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ABSTRACT Here, we introduce a new estimate on the areal extent and volume of globally dispersed Youngest Toba Tuff ash by considering the decay of grain size and primary ash thickness (PAT). The areal extent of ash dispersal is modelled by interpolating the farthest sites in four directions. For this modelling, it is assumed that (i) PAT at the farthest newly identified site is equal to the maximum size of grains retrieved and (ii) the ash particles blanket the earth up to the farthest sites in a non‐discrete manner. The volume of ash‐fall is calculated using two approaches: (i) the Voronoi tessellation and (ii) a GIS‐aided mathematical calculation. When the Voronoi tessellation estimated a maximum and minimum volume of ash as 2089 and 1276 km3, the GIS‐aided mathematical calculation yielded 1573 and 1312 km3 of dense‐rock equivalent, respectively. Thus, the GIS method provided a more narrower range than the Voronoi method. [ABSTRACT FROM AUTHOR]

We investigate the hyperuniformity of marked Gibbs point processes that have weak dependencies among distant points whilst the interactions of close points are kept arbitrary. Various stability and range assumptions are imposed on the Papangelou intensity in order to prove that the resulting point process is not hyperuniform. The scope of our results covers many frequently used models, including Gibbs point processes with a superstable, lower-regular, integrable pair potential, as well as the Widom–Rowlinson model with random radii and Gibbs point processes with interactions based on Voronoi tessellations and nearest-neighbour graphs. [ABSTRACT FROM AUTHOR]

High noise resistance and high boundary fitting accuracy have always been the goals of image classification. However, the two mutually constrain each other, making it extremely difficult to reach equilibrium. To deal with this problem, the unsupervised image classification algorithm based on fully fuzzy Voronoi tessellation is proposed. It extends Voronoi tessellation from hard to fuzzy, and proposes a hierarchical fuzzy membership model, i.e., pixels fuzzily belong to Voronoi polygons and polygons fuzzily belong to clusters. The objective function is established based on the hierarchical fuzzy membership model by fully considering the transitivity of fuzziness between different levels. Then, the optimal classification result can be obtained by the fuzzy comprehensive decision theory under the best parameter solution. The first level retains the flexibility of pixels while modeling spatial constraints. The second level determines which class the polygon belongs to under the constraint of the first level. It provides an effective way of balancing noise resistance and boundary fitting. In addition, the Voronoi tessellation is explicitly expressed in the objective function in the form of the mathematical model, which allows it to obtain the optimal value through analytical solutions instead of the previous random sampling method. It greatly increases the convergence speed of the algorithm. Experiments have been performed on simulated and several remote sensing images with seven comparing algorithms to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The influence of polar, water-miscible organic solvents (POS) on protein structure, stability, and functional activity is a subject of significant interest and complexity. This study examines the effects of acetonitrile (ACN), a semipolar, aprotic solvent, on the solvation properties of blocked Ace-Gly-X-Gly-Nme tripeptides (where Ace and Nme stands for acetyl and N-methyl amide groups respectively and X is any amino acid) through extensive molecular dynamics simulations. Individual simulations were conducted for each peptide, encompassing five different ACN concentrations within the range of χACN = 0.1–0.9. The preferential solvation parameter (Γ) calculated using the Kirkwood-Buff integral method was used for the assessment of peptide interactions with water/ACN. Additionally, weighted Voronoi tessellation was applied to obtain a three-way data set containing four time-averaged contact surface area types between peptide atoms and water/ACN atoms. A mathematical technique known as N-way Partial Least Squares (NPLS) was utilized to anticipate the preferential interactions between peptides and water/ACN from the contact surface areas. Furthermore, the temperature dependency of peptide-solvent interactions was investigated using a subset of 10 amino acids representing a range of hydrophobicities. MD simulations were conducted at five temperatures, spanning from 283 to 343 K, with subsequent analysis of data focusing on both preferential solvation and peptide-solvent contact surface areas. The results demonstrate the efficacy of utilizing contact surface areas between the peptide and solvent constituents for successfully predicting preferential interactions in water/ACN mixtures across various ACN concentrations and temperatures. [ABSTRACT FROM AUTHOR]

With advances in technology and growing user needs, satellite communication is changing over time. Efficiently managing resources across diverse satellite coverage areas can be significantly enhanced through the application of Artificial Intelligence (AI) and Machine Learning (ML). The intended project seeks to employ fundamental machine learning algorithms, including Weighted k-means and Gaussian Mixture Model (GMM), to cluster user demands within a designated geographical region. This approach aims to optimize the utilization of satellite bandwidth in a multi-beam satellite system. A comparison of the results obtained using two techniques indicates improved performance of the GMM in terms of allocating the user demands. To ensure effective coverage, the clusters are transformed into shapes that match the coverage areas of the satellite. A technique called Voronoi Tessellation is used to create irregular polygons, and then these polygons are approximated as ellipses to cover the clusters more effectively. [ABSTRACT FROM AUTHOR]

