we systematically investigate the size‐dependent effective elastic properties of polycrystalline silicon. This is realized by gradually reducing the thickness of such components, starting from a structure usually referred to as representative volume element. Based on the framework of continuum mechanics, we specify unit cell problems for aggregates whose microstructures are build artificially based on first‐order properties through tessellations. The effective responses of virtual material tests are determined by the aid of the finite element method. Based on a larger number of computational simulations with different but equivalent microstructures, the effective elastic properties of silicon polycrystals are evaluated statistically. The findings are examined with regard to geometrically‐induced symmetries by several methods. For the unconstrained configurations examined here, results show an increase in the scattering of the results where the average stiffness decreases with decreasing structural thickness. These outcomes are also compared to analytical estimates for silicon bulk configurations. This comparison indicates that the average stiffness varies in between a reasonable mean and the isotropic first‐order lower bound of the silicon bulk. Compared to experimental findings, admissible bounds of the stiffnesses are clearly outlined. [ABSTRACT FROM AUTHOR]

Blaschke–Santaló diagrams are images of maps defined on a set of parameters, taking values into an Euclidean space. Typically, the dimension of the source space is high, possibly infinite, while the target space is two or three dimensional. These diagrams help characterize geometrically various inequalities and are of particular interest in the field of shape optimization. We propose a numerical method, based on Centroidal Voronoi Tessellations, which produces sample points in the parameter space that have uniformly distributed images in the Blaschle–Santaló diagram, therefore providing an accurate description of the latter. Compared with the classical Monte Carlo methods, which simply use a large number of images corresponding to random parameters, the method proposed is computationally efficient and precise. Simulations for two and three dimensional diagrams are presented involving examples in algebra and shape optimization. [ABSTRACT FROM AUTHOR]

In this paper is given an elementary proof of Lester's theorem using the formulas for the distances between the points O, N, F+, F-. Also, using the properties of the orthocentroidal circle and cosymmedian triangles, other quadruples of concyclic points are indicated. [ABSTRACT FROM AUTHOR]

We have utilized the density functional theory (DFT) in conjunction with graph‐theoretical techniques to compute the vibrational, electronic and topological properties of porous nanographenes starting with the building blocks of kekulene, septulene, extended kekulenes, and circumkekulene. Furthermore, graph theoretically based spectral polynomials and other topological properties including Kekulé counts, delocalization energies, and resonance energies are computed for such structures and larger tessellations of kekulenes which are precursors to nanographene belts with multiple pores. The success of the DFT methods is demonstrated with the computed vibrational modes and infrared and Raman spectra of several of these structures. The computed spectral polynomials and the spectra reveal the underlying patterns of the energy levels and structural features and hence suggest the possibility of integration of graph theory with quantum chemical techniques for the computations of properties of large porous graphenes including the possibility of the Pariser–Parr–Pople (PPP) method with parameters extracted from machine learning of the DFT computations on a combinatorial library of precursors. Finally, the computations reveal that the porous structures can be tailored for sequestration of various ions including heavy metal ions for environmental remediation. [ABSTRACT FROM AUTHOR]

Girehs are an important esthetic tool in Islamic architecture. The introduction of deformable Girehs can be considered as a significant solution in the areas of flexibility and authenticity in contemporary architecture. By investigating the configurations of different Girehs based on their configurational authenticity, the present study presents a method to make the studied Girehs deformable. The presented methodology can be generalized for all types of Girehs. The deployment of Girehs in a constant perimeter and the generation of new authentic Gireh with deformable configuration are among the main features of the proposed method. The method is based on the PIC methodology, which uses the change in the angle of the Gireh elements in underlying generative tessellation based on the family of the Gireh (acute, median, obtuse). The fixed points of the deformable Girehs are positioned in the midpoints of the sides of the underlying polygons. Also, to address the issue of the increased lengths of the elements and integrated movement, telescope elements and scissor structure have been used. [ABSTRACT FROM AUTHOR]

Purpose: To investigate pathogenic variants in six families with cone--rod dystrophy (CORD) presenting various inheritance patterns by using wholeexome sequencing (WES) and analyzing phenotypic features. Methods: A total of six families with CORD were enrolled in Ningxia Eye Hospital for this study. The probands and their family members received comprehensive ophthalmic examinations, and DNA was abstracted from patients and family members. Whole-exome sequencing was performed on probands to screen the causative variants, and all suspected pathogenic variants were determined via Sanger sequencing. Furthermore, co-segregation analysis was performed on available family members. The pathogenicity of novel variants was predicted using in silico analysis and evaluated according to the American College of Medical Genetics and Genomics (ACMG) guidelines. Results: Of the six families, two families were assigned as X-linked recessive (XL), two families were assigned as autosomal recessive (AR), and two families were assigned as autosomal dominant (AD). Pathogenic variants were detected in CACNA1F in two X-linked recessive probands, among which family 1 had a hemizygous frameshift variant c.2201del (p.Val734Glyfs*17) and family 2 had a hemizygous missense variant c.245G>A (p.Arg82Gln). Both probands had high myopia, with fundus tessellation accompanied by abnormalities in the outer structure of the macular area. The homozygous splice variant c.2373 + 5G>T in PROM1 and the homozygous nonsense variant c.604C>T (p.Arg202Ter) in ADAM9 were detected in two autosomal recessive families of the probands. Both probands showed different degrees of atrophy in the macular area, and the lesions showed hypofluorescence changes in autofluorescence. The heterozygous variation in CRX c.682C>T (p.Gln228Ter) was detected in two autosomal dominant families. The onset age of the two probands was late, with better vision and severe macular atrophy. According to ACMG guidelines and the analysis of online in silico tools, all variations were labeled as potentially harmful or pathogenic. Conclusion: Pathogenic variants in CACNA1F, PROM1, ADAM9, and CRX genes were identified in six families affected by the diverse inheritance patterns of CORD. Furthermore, the potential impact of the nonsense-mediated decay (NMD) mechanism on the manifestation of CORD phenotypes was examined and addressed. Simultaneously, the spectrum of pathogenic variants and clinical phenotypes associated with the CORD gene was extended. [ABSTRACT FROM AUTHOR]

