Research and development of heterogeneous small cell in cellular network accommodates the proliferation of data-hungry devices and applications. Meanwhile, for challenges in providing high-data-rate ...transmission in poor coverage area, utilizing unmanned aerial vehicles (UAVs) provides a promising solution attracting tremendous attention. However, tight integration of UAVs creates an obstruction in existing network to acquire high efficient resource utilization, which needs investigation in 3 D network architecture. In this letter, we propose a resource allocation optimization mechanism to minimize mean packet transmission delay in 3 D cellular network with multi-layer UAVs. Numerical results demonstrate effectiveness of the proposed algorithm, where optimal spectrum and power allocation can provide minimum packet transmission delay.
This paper presents a three-dimensional mesoscale model of concrete with random packing of spherical aggregates, in which the mortar and interfacial transition zone (ITZ) are discretized based on the ...Voronoi tessellation. A non-steady state model is developed to simulate the chloride diffusion-sorption behavior, with different water diffusion coefficients for wetting and drying processes, respectively. The results confirm general suitability of Voronoi diagram in element mesh generation. Large deviations in the chloride profile predictions may be generated if a single value or unified equation is used for the water diffusion coefficient of both wetting and drying processes. The peak chloride concentration increases with the exposure time. The overall chloride concentration increases as the porosity increases and the tortuosity decreases. Sensitivity analyses suggest that, compared with porosity and constrictivity, tortuosity has a more significant effect on the overall chloride concentration.
The atomic-scale structure of disordered materials like liquids and glasses has often been studied using the Voronoi tessellation method. This method divides the space containing atoms into regions ...called Voronoi polyhedra. Each polyhedron contains one atom. When two polyhedra share a common face, the atoms in the polyhedra are regarded as being connected by a bond. The bonded atoms and their common neighbors form a bipyramidal cluster, whose topology is related to the shape of the common face: when a common face is an n-gon, the cluster is an n-gonal bipyramid. Therefore, the topological order of a material can be characterized by the frequency distribution of the shapes of common faces. However, this approach does not tell anything about the chemical order: how different types of atoms are arranged in the clusters. In this paper, we propose a method for classifying bipyramidal clusters by chemi-topology, namely according to not only the topology of the cluster but also the chemical arrangement in the cluster. Since a bipyramidal cluster is made up of edge-sharing tetrahedral clusters, we also propose a method for classifying tetrahedral clusters. The function to characterize the atomic structures of materials using the proposed methods has been added to the Vorotis software. We describe the usage of this function. As a demonstration, we apply the proposed methods to characterize the structural difference between the liquid and glass states of a model alloy.
Voronoi tessellation (VT) is commonly used for spatial segmentation, surface reconstruction, local structure analysis, and so on. In VT two points are neighbors to each other if they share a common ...bisection-facet (edge in the two-dimensional case). Such definition of neighborhood is different from the concept based on Euclidean distance. In this paper, the inconsistency between Voronoi neighbors and Euclidean neighbors in 2D and 3D cases is discussed. The Voronoi Neighbor Anomaly (VNA) has been defined as that for a given atom, VT identifies farther atoms as neighbors but fail to identify nearer atoms as neighbors. The VNA is theoretically proved to be possible and the conditions are studied in 2D and 3D based on the Delaunay triangles and polyhedrons, respectively. Furthermore, by employing VT and the largest standard cluster analysis (LSCA) to quantify neighborhood between atoms to a MD simulated cooling of liquid metal Ta, the VNA cases are indeed found in the system. It is also shown that as the disordered degree of a system increases, the probability of VNA increases. These findings clarify a potential issue of VT in characterizing local structures, particularly disordered systems. The proposed VNA could be linked to other structural characteristics, which deserves further studies.
•Voronoi tessellation (VT) may lost neighbors when applied to disordered systems.•If a closer point is not a neighbor but a farther point is, neighbor-lost occurs.•Extensive analysis and clarification of the conditions for neighbor-lost.•Clarified the applicable conditions of using VT to define neighbors.
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.
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•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.
A methodology is presented for the generation and meshing of large-scale three-dimensional random polycrystals. Voronoi tessellations are used and are shown to include morphological properties that ...make them particularly challenging to mesh with high element quality. Original approaches are presented to solve these problems: (i) “geometry regularization”, which consists in removing the geometrical details of the polycrystal morphology, (ii) “multimeshing” which consists in using simultaneously several meshing algorithms to optimize mesh quality, and (iii) remeshing, by which a new mesh is constructed over a deformed mesh and the state variables are transported, for large strain applications. Detailed statistical analyses are conducted on the polycrystal morphology and mesh quality. The results are mainly illustrated by the high-quality meshing of polycrystals with large number of grains (up to 10
5), and the finite element method simulation of a plane strain compression of
ε
=
1.4 of a 3000-grain polycrystal. The presented algorithms are implemented and distributed in a free (open-source) software package: Neper.