This study investigates the morphological evolution of river particles and their mechanical behavior during sediment transport. River particles exhibit distinct shape differences between upstream and downstream sections, with particles becoming progressively rounded downstream. The rounding process is quantitatively described using morphological indices. The analysis reveals upstream particles are more angular, while downstream particles become increasingly rounded due to erosion and abrasion, modeled by a unified abrasion function. The Loop subdivision method effectively simulates this gradual rounding process. Additionally, the Discrete Element Method (DEM) calculates the natural angle of repose for particles with varying erosion levels, showing angles ranging from 38.2° for angular particles to 34.4° for rounded particles, closely matching field observations. The numerical results effectively demonstrate the interlocking effect caused by particle morphology. This research enhances the understanding of sediment transport dynamics and provides a robust framework for modeling particle shape evolution. [ABSTRACT FROM AUTHOR]

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The volumes of atoms and molecules obtained by means of quantum theory of atoms in molecules (VAM) in previously reported π and σ complexes were compared with those revealed from the Hirshfeld surfaces (VHS) and the Voronoi tessellation (VVD). For metal atoms, VHS and VVD are close to VAM values. The Voronoi tessellation underestimates volumes of heavy and low-coordinated metal atoms by 27% in average, while for s- and d-metal ions in σ-complexes VVD deviates from VAM by 6% in average only. The Hirshfeld surfaces underestimate volumes of metal atoms in π-complexes by 17% and overestimate those in σ-complexes by 30% in average. Any correlation between atomic volumes of non-metals is absent; however, VHS and VVD values for polyatomic (even diatomic) molecules deviated from VAM by 11% in average. All three methods indicate constancy of molecular volumes in crystals. Sensitivity of three methods to detect trends in atomic and molecular volumes over different datasets was discussed. [ABSTRACT FROM AUTHOR]

The cellular behavior of Voronoi tessellation has generated interest due to its applicability in various fields and its notable structural properties. Controlling factors such as the gradient of the cells, the position of seed points, and the thickness of the arms allows for adjusting rigidity and flexibility according to specific needs. This article analyzes the state of the art of this technique, exploring its modification for applications in engineering and design, complemented with information on natural structural properties. This comprehensive analysis provides a complete overview of Voronoi tessellation and its potential in engineering and design, categorizing methodologies according to selected processing methods and highlighting techniques for altering structural behavior. Additionally, it emphasizes the integration of biomimetic approaches, connecting nature with technology to foster continuous innovation. Finally, this article addresses encountered limitations, offering future perspectives for the cellular technique and highlights the complexity of reproducibility due to reserved or generalized steps, despite the significant diversity in implemented techniques. [ABSTRACT FROM AUTHOR]

AbstractThe aging process or flow-induced vibration of reactor cores may lead to increased mechanical vibrations, affecting the reliability of in-core sensors and necessitating a robust solution for robust field reconstruction. This work tackles the challenges of reconstructing multiphysics fields from sparse and movable measurements by introducing an advanced framework that integrates various machine learning models with Voronoi tessellation. Our approach, building upon the Voronoi tessellation-assisted Convolutional Neural Network (VCNN), expands the capabilities to include a wider array of neural network architectures such as Convolutional Neural Networks (CNNs), Fourier Neural Operator (FNO), Dilated ResNet Encode-Process-Decode (DilResNet), Dilated Convolution Neural Operator (DCNO), Galerkin Transformer (GT), U-shaped Neural Operator (UNO), and Multiwavelet-based Operator (MWT). The effectiveness of these models is evaluated and validated through numerical tests based on the International Atomic Energy Agency benchmark, particularly noting average relative errors below 5% and 10% in the $${L_2}$$L2 norm and $${L^\infty }$$L∞ norm, respectively, within a 5-cm amplitude around sensor nominal locations. The developed software toolkit encapsulates these architectures, providing a versatile option for nuclear engineers to reconstruct different types of physical fields efficiently. [ABSTRACT FROM AUTHOR]

The recycling of materials is in line with the policy of a closed-loop economy and is currently an option for managing waste in order to reuse it to create new products. To this end, 3D printing is being used to produce materials not only from pure polymers but also from their composites. Further development in this field seems interesting and necessary, and the use of recycled materials will help to reduce waste and energy consumption. This article deals with the use of degradable waste materials for the production of insulating materials by 3D printing. For the study, samples with different numbers of layers (one and five), composite thickness (20, 40, 60, 80, and 100 mm) and composition (including colored resins that were transparent, black, gray, and metallized, as well as resins that were colored gray using soybean oil and gray using natural fibers) were made. The role of natural fillers was played by glycerin and biomass ash with a weight ratio of 5%. The finished materials were tested, and the values of the coefficient of thermal resistance and heat transfer were determined. The best thermal properties among the tested materials were distinguished by a five-layer sample made of soybean-oil-based resin with a thickness of 100 mm. This sample's heat transfer coefficient was: 0.16 W/m2K. As a material for thermal insulation in 3D printing technology, biodegradable components have great potential. [ABSTRACT FROM AUTHOR]

A mathematical procedure enabling the transformation of an arbitrary tessellation of a surface into a bi-colored, complete graph is introduced. Polygons constituting the tessellation are represented by vertices of the graphs. Vertices of the graphs are connected by two kinds of links/edges, namely, by a green link, when polygons have the same number of sides, and by a red link, when the polygons have a different number of sides. This procedure gives rise to a semi-transitive, complete, bi-colored Ramsey graph. The Ramsey semi-transitive number was established as R t r a n s (3 , 3) = 5 Shannon entropies of the tessellation and graphs are introduced. Ramsey graphs emerging from random Voronoi and Poisson Line tessellations were investigated. The limits ζ = lim N → ∞ N g N r , where N is the total number of green and red seeds, N g and N r , were found ζ = 0.272 ± 0.001 (Voronoi) and ζ = 0.47 ± 0.02 (Poisson Line). The Shannon Entropy for the random Voronoi tessellation was calculated as S = 1.690 ± 0.001 and for the Poisson line tessellation as S = 1.265 ± 0.015. The main contribution of the paper is the calculation of the Shannon entropy of the random point process and the establishment of the new bi-colored Ramsey graph on top of the tessellations. [ABSTRACT FROM AUTHOR]