Current work presents a new approach to quantum surface codes on compact surfaces with genus g ≥ 2 using the identification of these surfaces with hyperbolic polygons and hyperbolic semi-regular tessellations. This method generalizes other contructions, and we show that this approach may give rise to codes with very good parameters. We present tables with several examples of these codes whose parameters had not been shown before. [ABSTRACT FROM AUTHOR]

Assessment of the seismic damage of coal mine overburden (OB) dump slopes gets compromised due to negligence of the consideration of heterogeneity in the shape and size of its particles. In this paper, in situ material parameters for an OB dump slope were evaluated through multichannel analysis of surface waves (MASW) investigations performed at the Jambad opencast coal mine of India. To realistically simulate the heterogeneity of the OB dump materials, Voronoi tessellation scheme coupled with extended finite-element method (XFEM) (using RS2 software) was employed. Behavior of a double-benched OB dump slope under earthquake excitations with a wide range of strong motion parameters (such as peak ground acceleration, predominant frequency, bracketed duration, and Arias intensity) was investigated through XFEM. The influence of strong motion parameters on the seismic behavior of a double-benched OB dump slope was reported in terms of transient (during the earthquake motion) and permanent deformation (after the earthquake motion) at various key points of the slope. Finally, the levels of damage experienced by the OB dump slope under earthquake ground motions were assessed qualitatively. The study would be advantageous for the mining industry in framing the safety guidelines for OB dump slopes in coal mine areas susceptible to earthquakes. The performance of a double-benched coal mine overburden (OB) dump slope under earthquake excitations with a wide range of strong ground motion parameters (such as peak ground acceleration, predominant frequency, bracketed duration, and Arias intensity) was investigated by employing Voronoi tessellation scheme coupled with extended finite-element method (XFEM). The influence of strong ground motion parameters on the seismic behavior of the double-benched OB dump slope was reported in terms of transient (during the earthquake motion) and permanent or residual deformation of the slope at various critical points. Further, the levels of damage experienced by the OB dump slope under earthquake ground motions were assessed qualitatively. This research work may provide guidance to practicing engineers for considering the heterogeneity of the OB dump slope while assessing its seismic performance. The study is going to be useful for the design of OB dump slopes for coal mines located in a seismically active region. If the site-specific earthquake parameters are available, the study may provide important aspects of seismic design of the OB dump slope. [ABSTRACT FROM AUTHOR]

In high dose rate brachytherapy, the catheter positions are crucial to the delivery of the treatment. Currently, the most common approach for prostate cancer is with the use of a template to guide catheters. New approaches which are not bound to such templates and offer a wider variety of insertion patterns are being developed, for example, with robotic insertion or personalized 3D-printed template. Many algorithms have been developed to tackle the problem of catheter insertion such as GOMEA or centroidal voronoi tessellation (CVT). The principal trade-off between different algorithms is speed versus quality. We use a deep learning approach to be more efficient; simultaneously being fast and offering good catheter optimization. The approach chosen is reinforcement learning (RL), which has been successfully used to beat the best known solution of traditional algorithms for Chess and Go. The advantage of a RL approach is that they do not need a dataset to be trained which in turn can offer original solutions to known problems. A RL algorithm is implemented using PyTorch Stable Baselines 3. The model chosen is the off-policies algorithm Soft Actor Critic (SAC). The task of the model is to insert a specific number of catheters inside the prostate anatomy. The input consists of the projected 2D anatomy of the prostate and the urethra (as it would be done for a CVT algorithm). The output of the model gives the catheters positions. The reward function used is negative when the model tries to insert catheters inside (or too close to) the urethra as well as catheters fully outside the prostate. When all catheters are inserted correctly, the reward function is positive. In order to evaluate the reward, first, the catheter insertion provided by our in-house CVT is used as a baseline for comparison. Second, our in-house multicriteria optimization (gMCO) is used on the RL predicted catheters and the values of each objective for all plans at the end of the optimization is compared to the one obtained with CVT. The objectives contain prescription dose to the target and protection of Organs At Risk (OAR). The lower the objective functions are compared to CVT, the better is the reward. The training set, and test set, each consists of 30 different prostate anatomies. The model is trained over 500 000 steps and in the case where the insertions are valid, gMCO is used to generate 500 plans. For now, only a single model is trained on inserting 16 catheters. The model takes 3 seconds to load, generate the catheters and send the configuration to gMCO compared to CVT which takes close to 10 seconds for the same task. After training, the model managed to get a similar or better mean objective compared to CVT for 15 cases (50%) in the training set. The model struggled with the test set; it still manages to find lower objectives for at least one plan out of 500 in 3 cases, but not enough so that the mean of a single case is lower than CVT. Focusing on a case where the model performs better than CVT, see table 1. The CVT insertion does not achieve V125%[%] of the urethra equal to 0 while simultaneously having a target V100%[%] higher than 95 for any of the 500 generated plans, for this specific case. Likewise, the urethra D10%[Gy] is higher. In general, CVT manages to achieve a higher V100%[%] of the target compared to our model, but in those cases the OARs doses are higher. Even though the results are preliminary, the catheter patterns observed with the model are as good or better than CVT for a few cases. In order to achieve better results in the test case, we aim to use a greater number of patients which will help the model generalize. The next phase will involve 3D images to take into account the bladder and rectum anatomy. Another approach would be to modify the reward signal in order to take into account DVH indices instead of the gMCO's objective function. [ABSTRACT FROM AUTHOR]