We study the Langevin dynamics of a physical system with manifold structure M⊂Rp based on collected sample points {xi}i=1n⊂M that probe the unknown manifold M. Through the diffusion map, we first ...learn the reaction coordinates {yi}i=1n⊂N corresponding to {xi}i=1n, where N is a manifold diffeomorphic to M and isometrically embedded in Rℓ with ℓ≪p. The induced Langevin dynamics on N in terms of the reaction coordinates captures the slow time scale dynamics such as conformational changes in biochemical reactions. To construct an efficient and stable approximation for the Langevin dynamics on N, we leverage the corresponding Fokker-Planck equation on the manifold N in terms of the reaction coordinates y. We propose an implementable, unconditionally stable, data-driven finite volume scheme for this Fokker-Planck equation, which automatically incorporates the manifold structure of N. Furthermore, we provide a weighted L2 convergence analysis of the finite volume scheme to the Fokker-Planck equation on N. The proposed finite volume scheme leads to a Markov chain on {yi}i=1n with an approximated transition probability and jump rate between the nearest neighbor points. After an unconditionally stable explicit time discretization, the data-driven finite volume scheme gives an approximated Markov process for the Langevin dynamics on N and the approximated Markov process enjoys detailed balance, ergodicity, and other good properties.
In this study, the Voronoi-based breakable block model (VBBM) based on the combined finite-discrete element method (FDEM) is used to investigate the failure mechanism of mine pillars and the ...rock-rockbolt interactions. The mechanical parameters of grout-rock and grout-bolt interfaces of a fully-grouted bolt are calibrated via numerical pull-out tests. Then, uniaxial compression tests are carried out on the reinforced pillars. The kinetic energy release rate (KERR) and crack aperture (CA) are used to evaluate the reinforcement effect. The results revealed that the VBBM can effectively characterize the damage failure mechanisms of spalling on the pillar surface and conjugate shear failure in the core zone of the pillar and reproduce the pre-peak nonlinear deformation and post-peak pseudo-ductile behaviors. The passive confining pressure generated by rockbolts is activated only when the rock mass produces sufficient deformation, and the constraints generated by different numbers of rockbolts can only affect the post-peak behavior of the pillar. There is a gradient feature in the internal deformation of the pillar from the shallow surface to the core. If the rockbolt density meets the strain demand, then rockbolts can delay the inward expansion of cracks by generating local constraints and can effectively fix the spalling rock blocks. With increasing support pressure, the CA and KERR exhibit a decreasing trend and strong power-exponential relationships with support pressure, indicating that there is a transition interval of support pressure and an optimal value for setting the rockbolt density.
•A novel numerical model (VBBM) is utilized to characterize the damage mechanisms of mine pillars.•The approach of combining the VBBM and the fully-grouted rockbolts is first used to explore the reinforcement effect.•The crack aperture and kinetic energy release rate are used to quantify the support effect.
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•Model can be used to analyze the effect of coefficient of variation on real foams.•The distribution of foam-cell volumes is dependent on sphere volumes distribution.•The statistical ...data of modeled foams is very close to that of real materials.•The average number of faces varies from 13.56 to 14.43 for different CVs.•Porosity decreases with ds/E(d), while surface area increases with ds/E(d).
This work proposes an original geometrical model based on randomly packed spheres using Laguerre-Voronoi tessellations to simulate geometrical and topological characteristics in the microstructure of open cell foams. The model can be used to analyze the effect of coefficient of variation on the pores distribution in real foams. The distribution of foam-cell volumes in foam structures generated in this work is dependent on the log-normal distribution of sphere volumes in corresponding randomly packed spheres. The statistical data of modeled foam structures, including distribution of the cell volume, face and edge number is very close to the characteristics of real materials. The results also show that a higher coefficient of variation in the sphere diameter would decrease the average number of faces per cell. The average number of faces varies from 13.56 to 14.43 for different coefficients of variation of sphere diameter, while the average number of faces in the Poisson-Voronoi tessellation structures is approximately 15.5. Furthermore, the porosity of foam structures, ε, decreases with the ratio of strut diameter to the average diameter of randomly packed spheres, ds/E(d), while the specific surface area of foams, SV, increases with ds/E(d).
The introduction of 3D printing into the manufacturing of ceramic components offers new possibilities to fabricate porous bioceramic scaffold with biomimetic morphology, customized-designed shape and ...suitable mechanical property for bone tissue engineering. However, most of 3D printed porous ceramic scaffolds are prepared from the array of unit cells, which do not exploit the whole potential of additive manufacturing. In this paper, a novel biomimetic porous beta-tricalcium phosphate (β-TCP) scaffolds with trabecular-like morphology were obtained based on three dimension (3D) Voronoi tessellation method and generated design. This bionic pore structure is fabricated via photopolymer-based digital light processing (DLP) 3D printing technique, a suitable 30 wt% β-TCP ceramic slurry with the addition of adjuvants was prepared. After optimized debinding-sintering process according the TG-DSC analysis, the β-TCP scaffolds showed fully interconnected trabecular-like pore structure with tailorable pore size (360 μm–1200 μm) and porosity (45%–75%) and compact microstructure. Combining compressive tests and finite element analysis (FEA), the relationship between inputting parameters, pore structure and compressive strength is investigated. Thus, the mechanical strength of the trabecular-like β-TCP scaffolds could be predicted and tuned in the initial generated design stage. In addition, the shrinkage ratio and XRD pattern are also detected. The method proposed in this study may provide an efficient bionic design intended for tissue engineering applications.
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