VORO++ is a software library written in C++ for computing the Voronoi tessellation, a technique in computational geometry that is widely used for analyzing systems of particles. VORO++ was released in 2009 and is based on computing the Voronoi cell for each particle individually. Here, we take advantage of modern computer hardware, and extend the original serial version to allow for multithreaded computation of Voronoi cells via the OpenMP application programming interface. We test the performance of the code, and demonstrate that it can achieve parallel efficiencies greater than 95% in many cases. The multithreaded extension follows standard OpenMP programming paradigms, allowing it to be incorporated into other programs. We provide an example of this using the VoroTop software library, performing a multithreaded Voronoi cell topology analysis of up to 102.4 million particles. Program summary: Program title: VORO++ CPC Library link to program files: https://doi.org/10.17632/tddc4w4zkk.1 Developer's repository link: https://github.com/chr1shr/voro Licensing provisions: BSD 3-clause (with LBNL modification) Programming language: C++ External routines/libraries: OpenMP Nature of problem: Multithreaded computation of the Voronoi tessellation in two and three dimensions Solution method: The VORO++ library is built around several C++ classes that can be incorporated into other programs. The two largest components are the container. classes that spatially sort input particles into a grid-based data structure, allowing for efficient searches of nearby particles, and the voronoicell. classes that represent a single Voronoi cell as an arbitrary convex polygon or polyhedron. The Voronoi cell for each particle is built by considering a sequence of plane cuts based on neighboring particles, after which many different statistics (e.g. volume, centroid, number of vertices) can be computed. Since each Voronoi cell is calculated individually, the Voronoi cells can be computed using multithreading via OpenMP.

In the realm of satellite communication, where the importance of efficient spectrum utilization is growing day by day due to the increasing significance of this technology, dynamic resource management has emerged as a pivotal consideration in the design of contemporary multi-beam satellites, facilitating the flexible allocation of resources based on user demand. This research paper delves into the pivotal role played by machine learning and artificial intelligence within the domain of satellite communication, particularly focusing on spot beam satellites. The study encompasses an evaluation of machine learning’s application, whereby an extensive dataset capturing user demand across a specific geographical area is subjected to analysis. This analysis involves determining the optimal number of beams/clusters, achieved through the utilization of the knee-elbow method predicated on within-cluster sum of squares. Subsequently, the demand data are equitably segmented employing the weighted k-means clustering technique. The proposed solution introduces a straightforward yet efficient model for bandwidth allocation, contrasting with conventional fixed beam illumination models. This approach not only enhances spectrum utilization but also leads to noteworthy power savings, thereby addressing the growing importance of efficient resource management in satellite communication.

The Voronoi grain-based breakable block model (VGBBM) based on the combined finite-discrete element method (FDEM) was proposed to explicitly characterize the failure mechanism and predict the deformation behavior of hard-rock mine pillars. The influence of the microscopic parameters on the macroscopic mechanical behavior was investigated using laboratory-scale models. The field-scale pillar models (width-to-height, W/H=1, 2 and 3) were calibrated based on the empirically predicted stress-strain curves of Creighton mine pillars. The results indicated that as the W/H ratios increased, the VGBBM effectively predicted the transition from strain-softening to pseudo-ductile behavior in pillars, and explicitly captured the separated rock slabs and the V-shaped damage zones on both sides of pillars and conjugate shear bands in core zones of pillars. The volumetric strain field revealed significant compressional deformation in core zones of pillars. While the peak strains of W/H=1 and 2 pillars were relatively consistent, there were significant differences in the strain energy storage and release mechanism. W/H was the primary factor influencing the deformation and strain energy in the pillar core. The friction coefficient of the structural plane was also an important factor affecting the pillar strength and the weakest discontinuity angle. The fracture surface was controlled by the discontinuity angle and the friction coefficient. This study demonstrated the capability of the VGBBM in predicting the strengths and deformation behavior of hard-rock pillars in deep mine design.