To enhance the material utilization rate in hot forging of straight teeth face gears, an optimization model of the process parameters was built. The "protrusion" volume generated during hot forging was used as the optimization objective, while the maximum stress was used as the constraint. And key parameters crucial to the hot forging process, including deformation temperature, friction factor, mold preheating temperature, and forging strike speed, were selected as design variables. To evaluate the "protrusion" volume and maximum stress under different process parameters, the inherited Latinized centroidal Voronoi tessellation (ILCVT) method was used to generate training samples containing initial design points. Subsequently, the hot forging process of spur gears was simulated by using deform-3D software. The Kriging model was introduced to model the implicit relationship between design variables and performance responses. The simulated annealing algorithm was introduced. Moreover, the disturbance model, annealing temperature attenuation method, and temperature variation strategy were improved to enhance the algorithm search efficiency. The optimized forging process parameters were workpiece deformation temperature of 1 049 °C, friction factor of 0.32, mold preheating temperature of 206 °C, and forging strike speed of 249 mm/s. The effectiveness of the optimization results were verified through a combination of simulation and experimental methods. The results show that the optimized process parameters effectively reduces the "protrusion" volume. [ABSTRACT FROM AUTHOR]

Origami tessellations, whose crease pattern has translational symmetries, have attracted significant attention in designing the mechanical properties of objects. Previous origami-based engineering applications have been designed based on the "uniform-folding" of origami tessellations, where the folding of each unit cell is identical. Although "nonuniform-folding" allows for nonlinear phenomena that are impossible through uniform-folding, there is no universal model for nonuniform-folding, and the underlying mathematics for some observed phenomena remains unclear. Wavy folded states that can be achieved through nonuniform-folding of the tubular origami tessellation called a waterbomb tube are an example. Recently, the authors formulated the kinematic coupled motion of unit cells within a waterbomb tube as the discrete dynamical system and identified a correspondence between its quasiperiodic solutions and wavy folded states. Here, we show that the wavy folded state is a universal phenomenon that can occur in the family of rotationally symmetric tubular origami tessellations. We represent their dynamical system as the composition of the two 2D mappings: taking the intersection of three spheres and crease pattern transformation. We show the universality of the wavy folded state through numerical calculations of phase diagrams and a geometric proof of the system's conservativeness. Additionally, we present a non-conservative tubular origami tessellation, whose crease pattern includes scaling. The result demonstrates the potential of the dynamical system model as a universal model for nonuniform-folding or a tool for designing metamaterials. [ABSTRACT FROM AUTHOR]

Graph labeling allows for the representation of additional attributes or properties associated with the vertices, edges, or both of graphs. This can provide a more comprehensive and detailed representation of the system being modeled, allowing for a richer analysis and interpretation of the graph. Graph labeling in ladder graphs has a wide range of applications in engineering, computer science, physics, biology, and other fields. It can be applied to various problem domains, such as image processing, wireless sensor networks, VLSI design, bioinformatics, social network analysis, transportation networks, and many others. The versatility of ladder graphs and the ability to apply graph labeling to them make them a powerful tool for modeling and analyzing diverse systems. If a function Υ is an injective vertex assignment in { 1 , 2 , ... q + 1 } and the inductive edge assignment function Υ * in { 1 , 2 , ... q } is expressed as a graph with q edges, defined as Υ * (u v) = 2 [ Υ (u) 2 + Υ (u) Υ (v) + Υ (v) 2 ] 3 [ Υ (u) + Υ (v) ] , then the function is referred to as F-centroidal mean labeling. This is known as the F-centroidal mean criterion. Here, we have determined the F-centroidal mean criteria of the graph ladder, slanting ladder, triangular ladder, T L n ∘ S m , S L n ∘ S m for m ≤ 2 , double-sided step ladder, D n * , and diamond ladder. [ABSTRACT FROM AUTHOR]

Multi-robot coverage systems are widely used in operations such as environmental monitoring, disaster rescue, and pollution prevention. This study considers inherent positioning errors in positioning systems and ground mobile robots with limited communication distance and poor quality in practice. A centroidal Voronoi tessellation algorithm-based formation control technology for multi-robots is optimized. First, by constructing buffered Voronoi cells (BUVCs) for each robot, the collision avoidance ability of the multi-robot formation movement is improved. Next, the formation control problem of multi-robots in a limited communication range and non-convex environment is realized via discrete Voronoi partitioning, a communication distance constraint, and an obstacle avoidance strategy. Simulation and experiment results demonstrate that the proposed method can effectively solve the position generation problem of multi-robot coverage systems in a non-convex environment with actual sizes of the robots and positioning system errors and can further improve the collision avoidance performance of robots and the robustness of BUVC algorithms. [ABSTRACT FROM AUTHOR]

The simulation of complex deformation problems often requires enrichment techniques that introduce local high‐resolution detail on a generally coarse discretization. The use cases include spatial or temporal refinement of the discretization, the simulation of composite materials with phenomena occurring at different scales, or even codimensional simulation. We present an efficient simulation enrichment method for both local refinement of the discretization and codimensional effects. We dub our method Voronoi filters, as it combines two key computational elements. One is the use of kinematic filters to constrain coarse and fine deformations, and thus provide enrichment functions that are complementary to the coarse deformation. The other one is the use of a centroidal Voronoi discretization for the design of the enrichment functions, which adds high‐resolution detail in a compact manner while preserving the rigid modes of coarse deformation. We demonstrate our method on simulation examples of composite materials, hybrid triangle‐based and yarn‐level simulation of cloth, or enrichment of flesh simulation with high‐resolution detail. [ABSTRACT FROM AUTHOR]

The elementary effects method is a screening global sensitivity measure to identify the few important inputs in a model which contains many inputs. In this work, a new advanced trajectory design method (NAT method) is developed to calculate the global sensitivity indices based on the elementary effects method. The conception of trajectory cube is proposed to define a trajectory, and then the central point of trajectory is defined. The quantitative relationship is constructed between the sample points in a trajectory and the central point in the trajectory. By taking exploration coverage and exploration accuracy into consideration, the length of the trajectory cube, i.e. exploration step length, is derived quantitatively. Before generating sampling points, the NAT method needs to generate central points of trajectories at first. In order to facilitate a better scanning of the input space, Sobol's sequence and centroidal Voronoi tessellation (CVT) sampling are adopted. Next, sampling points of the trajectories are generated according to the relationship between sampling points and central points of trajectories. Afterward, the global sensitivity indices of the elementary effects can be estimated by the trajectories resulted from the NAT method. Compared with the advanced trajectory sampling design method proposed by Campolongo et al. in 2007, the NAT method decreases the computational cost and improves the accuracy in screening important inputs, and it is demonstrated by the numerical examples. [ABSTRACT FROM AUTHOR]