The paper explores enhancing the mechanical behavior of stochastic lattice structures through a semi-controlled design approach. By leveraging the Gibson-Ashby model and predefined geometric routines, the study aims to optimize the mechanical response of lattice structures under compressive stress. Transitioning from stochastic to semi-controlled tessellation using Rhinoceros 7 software enables more predictable deformation behavior. Design parameters such as node formation, strut thickness, and lattice generation patterns are correlated with relative density to regulate stiffness and strength. Experimental validation using Acrylic Styrene Acrylonitrile (ASA) filament demonstrates the effectiveness of the proposed design model. The research emphasizes the importance of understanding internal mechanics by introducing a novel design approach to control geometry and topology arrangement in shaping lattice properties. By introducing a semi-controlled mechanism, the study seeks to improve the reliability and uniformity of mechanical responses in lattice structures. The findings highlighted the benefits of semi-controlled design approaches in achieving tailored mechanical properties. Specimens were compression tested in quasi-static uniaxial loading and showed that structures created with parabolic distribution dimensioned by h p = 0.5 h v originated the most reliable and most vital mechanical response compared with other design models, including typical Voronoi distribution. The improved mechanical response in between proposed design models constantly progressed by about 15% on average consecutively, starting from the parabolic distribution dimensioned by h p = 1.0 h v as the weakest ranked, up to the best one, dimensioned by h p = 0.5 h v , even better than the typical Voronoi distribution. The proposed design model has introduced an entirely novel approach that significantly enhances the product's volume tessellation using routines that guarantee the validity of geometric and topologic entities. Uniaxial compression tests on lattice blocks highlighted the effect of the proposed approach on the mechanical properties of these structures, having shown particularly crucial repeatability and stability. Overall, the paper contributes to advancing the field of lightweight lattice structures through the novel design methodology and material characterization. [ABSTRACT FROM AUTHOR]

Conglomerate reservoirs are important oil and gas resources that require hydraulic fracturing for stimulation. However, the heterogeneity of conglomerate rocks causes fractures to propagate irregularly, complicating the fracturing design. To provide insight into the complex fracture behavior in conglomerate rocks, a three-dimensional (3D) hydromechanical numerical model based on the discrete element method (DEM) was proposed in this study. Besides, a novel approach combining the grain-based DEM with Voronoi tessellation was adopted to depict the geometrical characteristics of conglomerate rocks. Considering the rock matrix-interface-gravel structure, the effects of various influencing factors including the strength and permeability, in situ stress difference, fluid properties and injection scheme on the fracture propagation and induced microseismic events were investigated. Two fracture behaviors, penetration and deflection, were summarized. Finally, the mechanisms of different fracture behaviors were discussed, revealing the joint effects of various factors on the fracture behavior. To predict the fracture behavior in conglomerate rocks, an explainable machine learning framework comprising the extreme gradient boosting and the shapley additive explanations was adopted, which attained high accuracy on the testing set. It can also provide comprehensive explanations for the predicted results, offering support for practical decisions. [ABSTRACT FROM AUTHOR]

In this research, we propose a novel technique for visualizing nonstationarity in geostatistics, particularly when confronted with a single realization of data at irregularly spaced locations. Our method hinges on formulating a statistic that tracks a stable microergodic parameter of the exponential covariance function, allowing us to address the intricate challenges of nonstationary processes that lack repeated measurements. We implement the fused lasso technique to elucidate nonstationary patterns at various resolutions. For prediction purposes, we segment the spatial domain into stationary sub-regions via Voronoi tessellations. Additionally, we devise a robust test for stationarity based on contrasting the sample means of our proposed statistics between two selected Voronoi subregions. The effectiveness of our method is demonstrated through simulation studies and its application to a precipitation dataset in Colorado. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

The paper presents efficiently realized approximations of random functions, which have been developed by the authors and are numerically simulated for study of stochastic processes of particle transfer, including the problems of process criticality fluctuations in random media with multiplication. Efficient correlation-randomized algorithms are constructed for approximating an ensemble of particle trajectories using a correlation function or only a correlation scale of medium. A simple grid model of an isotropic random field is formulated, which reproduces a given average correlation length. This ensures high accuracy in solving stochastic transfer problems for a small correlation scale. The algorithms are tested by solving a test problem of photon transfer and a problem of estimating the overexponential average particle flux in a random medium with multiplication. [ABSTRACT FROM AUTHOR]

Abstract Dynamic failure widely exists in rock engineering, such as excavation, blasting, and rockburst. However, the quantitative measurement of the dynamic damage process using experimental methods remains a challenge. In this study, a SHPB modeling technique is established based on Voronoi-based DDA to study the damage evolution of Fangshan granite under dynamic loading. The assessment of cracking along the artificial joints among Voronoi sub-blocks is conducted using the modified contact constitutive law. A calibration procedure has been implemented to investigate the rock dynamic properties quantitatively. The dispersion and damping effect can be effectively eliminated by regular discretization in SHPB bars, based on which the dynamic stress equilibrium can be satisfied. To reproduce the loading rate effect of the dynamic compressive strength, which has been observed in the experiment, a modification strategy considering the influence of the rate effect on the strength meso-parameters is proposed. Using this strategy, the peak stresses of the transmitted waves predicted by DDA match well with those obtained from experiments conducted at different loading rates. The simulation results show that more microcracks are generated and the proportion of tensile cracks decreases as the loading rate increases. Furthermore, the dynamic mechanical behavior and fracturing process have also been discussed and compared with the experiments. The results show that the established SHPB system is a powerful tool for quantitative analysis of rock dynamics problems and can handle more complex problems in the future.