The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is frequently utilized in engineering, biology and finance. Although stochastic gradient descent is a well-known stochastic optimization technique for solving the approximate optimal control problem, it often exhibits a slow convergence rate due to the inherent variance in gradient approximation. To address this issue, we propose a more efficient stochastic optimization algorithm based on Centroidal Voronoi Tessellation sampling. This strategy reduces the error in gradient estimation compared to the conventional mini-batch stochastic gradient descent method. Our approach involves dividing the whole snapshot set into several Voronoi cells with low variance and extracting samples with good uniformity from each region to construct an unbiased estimation of the full gradient. Our method can economically and stably approximate numerical optimal control functions even with a fixed step size. Numerical results demonstrate that the proposed method is a reliable algorithm with great potential for applications in the field of optimization. • An efficient stochastic optimization algorithm is proposed based on the CVT sampling. • The proposed method reduces the variance compared to the SGD method. • The proposed method can economically and stably approximate optimal control functions. • The proposed method has great application potential in the field of optimization. [ABSTRACT FROM AUTHOR]

In this paper, we present a mesh topology-based stabilization approach to suppress spurious pressure modes in 3D nearly-incompressible finite elasticity. The focus lies on a mixed formulation with lowest-order approximation for the displacement and pressure fields. Motivated by the fact that the popular H1/P0 element does not fulfill the inf-sup condition, all possible local spurious pressure modes are derived on a patch of elements. The nullspace method is used to determine all spurious pressure solutions. From this, the topological requirements of the finite element mesh are established. We conclude that no more than four elements are allowed to intersect in the same vertex to overcome local checkerboarding. To fulfill this requirement, we employ non-degenerate 3D Voronoi diagrams with several different site distributions. These result in random, centroidal, and honeycomb Voronoi meshes. The resulting convex polyhedral elements are discretized by a polyhedral mixed finite element based on the lowest possible interpolation pair. The numerical examples illustrate that spurious pressure modes do not occur for any degree of mesh refinement as long as the topological mesh requirements are met. Furthermore, it is shown that the numerical inf-sup test is passed. By violating the topological requirements, it is shown that a stable pressure field cannot be guaranteed and the checkerboard phenomenon is provoked. [ABSTRACT FROM AUTHOR]

This paper investigates the compressive and shear properties of nanoporous gold (np-Au) coated with different ultrathin metallic materials (i.e., platinum and silver) via molecular dynamics simulations. Atomistic models used for the geometric representation of coated and uncoated np-Au structures are generated through a modeling technique based on the Voronoi tessellation method. Three different coating thickness values are used to examine the role of thickness for the coating performance under compressive and shear loading by comparing the mechanical characteristics of the atomistic models such as Young's modulus, yield, and ultimate strengths. Moreover, adaptive common neighbor analyses are carried out by monitoring the evolution of the crystal structure of the specimens during the loading process. In this way, the deformation mechanisms of coated and uncoated nanoporous specimens are identified thoroughly. As a key finding from the simulation results, it is observed that the mechanical properties of np-Au are crucially dependent on the type of the coating material. However, a significant improvement on the toughness within the plastic regime is demonstrated for all types of coating materials and loading conditions. [ABSTRACT FROM AUTHOR]

It is argued that Voronoi tessellation theory can be used to model the observed diffusion of microgel particles in a highly compressed microgel colloid. It is shown that this model is able to account for the fact that even when the microgel colloid is highly compressed, the particles can diffuse, while the diffusion rate decreases as the degree of compression of the microgel colloid increases, as observed. [ABSTRACT FROM AUTHOR]

We present a probabilistic classification algorithm to understand the structural transition of supercritical Lennard-Jones (LJ) fluid. The classification algorithm is designed based on the exploratory data analysis on the nearest Voronoi neighbors of subcritical vapor and liquid. The algorithm is tested and applied to LJ type fluids modeled with the truncated and shifted potential and the Weeks-Chandler-Andersen potential. The algorithm makes it available to locate the Widom delta, which encloses the supercritical gas-liquid boundary and the percolation transition loci in a geometrical manner, and to conjecture the role of attractive interactions on the structural transition of supercritical fluids. Thus, the designed algorithm offers an efficient and comprehensible method to understand the phase behavior of a supercritical mesophase. [ABSTRACT FROM AUTHOR]

The solubility of 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF6]) ionic liquid (IL) in water is much less, whereas it is highly soluble in alcohol. The composition dependent structural and dynamical properties of [BMIM][PF6] in methanol and ethanol have been investigated by using all-atom molecular dynamics simulation. Though the density of IL/alcohol binary mixtures is nearly identical for different alcohol mole fractions, we observe the unalike structural and dynamical properties of the IL in methanol and ethanol due to different local environments of the IL and polarity of the solvent. Voronoi polyhedral analysis exhibits strong dependence of local environments on alcohol concentrations. Void and neck distribution in Voronoi tessellation are approximately Gaussian for pure IL, but it deviates from the Gaussian behavior at very high alcohol concentration. At low alcohol concentration, void and neck distributions of [BMIM]+ with [PF6]− in both methanol and ethanol are almost identical, whereas the distributions in ethanol are broader with lesser intensity than in methanol at high alcohol concentration. This suggests the existence of a very few larger free space in ethanol than in methanol. Although peak positions in the void and neck distributions in ethanol are at larger void and neck radius than in methanol, peak intensity for medium sized void in methanol is significantly higher than in ethanol. Thus the translational motion of both [BMIM]+ and [PF6]− and the rotational motion of [BMIM]+ are faster in methanol than in ethanol. Hydrogen bonding of [BMIM]+ with [PF6]− is more predominate than the alcohols, hence cation-anion hydrogen bonding plays an important role in determining self-diffusion coefficient (D) of [BMIM]+, whereas for [PF6]−, cooperative motion due to hydrogen bonding with the alcohols is indispensable. [ABSTRACT FROM AUTHOR]

In our previous paper [ 5 ], we introduced a hyperbolic jigsaw construction and constructed infinitely many noncommensurable, nonuniform, non-arithmetic lattices of |$\textrm{PSL}(2,{\mathbb R})$| with cusp set |$\mathbb{Q} \cup \{\infty \}$| (called pseudomodular groups by Long and Reid [ 4 ]), thus answering a question posed by Long and Reid. In this paper, we continue with our study of these jigsaw groups exploring questions of arithmeticity, pseudomodularity, and also related pseudo-Euclidean and continued fraction algorithms arising from these groups. We also answer another question of Long and Reid [ 4 ] by demonstrating a recursive formula for the tessellation of the hyperbolic plane arising from Weierstrass groups, which generalizes the well-known "Farey addition" used to generate the Farey tessellation. [ABSTRACT FROM AUTHOR]

In this paper, we discuss an alternative approach to the construction of decagonal geometric patterns. We show how one can construct geometric structures for a pattern using alternative tessellations. For the sake of simplicity, we deal here with decagonal geometry and one type of pattern only. However, most of our discussion can be continued with some changes for geometric patterns in other geometries (e.g., octagonal or dodecagonal). [ABSTRACT FROM AUTHOR]

This paper presents a signed distance field (SDF) approach for unified discrete element method (DEM) modeling of granular media using arbitrarily shaped particles. The SDF approach employs a generic SDF-based interface defined by an SDF function and a surface projection function to rigorously model particle shapes and their ensuing complications on contact operations in DEM modeling. The signed distance is defined positive inside particles and negative when outside, and the zeroth isosurface of the SDF is conveniently used to represent the particle surface. The surface of a particle is discretized into a set of nodes. Node-to-surface algorithms are formulated to check the signs of the pertaining distance for contact detection. An energy-conserving contact theory is further employed to derive the contact interaction forces according to the contact potential defined on each intruding node. Based on the unified shape-contact description by SDF, specialised grain shape models are further developed to recover classical shape models as special cases, including poly-super-ellipsoid, poly-super-quadrics, spherical harmonics, polyhedron, and level set. A weighted spherical centroidal Voronoi tessellation-based numerical scheme is further developed for rigorous particle surface discretization and reconstruction. Demonstrative examples are presented to validate and showcase the capabilities of the proposed SDF approach for DEM modeling of granular media. The computational aspects, including the memory consumption and computational efficiency of the proposed approach for various particle models, are discussed. [ABSTRACT FROM AUTHOR]

Purpose: Currently, in high‐dose rate (HDR) brachytherapy planning, the catheter's positions are often selected by the planner, which involves the planner's experience. The catheters are then inserted using a template that helps to guide the catheters. For certain applications, it is of interest to choose the optimal location and number of catheters needed for dose coverage and potential decrease of the treatment's toxicity. Hence, it is of great importance to develop patient‐specific algorithms for catheters and dose optimization. Methods: A modified Centroidal Voronoi tessellation (CVT) algorithm is implemented and merged with a graphics processing unit (GPU)‐based multi‐criteria optimization algorithm (gMCO). The CVT algorithm optimizes the catheters' positions, and the gMCO algorithm optimizes the dwell times and dwell positions. The CVT algorithm can be used simultaneously for insertion with or without a template. Some improvements to the CVT algorithm are presented such as a new way of considering the area that needs to be covered. One hundred eight previously treated prostates HDR cases using real‐time ultrasound are used to evaluate the different optimization procedures. The plan robustness is evaluated using two types of errors: deviations (random) in the insertion and deviation (systematic) in the reconstruction of the catheters. Results: Using gMCO on clinically inserted catheter increases the acceptance rate by 37% for Radiation Therapy Oncology Group (RTOG) criteria. Our results show that all the patients respect RTOG criteria with 11 catheters using CVT+gMCO with a template of 5 mm. The number of catheters needed for all patients to respect RTOG criteria with the freehand technique is 10 catheters using CVT+gMCO. When deviations are introduced, using a template, the acceptance rate goes to 85% with 3 mm deviations using 11 catheters. This decrease is less significant when the number of catheters is higher, decreasing by less than 5% with a 3 mm deviation using 13 catheters or more. In conclusion, it is feasible to decrease the number of catheters needed to treat most patients. Conclusions: Some cases still need a high number of catheters to reach the plan's criteria. Using gMCO allows an increase in the plan quality, while using CVT reduces the number of catheters. A higher number of catheters equates to plans that are more robust to deviations. [ABSTRACT FROM AUTHOR]

Through the glasses of didactic reduction, we consider a (periodic) tessellation Δ$\Delta$ of either Euclidean or hyperbolic n$n$‐space M$M$. By a piecewise isometric rearrangement of Δ$\Delta$ we mean the process of cutting M$M$ along corank‐1 tile‐faces into finitely many convex polyhedral pieces, and rearranging the pieces to a new tight covering of the tessellation Δ$\Delta$. Such a rearrangement defines a permutation of the (centers of the) tiles of Δ$\Delta$, and we are interested in the group PI(Δ)$PI(\Delta)$ of all piecewise isometric rearrangements of Δ$\Delta$. In this paper, we offer (a) an illustration of piecewise isometric rearrangements in the visually attractive hyperbolic plane, (b) an explanation on how this is related to Richard Thompson's groups, (c) a section on the structure of the group pei(Zn)$(\mathbb {Z}^n)$ of all piecewise Euclidean rearrangements of the standard cubically tessellated Rn$\mathbb {R}^n$, and (d) results on the finiteness properties of some subgroups of pei(Zn)$(\mathbb {Z}^n)$. [ABSTRACT FROM AUTHOR]