High noise resistance and high boundary fitting accuracy have always been the goals of image classification. However, the two mutually constrain each other, making it extremely difficult to reach equilibrium. To deal with this problem, the unsupervised image classification algorithm based on fully fuzzy Voronoi tessellation is proposed. It extends Voronoi tessellation from hard to fuzzy, and proposes a hierarchical fuzzy membership model, i.e., pixels fuzzily belong to Voronoi polygons and polygons fuzzily belong to clusters. The objective function is established based on the hierarchical fuzzy membership model by fully considering the transitivity of fuzziness between different levels. Then, the optimal classification result can be obtained by the fuzzy comprehensive decision theory under the best parameter solution. The first level retains the flexibility of pixels while modeling spatial constraints. The second level determines which class the polygon belongs to under the constraint of the first level. It provides an effective way of balancing noise resistance and boundary fitting. In addition, the Voronoi tessellation is explicitly expressed in the objective function in the form of the mathematical model, which allows it to obtain the optimal value through analytical solutions instead of the previous random sampling method. It greatly increases the convergence speed of the algorithm. Experiments have been performed on simulated and several remote sensing images with seven comparing algorithms to demonstrate the effectiveness of the proposed algorithm.

The optimization of structure and thermal properties in 3D-printed insulation materials remains an underexplored area in the literature. This study aims to address this gap by investigating the impact of 3D printing on the thermal properties of manufactured cellular composites. The materials studied were closed-cell foams with a complex cell structure based on the Voronoi cell model, manufactured using incremental technology (3D printing). The influence of the cellular structure of the composite, the type of material used, and the number of layers in the composite structure on its thermal properties, i.e., thermal conductivity coefficient, thermal resistance, and coefficient of heat transfer, was analyzed. Samples of different types of thermosetting resins, characterized by different values of emissivity coefficient, were analyzed. It was shown that both the type of material, the number of layers of the composite, and the number of pores in its structure significantly affect its thermal insulating properties. Thermal conductivity and permeability depended on the number of layers and decreased up to 30% as the number of layers increased from one to four, while thermal resistance increased to 35%. The results indicate that material structure is key in regulating thermal conduction. Controlling the number of cells in a given volume of composite (and thus the size of the air cells) and the number of layers in the composite can be an effective tool in designing materials with high insulation performance. Among the prototype composites produced, the best thermal performance was that of the metalized four-layer cellular composites (λ = 0.035 ± 0.002 W/m·K, Rc = 1.15 ± 0.02 K·m2/W, U = 0.76 ± 0.01 W/m2·K). [ABSTRACT FROM AUTHOR]

In this paper, a numerical and experimental study on in-plane guided wave propagation in polycrystalline microstructure is presented. For numerical study, Voronoi tessellation is used to generate the microstructure considering the concept of regularity parameter. It helped in producing equiaxed grains of microstructure, which resembles the texture of natural polycrystalline structure. In-plane guided wave propagation, resulting in simultaneous P and S wave transmission in two-dimensional (2-D) microstructure is simulated using a commercial finite element (FE) package, using graphics processing unit (GPU) based computing. Experimental verification of the in-plane guided wave propagation model is performed in the Rayleigh regime. The in-house experiments are performed on Inconel-600 plate using piezoelectric wafers as transducers. Though considerable work has been reported on P-wave characterization in a polycrystalline material, the study of in-plane guided waves is limited. It is found that within Rayleigh regime, the attenuation behavior of the in-plane guided wave shows a frequency dependency that is substantially less compared to the bulk wave in the 2-D polycrystalline microstructure. The model is first validated with the existing literature, particularly for the attenuation characterization in the Rayleigh regime. For in-plane guided waves, firstly, the numerical and experimental time-domain responses showing P and S waves are presented for different excitation frequencies. Within Rayleigh regime, the experimental and numerical group velocities and attenuation are in good agreement. Next, the attenuation characteristics are studied in the frequency range corresponding to the Rayleigh regime for different grain sizes. A new attenuation coefficient is proposed that relates the attenuation of bulk and in-plane guided waves. The study of in-plane guided wave in polycrystalline material will help in the ultrasonic investigation of defects and flaws in such materials. [ABSTRACT FROM AUTHOR]

This paper introduces a novel approach, namely Variable-Periodic Voronoi Tessellation (VPVT), for the bio-inspired design of porous structures. The method utilizes distributed points defined by a variable-periodic function to generate Voronoi tessellation patterns, aligning with a wide diversity of artificial or natural cellular structures. In this VPVT design method, the truss-based architecture can be fully characterized by design variables, such as frequency factors, thickness factors. This approach enables the optimal design of porous structures for both mechanical performance and functionality. The varied, anisotropic cell shapes and sizes of VPVT porous structures provide significantly greater design flexibility compared to typical isotropic porous structures. In addition, the VPVT method not only can design micro-macro multiscale materials, but is also applicable for the design of meso-macro scale truss-based porous structures, such as architecture constructions, biomedical implants, and aircraft frameworks. This work employs a Surrogate-assisted Differential Evolution (SaDE) method to perform the optimization process. Numerical examples and experiments validate that the proposed design achieves about 51.1% and 47.8% improvement in compliance performance and damage strength, respectively, than existing studies.