Quality-diversity (QD) algorithms evolve behaviorally diverse and high-performing solutions. To illuminate the elite solutions for a space of behaviors, QD algorithms require the definition of a suitable behavior space. If the behavior space is high-dimensional, a suitable dimensionality reduction technique is required to maintain a limited number of behavioral niches. While current methodologies for automated behavior spaces focus on changing the geometry of the behavior space or on unsupervised learning of its key features, there remains a need for customizing behavioral diversity to a particular meta-objective specified by the end user. In the newly emerging framework of QD Meta-Evolution, or QD-Meta for short, one evolves a population of QD algorithms, each with different algorithmic and representational characteristics, to optimize the algorithms and their resulting archives to a user-defined meta-objective. Despite promising results compared to traditional QD algorithms, QD-Meta has yet to be compared to state-of-the-art behavior space automation methods, such as centroidal voronoi tessellations multidimensional archive of phenotypic elites (CVT-MAP-Elites) and autonomous robots realizing their abilities (AURORAs). This article performs an empirical study of QD-Meta on function optimization and multilegged robot locomotion benchmarks. Results demonstrate that QD-Meta archives provide improved average performance and faster adaptation to a priori unknown changes to the environment when compared to CVT-MAP-Elites and AURORA. A qualitative analysis shows how the resulting archives are tailored to the meta-objectives provided by the end user. [ABSTRACT FROM AUTHOR]

We present MPAS-Seaice, a sea-ice model which uses the Model for Prediction Across Scales (MPAS) framework and spherical centroidal Voronoi tessellation (SCVT) unstructured meshes. As well as SCVT meshes, MPAS-Seaice can run on the traditional quadrilateral grids used by sea-ice models such as CICE. The MPAS-Seaice velocity solver uses the elastic–viscous–plastic (EVP) rheology and the variational discretization of the internal stress divergence operator used by CICE, but adapted for the polygonal cells of MPAS meshes, or alternatively an integral ("finite-volume") formulation of the stress divergence operator. An incremental remapping advection scheme is used for mass and tracer transport. We validate these formulations with idealized test cases, both planar and on the sphere. The variational scheme displays lower errors than the finite-volume formulation for the strain rate operator but higher errors for the stress divergence operator. The variational stress divergence operator displays increased errors around the pentagonal cells of a quasi-uniform mesh, which is ameliorated with an alternate formulation for the operator. MPAS-Seaice shares the sophisticated column physics and biogeochemistry of CICE and when used with quadrilateral meshes can reproduce the results of CICE. We have used global simulations with realistic forcing to validate MPAS-Seaice against similar simulations with CICE and against observations. We find very similar results compared to CICE, with differences explained by minor differences in implementation such as with interpolation between the primary and dual meshes at coastlines. We have assessed the computational performance of the model, which, because it is unstructured, runs with 70 % of the throughput of CICE for a comparison quadrilateral simulation. The SCVT meshes used by MPAS-Seaice allow removal of equatorial model cells and flexibility in domain decomposition, improving model performance. MPAS-Seaice is the current sea-ice component of the Energy Exascale Earth System Model (E3SM). [ABSTRACT FROM AUTHOR]

Voronoi diagrams and their computation are well known in the Euclidean L2 space. They are easy to sample and render in generalized Lp spaces but nontrivial to construct geometrically. Especially the limit of this norm with p → ∞ lends itself to many quad‐ and hex‐meshing related applications as the level‐set in this space is a hypercube. Many application scenarios circumvent the actual computation of L∞ diagrams altogether as known concepts for these diagrams are limited to 2D, uniformly weighted and axis‐aligned sites. Our novel algorithm allows for the construction of generalized L∞ Voronoi diagrams. Although parts of the developed concept theoretically extend to higher dimensions it is herein presented and evaluated for the 2D and 3D case. It further supports individually oriented sites and allows for generating weighted diagrams with anisotropic weight vectors for individual sites. The algorithm is designed around individual sites, and initializes their cells with a simple meshed representation of a site's level‐set. Hyperplanes between adjacent cells cut the initialization geometry into convex polyhedra. Non‐cell geometry is filtered out based on the L∞ Voronoi criterion, leaving only the non‐convex cell geometry. Eventually we conclude with discussions on the algorithms complexity, numerical precision and analyze the applicability of our generalized L∞ diagrams for the construction of Centroidal Voronoi Tessellations (CVT) using Lloyd's algorithm. [ABSTRACT FROM AUTHOR]

• A comparative study on initial sampling methods for the single step Kriging is conducted. • Latin Centroidal Voronoi Tessellation or Good Lattice Point Method performs better than LHS as an initial sampling method. • A comparative study on hybrid adaptive schemes for Kriging-based probability estimation is implemented. • The proposed hybrid scheme "Good Lattice Point Method + U-learning + Error-based Stopping Criteria" performs the best. Over the past decade, researches on adaptive Kriging-based reliability estimation have been focused on enhancing its performance from three aspects including the simulation methods, learning functions, and stopping criteria, whereas few efforts have been dedicated to give a comprehensive guidance on design of experiment of the initial sampling methods, which directly influences the performance of the surrogate and surrogate-based reliability estimation. This paper presents a comparative study on the adaptive modeling schemes for Kriging-based reliability estimation. Comparison on six common sampling methods for the single step Kriging is conducted with a typical numerical example, to find an optimal initial sampling scheme for the surrogates. A comparative study on the performance of the hybrid adaptive schemes for the adaptive Kriging, each of which includes the initial sampling method, the learning scheme and the corresponding stop criterion, is then implemented on three typical examples, in order to heuristically provide a unique hybrid adaptive scheme for Kriging-based structural reliability estimation. It can synthetically consider the dimension of the input variables, the nonlinearity of the limit-state function and the application scenarios. [ABSTRACT FROM AUTHOR]

Summary: The performance of adaptive estimators that employ embedding in reproducing kernel Hilbert spaces (RKHS) depends on the choice of the location of basis kernel centers. Parameter convergence and error approximation rates depend on where and how the kernel centers are distributed in the state‐space. In this article, we develop the theory that relates parameter convergence and approximation rates to the position of kernel centers. We develop criteria for choosing kernel centers in a specific class of systems by exploiting the fact that the state trajectory regularly visits the neighborhood of the positive limit set. Two algorithms, based on centroidal Voronoi tessellations and Kohonen self‐organizing maps, are derived to choose kernel centers in the RKHS embedding method. Finally, we implement these methods on two practical examples and test their effectiveness. [ABSTRACT FROM AUTHOR]

Porous materials have significant advantages, such as their light weight and good specific energy absorption. This paper presents the designs of two ordered Voronoi structures, a truncated octahedron (Octa) and a rhombic dodecahedron (Dodeca), based on spatial Voronoi tessellation. Through a numerical analysis, the dynamic behavior, deformation and energy absorption of the two porous structures under different impact energies were explored. According to the energy-absorption index, the effects of porosity, rotating unit cell and unit-cell shape on the energy absorption of the porous structures were quantitatively evaluated. The study shows that, for Dodeca and Octa structures subjected to various impact energies, the force-displacement curves exhibit three modes. The porosity, rotational unit cell and unit-cell shape play a crucial role in affecting the impact resistance of porous structures. The work in this paper proposes an effective way to improve the energy-absorption capacity of porous structures under different impact energies. At the same time, a new understanding of the deformation mechanism of Octa and Dodeca was obtained, which is significant for the impact-resistance design and energy-absorption evaluation of porous structures. [ABSTRACT FROM AUTHOR]

The geometric kernel (or simply the kernel) of a polyhedron is the set of points from which the whole polyhedron is visible. Whilst the computation of the kernel of a polygon has been largely addressed in the literature, fewer methods have been proposed for polyhedra. The most acknowledged solution for kernel estimation is to solve a linear programming problem. We present a geometric approach that extends and optimizes our previous method (Sorgente, 2021). Experimental results show that our method is more efficient than the algebraic approach over polyhedra with a limited number of vertices and faces, making it particularly suitable for the analysis of volumetric tessellations with non-convex elements. The method is also particularly efficient in detecting non-star-shaped polyhedra. Details on the technical implementation, and discussions on the pros and cons of the method, are also provided. [Display omitted] • Computation of the kernel of a polyhedron using a geometric approach. • Robust kernel estimation using geometric exact predicates. • An efficient kernel estimation algorithm suitable for volumetric tessellations with non-convex polyhedra. [ABSTRACT FROM AUTHOR]

Distributed and networked mobile sensor platforms using unmanned aerial and/or ground vehicles to survey areas of interest offer a safer and more efficient method for radiological contamination mapping; however, most applications rely on uniformly sweeping of the area in a raster-type motion without utilizing the information available in a dynamic sense. We have developed a fully autonomous optimal motion planning procedure for networks with two or more mobile sensors. The procedure utilizes well-established concepts of Gaussian processes in combination with control laws based on centroidal Voronoi tessellations to achieve optimal next-iteration sensor movements. A new method of informing optimal motion planning is proposed, whereby the absolute difference between the prior and current full-map prediction, referred to as the prediction-difference map, is used as the spatial density function within each Voronoi cell, providing immediate and iterative feedback for dynamic use of available information. The Gaussian process regression model used to estimate the contamination in unvisited locations also provides prediction uncertainties, and can be used as a quantitative metric to assess the confidence in the calculated contamination map; these estimates and prediction uncertainties are unavailable for standard uniform survey routines as they can only produce maps in the vicinity of observed locations. We present through simulation the achievable performance gains from using this new method by directly comparing to a uniform survey method. Results show that using the prediction-difference maps to inform motion planning procedures offers a faster rate of producing an accurate and convergent map relative to a uniform survey route. [ABSTRACT FROM AUTHOR]

The Functional Quantization (FQ) method was developed for the approximation of random processes with optimally constructed finite sets of deterministic functions (quanta) and associated probability masses. The quanta and the corresponding probability masses are collectively called a " quantizer ". A method called "Functional Quantization by Infinite-Dimensional Centroidal Voronoi Tessellation" (FQ-IDCVT) was developed for the numerical implementation of FQ. Compared to other methodologies, the FQ-IDCVT algorithm has the advantages of versatility, simplicity, and ease of application. The FQ-IDCVT algorithm was proved to be able to capture the overall stochastic characteristics of random processes. However, for certain time instants of the processes, the FQ-IDCVT algorithm may fail in approximating well the stochastic properties, which results in significant local errors. For instance, it may significantly underestimate the variances and overestimate the correlation coefficients for some time instants. In addition, the FQ concept was developed for the quantization of single-variate processes. A formal description of its application to multivariate processes is lacking in the literature. Therefore, this paper has two objectives: to extend the FQ concept to multivariate processes and to enhance the FQ-IDCVT algorithm so that its accuracy is more uniform across the various time instants for single-variate processes and applicable to multivariate processes. Along this line, the limitations of the FQ-IDCVT algorithm are explained, and a novel improved FQ-IDCVT algorithm is proposed. Four criteria are introduced to quantify the algorithms' global and local quantization performance. For illustration and validation purposes, four numerical examples of single-variate and multivariate, stationary and non-stationary processes with Gaussian and non-Gaussian marginal distributions were quantized. The results of the numerical examples demonstrate the performance and superiority of the proposed algorithm compared to the original FQ-IDCVT algorithm. • Optimally representative samples of multi-variate random processes. • Quantification of global and local effectiveness in capturing the sample space. • Numerical applications to single-variate and multivariate, stationary and non-stationary processes. • Numerical applications to random processes with Gaussian and non-Gaussian distributions. [ABSTRACT FROM AUTHOR]