This paper reports on the use of co-simulation techniques to build prototypes of co-operative autonomous robotic cyber-physical systems. Designing such systems involves a mission-specific planner algorithm, a control algorithm to drive an agent performing its task; and the plant model to simulate the agent dynamics. An application aimed at positioning a swarm of unmanned aerial vehicles (drones) in a bounded area, exploiting a Voronoi tessellation algorithm developed in this work, is taken as a case study. The paper shows how co-simulation allows testing the complex system at the design phase using models created with different languages and tools. The paper then reports on how the adopted co-simulation platform enables control parameters calibration, by exploiting design space exploration technology. The INTO-CPS co-simulation platform, compliant with the Functional Mock-up Interface standard to exchange dynamic simulation models using various languages, was used in this work. The different software modules were written in Modelica, C, and Python. In particular, the latter was used to implement an original variant of the Voronoi algorithm to tesselate a convex polygonal region, by means of dummy points added at appropriate positions outside the bounding polygon. A key contribution of this case study is that it demonstrates how an accurate simulation of a cooperative drone swarm requires modeling the physical plant together with the high-level coordination algorithm. The coupling of co-simulation and design space exploration has been demonstrated to support control parameter calibration to optimize energy consumption and convergence time to the target positions of the drone swarm. From a practical point of view, this makes it possible to test the ability of the swarm to self-deploy in space in order to achieve optimal detection coverage and allow unmanned aerial vehicles in a swarm to coordinate with each other.

Voronoi diagrams are widely used for area partitioning and coverage control. Nevertheless, their utilization in non-convex domains often necessitates additional computational procedures, such as diffeomorphism application, geodesic distance calculations, or the integration of local markers. Extending these techniques across diverse non-convex domains proves challenging. This paper introduces the adaptive centroidal Voronoi tessellation ( $\alpha $ CVT) algorithm, which combines iterative centroidal Voronoi tessellation ( $i$ CVT) with an innovative agent dropout and reinsertion strategy. This integration aims to enhance area coverage control in non-convex domains while maintaining adaptability across varied environments without the need for complex computational processes. The efficacy of this approach is validated through simulations involving non-convex domains with disjoint target areas, obstacles, and shape constraints for both homogeneous and heterogeneous agents. Additionally, the $\alpha $ CVT algorithm is extended for real-time coverage control scenarios. Performance metrics are employed to assess the distribution of partitioned Voronoi regions and the overall coverage of the target areas. Results demonstrate improved performance compared to methods that do not incorporate the agent dropout and reinsertion strategy.

The recycling of materials is in line with the policy of a closed-loop economy and is currently an option for managing waste in order to reuse it to create new products. To this end, 3D printing is being used to produce materials not only from pure polymers but also from their composites. Further development in this field seems interesting and necessary, and the use of recycled materials will help to reduce waste and energy consumption. This article deals with the use of degradable waste materials for the production of insulating materials by 3D printing. For the study, samples with different numbers of layers (one and five), composite thickness (20, 40, 60, 80, and 100 mm) and composition (including colored resins that were transparent, black, gray, and metallized, as well as resins that were colored gray using soybean oil and gray using natural fibers) were made. The role of natural fillers was played by glycerin and biomass ash with a weight ratio of 5%. The finished materials were tested, and the values of the coefficient of thermal resistance and heat transfer were determined. The best thermal properties among the tested materials were distinguished by a five-layer sample made of soybean-oil-based resin with a thickness of 100 mm. This sample’s heat transfer coefficient was: 0.16 W/m2K. As a material for thermal insulation in 3D printing technology, biodegradable components have great potential.

The cellular behavior of Voronoi tessellation has generated interest due to its applicability in various fields and its notable structural properties. Controlling factors such as the gradient of the cells, the position of seed points, and the thickness of the arms allows for adjusting rigidity and flexibility according to specific needs. This article analyzes the state of the art of this technique, exploring its modification for applications in engineering and design, complemented with information on natural structural properties. This comprehensive analysis provides a complete overview of Voronoi tessellation and its potential in engineering and design, categorizing methodologies according to selected processing methods and highlighting techniques for altering structural behavior. Additionally, it emphasizes the integration of biomimetic approaches, connecting nature with technology to foster continuous innovation. Finally, this article addresses encountered limitations, offering future perspectives for the cellular technique and highlights the complexity of reproducibility due to reserved or generalized steps, despite the significant diversity in implemented techniques.

In this study, the pseudo-discontinuum modeling technique, called continuum Voronoi block model (CVBM), was applied to represent the behavior of hard-rock pillars from underground mines subjected to high field stresses. The CVBM’s ability to produce numerical results consistent with the observed behavior of pillars is demonstrated through the numerical analysis of a hypothetical case and a back analysis of the Creighton mine pillar. The results show that the model can capture convergence displacements and explicitly show the formation of macro-fractures parallel to excavation walls, intact rock slabs, and V-shaped notches. These components are characteristics of brittle failure induced by highly stressed ground conditions. The studies presented in this work confirm the CVBM as a convenient tool for the numerical modeling of intact rock pillars excavated in deep underground mines.

Since its introduction, discontinuous deformation analysis (DDA) has been widely used in different areas of rock mechanics. By dividing large blocks into subblocks and introducing artificial joints, DDA can be applied to rock fracture simulation. However, parameter calibration, a fundamental issue in discontinuum methods, has not received enough attention in DDA. In this study, the parameter calibration of DDA for intact rock is carefully studied. To this end, a subblock DDA with Voronoi tessellation is presented first. Then, a modified contact constitutive law is introduced, in which the tensile and shear meso-strengths are modified to be independent of the bond lengths. This improvement can prevent the unjustified preferential failure of short edges. A method for imposing confining pressure is also introduced. Thereafter, sensitivity analysis is performed to investigate the influence of the calculated parameters and meso-parameters on the mechanical properties of modeled rock. Based on the sensitivity analysis, a unified calibration procedure is suggested for both cases with and without confining pressure. Finally, the calibration procedure is applied to two examples, including a biaxial compression test. The results show that the proposed Voronoi-based DDA can simulate rock fracture with and without confining pressure very well after careful parameter calibration.

Non-planar Polycrystalline Diamond Compact (PDC) cutters have been widely used in deep formations and have certain advantages in improving the rock-breaking efficiency. However, there are few studies on their rock-breaking mechanism, and most numerical cutting models do not consider the heterogeneity of rock. This paper introduced an innovative multi-ridge-curve-shaped (MRCS) cutter. A cutting model of heterogeneous granite is established based on the Voronoi tessellation method, the accuracy and reliability of rock cutting numerical model is verified by rock cutting experiment. The results illustrate that compared with cylindrical cutter and axe-shaped cutter, MRCS cutter has a rock-breaking effect similar to "ploughing" and "shoveling", with minor force and higher rock-breaking efficiency. And the mechanical specific energy (MSE), force and its fluctuation of MRCS cutter increase with the increase of back rake angle, while demonstrate a fluctuation with the increase of the number of ridges. The entire drillstring dynamic simulation results of three kinds of PDC bits illustrate that MRCS PDC bit has smaller fluctuation of weight on bit (WOB), weaker axial and lateral vibration strength during the drilling process, significantly improve the rate of penetrate (ROP) and save the drilling costs. The results of this study explore the rock-breaking mechanism of MRCS cutter and provide a theoretical basis for the structural optimization design of cutters in harder and abrasive heterogeneous formations. [ABSTRACT FROM AUTHOR]

We present VoroIF-GNN (Voronoi InterFace Graph Neural Network), a novel method for assessing inter-subunit interfaces in a structural model of a protein–protein complex, relying solely on the input structure without any additional information. Given a multimeric protein structural model, we derive interface contacts from the Voronoi tessellation of atomic balls, construct a graph of those contacts, and predict the accuracy of every contact using an attention-based GNN. The contact-level predictions are then summarized to produce whole interface-level scores. VoroIF-GNN was blindly tested for its ability to estimate the accuracy of protein complexes during CASP15 and showed strong performance in selecting the best multimeric model out of many. [ABSTRACT FROM AUTHOR]

Blood oxygenation level‐dependent (BOLD) functional magnetic resonance imaging (fMRI) is one of the most used imaging techniques to map brain activity or to obtain clinical information about human cortical vasculature, in both healthy and disease conditions. Nevertheless, BOLD fMRI is an indirect measurement of brain functioning triggered by neurovascular coupling. The origin of the BOLD signal is quite complex, and the signal formation thus depends, among other factors, on the topology of the cortical vasculature and the associated hemodynamic changes. To understand the hemodynamic evolution of the BOLD signal response in humans, it is beneficial to have a computational framework available that virtually resembles the human cortical vasculature, and simulates hemodynamic changes and corresponding MRI signal changes via interactions of intrinsic biophysical and magnetic properties of the tissues. To this end, we have developed a mechanistic computational framework that simulates the hemodynamic fingerprint of the BOLD signal based on a statistically defined, three‐dimensional, vascular model that approaches the human cortical vascular architecture. The microvasculature is approximated through a Voronoi tessellation method and the macrovasculature is adapted from two‐photon microscopy mice data. Using this computational framework, we simulated hemodynamic changes—cerebral blood flow, cerebral blood volume, and blood oxygen saturation—induced by virtual arterial dilation. Then we computed local magnetic field disturbances generated by the vascular topology and the corresponding blood oxygen saturation changes. This mechanistic computational framework also considers the intrinsic biophysical and magnetic properties of nearby tissue, such as water diffusion and relaxation properties, resulting in a dynamic BOLD signal response. The proposed mechanistic computational framework provides an integrated biophysical model that can offer better insights regarding the spatial and temporal properties of the BOLD signal changes. [ABSTRACT FROM AUTHOR]

In this paper, the microstructures of nanocomposite ceramic tool materials are represented through Voronoi tessellation. A cohesive element model is established to perform the crack propagation simulation by introducing cohesive elements with fracture criteria into microstructure models. Both intergranular and transgranular cracking are considered in this work. The influences of nanoparticle size, microstructure type, nanoparticle volume content and interface fracture energy are analyzed, respectively. The simulation results show that the nanoparticles have changed the fracture pattern from intergranular mode in single-phase materials to intergranular–transgranular–mixed mode. It is mainly the nanoparticles along grain boundaries that have an impact on the fracture pattern change in nanocomposite ceramic tool materials. Microstructures with smaller nanoparticles, in which there are more nanoparticles dispersed along matrix grain boundaries, have higher fracture toughness. Microstructures with a nanoparticle volume content of 15% have the most obvious transgranular fracture phenomenon and the highest critical fracture energy release rate. A strong interface is useful for enhancing the fracture toughness of nanocomposite ceramic tool materials. [ABSTRACT FROM AUTHOR]