The composition and temperature dependence of static and dynamic structures in NixNb1-x (x = 50-70 at. %) were systematically studied using molecular dynamics with a new-released semi-empirical embedded atom method potential by Mendelev. The calculated pair correlation functions and the structure factor match well with the experimental data, demonstrating the reliability of the potential within relatively wide composition and temperature ranges. The local atomic structures were then characterized by bond angle distributions and Voronoi tessellation methods, demonstrating that the icosahedral h0,0,12,0i is only a small fraction in the liquid state but increases significantly during cooling and becomes dominant at 300 K. The most abundant clusters are identified as ‹0,0,12,0› and distorted icosahedron ‹0,2,8,2›. The large fraction of these two clusters hints that the relatively good glass forming ability is near the eutectic point. Unlike Cu-Zr alloys, both the self-diffusion coefficient and shear viscosity are insensitive to compositions upon cooling in Ni-Nb alloys. The breakdownof the Stokes-Einstein relation happens at around 1.6Tg (Tg: glass transition temperature). In the amorphous state, the solid and liquid-like atoms can be distinguished based on the Debye-Waller factor ‹u2›. The insensitivity of the dynamic properties of Ni-Nb alloys to compositions may result from the relatively simple solidification process in the phase diagram, in which only one eutectic point exists in the studied composition range. [ABSTRACT FROM AUTHOR]

Mechanical perturbation of thin layers of pastes on a substrate results in anisotropic cracking during desiccation which allows for a controlled generation of crack patterns with a high relevance for industrial applications. In the present paper we propose a modeling framework to capture the anisotropy induced by initial perturbations which imprint directional dependent material features into the layer. Our approach is based on a random tessellation of the layer using convex polygons which are made anisotropic by elongating or compressing them along the direction of perturbation. Physical properties of the particles' cohesive contacts are determined by the geometrical characteristics of polygons giving rise to a well controlled anisotropy in the mechanical response of the material and in the structure of the fracture pattern emerging during shrinking. The main advantage of the approach is that both the structural disorder of the layer and the strength of anisotropy are controlled by a single parameter. Based on computer simulations we demonstrate that varying its two parameters the model reproduces the qualitative features of experimental findings and provides advantages over existing modeling approaches. • A discrete element model is proposed for anisotropic cracking of shrinking layers. • Anisotropy is introduced by a geometrical transformation of an isotropic lattice. • Disorder has a single source which affects also the mechanical features of the layer. • The model provides a reasonable agreement with experimental findings. [ABSTRACT FROM AUTHOR]

• Developing 2.5D CVT grids and refinement with unstructured vertical discretization. • Curve-fitting matches Voronoi cell edges with geological traces in horizontal projection. • Centroidal Voronoi grids in MODFLOW 6 for complex groundwater modeling. • Linking multiple unstructured-grid models in MODFLOW 6. An unstructured grid is a powerful data structure for a proper depiction of various geological features such as faults and pinch-outs and for groundwater simulation in a complex aquifer system. This study presents a mesh generation methodology based on 2.5D centroidal Voronoi tessellations (CVTs), which provides a great flexibility in specifying grid connections in 3D, matching irregular geometries, and adding high levels of refinement in areas of interest. Lloyd relaxation approximation is introduced to effectively guarantee the generation of centroidal Voronoi grids. A curve-fitting Voronoi gridding approach is developed to construct Voronoi cell edges conforming to intricated geological traces in the horizontal 2D projection with unstructured vertical discretization. A controlled refinement in spatial grid resolution has been demonstrated to prevent adverse impacts on groundwater flow simulations. The methodology is applied to the Southern Hills aquifer system in the Capital Area of Louisiana, USA. Significant groundwater depletion has occurred due to continuous and excessive withdrawals over decades for public supplies and industries. The Baton Rouge fault and the Denham-Springs Scotlandville fault are leaky barriers and have a significant influence on groundwater flow. A curve-fitting centroidal Voronoi grid is developed to simulate the effects of the two faults as leaky barriers. CVT-based high-fidelity unstructured multi-model groundwater modeling is conducted using MODFLOW 6 to allow more flexibility in model design. Complex groundwater flow in the Southern Hills aquifer system was revealed through the centroidal Voronoi unstructured grid. [ABSTRACT FROM AUTHOR]

[Display omitted] • Multidimensional data can be voxelized to obtain a simpler representation. • A simple likelihood function can be used in place of the Euclidean distance. • Classification can be done via partitioning the data into Voronoi regions. • Comparable inference performance with the SVM family of algorithms is achieved. Voronoi tessellations are used to partition the Euclidean space into polyhedral regions, which are called Voronoi cells. Labeling the Voronoi cells with the class information, we can map any classification problem into a Voronoi tessellation. In this way, the classification problem changes into a query of just finding the enclosing Voronoi cell. In order to accomplish this task, we have developed a new algorithm which generates a labeled Voronoi tessellation that partitions the training data into polyhedral regions and obtains interclass boundaries as an indirect result. It is called Supervised k-Voxels or in short Super-k. We are introducing Super-k as a foundational new algorithm and opening the possibility of a new family of algorithms. In this paper, it is shown via comparisons on certain datasets that the Super-k algorithm has the potential of providing comparable performance of the well-known SVM family of algorithms. [ABSTRACT FROM AUTHOR]

We give a brief review of 2D, Euclidean, centroidal Voronoi tessellations (CVTs). Dropping to the specific case of two-point CVTs, a rich interaction between calculus, geometry and analysis is uncovered. Narrowing further to "ellipse-like" shapes with order 2 rotational symmetry, a full characterization of possible two-point CVTs is given for these figures. One might expect the CVTs of symmetric figures with even rotational symmetry to always correspond to lines of symmetry of the figure. Surprisingly, this conjecture is false. We close the article showing how to generate counterexamples to this conjecture and provide some direction for further inquiry. [ABSTRACT FROM AUTHOR]