The paper explores enhancing the mechanical behavior of stochastic lattice structures through a semi-controlled design approach. By leveraging the Gibson-Ashby model and predefined geometric routines, the study aims to optimize the mechanical response of lattice structures under compressive stress. Transitioning from stochastic to semi-controlled tessellation using Rhinoceros 7 software enables more predictable deformation behavior. Design parameters such as node formation, strut thickness, and lattice generation patterns are correlated with relative density to regulate stiffness and strength. Experimental validation using Acrylic Styrene Acrylonitrile (ASA) filament demonstrates the effectiveness of the proposed design model. The research emphasizes the importance of understanding internal mechanics by introducing a novel design approach to control geometry and topology arrangement in shaping lattice properties. By introducing a semi-controlled mechanism, the study seeks to improve the reliability and uniformity of mechanical responses in lattice structures. The findings highlighted the benefits of semi-controlled design approaches in achieving tailored mechanical properties. Specimens were compression tested in quasi-static uniaxial loading and showed that structures created with parabolic distribution dimensioned by hp=0.5hv originated the most reliable and most vital mechanical response compared with other design models, including typical Voronoi distribution. The improved mechanical response in between proposed design models constantly progressed by about 15% on average consecutively, starting from the parabolic distribution dimensioned by hp=1.0hv as the weakest ranked, up to the best one, dimensioned by hp=0.5hv, even better than the typical Voronoi distribution. The proposed design model has introduced an entirely novel approach that significantly enhances the product’s volume tessellation using routines that guarantee the validity of geometric and topologic entities. Uniaxial compression tests on lattice blocks highlighted the effect of the proposed approach on the mechanical properties of these structures, having shown particularly crucial repeatability and stability. Overall, the paper contributes to advancing the field of lightweight lattice structures through the novel design methodology and material characterization.

Shannon entropy quantifying bi-colored Ramsey complete graphs is introduced and calculated for complete graphs containing up to six vertices. Complete graphs in which vertices are connected with two types of links, labeled as α-links and β-links, are considered. Shannon entropy is introduced according to the classical Shannon formula considering the fractions of monochromatic convex α -colored polygons with n α-sides or edges, and the fraction of monochromatic β -colored convex polygons with m β-sides in the given complete graph. The introduced Shannon entropy is insensitive to the exact shape of the polygons, but it is sensitive to the distribution of monochromatic polygons in a given complete graph. The introduced Shannon entropies S α and S β are interpreted as follows: S α is interpreted as an average uncertainty to find the green α − polygon in the given graph; S β is, in turn, an average uncertainty to find the red β − polygon in the same graph. The re-shaping of the Ramsey theorem in terms of the Shannon entropy is suggested. Generalization for multi-colored complete graphs is proposed. Various measures quantifying the Shannon entropy of the entire complete bi-colored graphs are suggested. Physical interpretations of the suggested Shannon entropies are discussed. [ABSTRACT FROM AUTHOR]

Given the importance of large-scale engineering applications of the superconducting compound Nb3Sn, both its use and performance under certain operating conditions have attracted the interest of applied superconductivity researchers and material scientists for several years now. Huge efforts are directed toward understanding the response to applied loads and predicting fracture damage within their internal microstructure; this is fundamental in the design of superconducting coils and magnets which must meet stringent requirements in terms of maximum thermal and electromagnetic loads. In this paper, the fracture behaviors in polycrystalline Nb3Sn and Nb3Sn filaments with composite structures are investigated using the micromechanical finite element (FE) models with Voronoi tessellation. First, the 2D and 3D Voronoi FE models of the polycrystalline Nb3Sn tensile tests are developed and validated to provide insight into the cracking behavior in the intergranular brittle fracture of polycrystalline Nb3Sn. A cohesive zone model is used to simulate crack propagation at the grain level model including grain boundary zones. It is found that the pre-existing cracks of polycrystals and martensitic phase transformation of grains significantly impact the fracture properties in polycrystalline Nb3Sn. Second, detailed FE models of powder-in-tube (PIT) and bronze route filaments with Voronoi structures for fracture analysis are then developed on the basis of experimental observations of sectional morphologies. The mechanism of crack initiation and propagation under tensile load have been investigated by analyzing the mechanical properties of each component and the characteristics of multi-scale composite structures of filaments. Furthermore, the damage situation is investigated in PIT filaments undergoing transverse compressive load. The proposed simulation method in this paper can be extended to the fracture and damage analysis of Nb3Sn superconducting wires with different layouts and fabrication processes. [ABSTRACT FROM AUTHOR]

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Modularity is a fundamental and intriguing property of fabrics. Given the same set of threads, one can construct different geometries and therefore physical behavior simply by changing how those threads are linked to each other. As a result, fabrics have been studied with great interest in engineering applications. However, most engineering applications model fabrics as composite structures reinforced with a secondary material that fills the gaps between thread elements. In this work, we first show the existence of threads that are space-filling without the need for other materials. We then introduce a simple approach to construct such space-filling threads by using a single modular element that can be obtained by partitioning a cube into two yin-yang type identical pieces. These yin-yang type congruent tiles can directly be constructed by using a parametric approach. Another property of these tiles is that they are foldable, i.e., they can be constructed by folding planar materials. We show that there exist infinitely many such congruent tiles. We further demonstrate that any 2-way 2-fold woven structure can be constructed by translated and rotated versions of such congruent tiles. [Display omitted] • We showed the existence of space-filling threads built with single modular element. • One element is obtained by partitioning cube into two yin-yang type identical pieces. • These yin-yang type parts can directly be constructed by using a parametric approach. • These tiles can be made foldable, i.e. can be constructed by folding planar material. • We show that there exist infinitely many such congruent tiles. [ABSTRACT FROM AUTHOR]