Despite the central role of mobility in wireless networks, analytical study on its impact on network performance is notoriously difficult. This paper aims to address this gap by proposing a random ...waypoint (RWP) mobility model defined on the entire plane and applying it to analyze two key cellular network parameters: handover rate and sojourn time. We first analyze the stochastic properties of the proposed model and compare it to two other models: the classical RWP mobility model and a synthetic truncated Levy walk model which is constructed from real mobility trajectories. The comparison shows that the proposed RWP mobility model is more appropriate for the mobility simulation in emerging cellular networks, which have ever-smaller cells. Then we apply the proposed model to cellular networks under both deterministic (hexagonal) and random (Poisson) base station (BS) models. We present analytic expressions for both handover rate and sojourn time, which have the expected property that the handover rate is proportional to the square root of BS density. Compared to an actual BS distribution, we find that the Poisson-Voronoi model is about as accurate in terms of mobility evaluation as hexagonal model, though being more pessimistic in that it predicts a higher handover rate and lower sojourn time.
In this paper, we present results of the reconstruction of the total grain size distribution (TGSD) of the material erupted during explosive volcanic eruptions at Campi Flegrei (Italy) considering ...all components (juvenile, lithic and crystal clasts). To date, the few TGSDs made available have been mostly reconstructed by assuming that the tephra deposits consisted of only one component. This simplification can introduce substantial bias in the interpretation of magma fragmentation mechanisms and significantly affect ash dispersion forecasts, since each tephra component has specific aerodynamic characteristics. By means of field investigations and laboratory analyses on samples collected from deposits of the Agnano-Monte Spina and Astroni eruptions, we reconstructed the TGSDs of juvenile, lithic and crystal components via the Voronoi tessellation method. Our results show how the systematic reconstruction of a TGSD, from the component-specific to the bulk TGSD, can provide important information on magma fragmentation mechanisms and wall-rock erosion processes. Results confirm that the bulk TGSD is the combination of the merging of different component subpopulations, according to their own TGSD, density and relative mass proportions. In addition, the integration of component analysis, TGSD and settling velocity data allowed characterization of the aerodynamic behaviour of each component at variable distances from the vent, which can be related to their own parent grain size distribution. The integration of new data from distal tephra deposits for the considered eruptions has thus allowed a reassessment of the erupted volumes of eruptions considered in this research, which are now 3.17 and 0.63 km
3
, for Agnano-Monte Spina and Astroni, respectively.
In article number 1808713, Ramses V. Martinez and co‐workers design low‐density 3D‐architected soft machines (ASMs) from CAD models via a Voronoi tessellation algorithm fabricated by 3D printing. On ...tendon‐based actuation, the ASMs deform according to the topologically encoded buckling of their structure, producing a wide range of motions benefitting from mechanical metamaterial behaviors, and enabling safe human‐robot interactions.
It has been a longstanding question how stars are packed or distributed in the universe. Here we show that the spatial distribution of stars follows some geometric rules although there may be local ...inhomogeneities. The topological and metric properties of their Voronoi tessellations exhibit a lognormal distribution. Moreover, these distributions can be connected with those established for the packing of spheres, corresponding to the loosest packing state. The findings provide a new angle to understand the packing structure of stars in the universe.
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•The packing of stars is studied in terms of the topological and metric properties of the Voronoi tessellation.•The spatial distribution of stars is shown to follow some geometric rules, quantified by the lognormal distribution.•The packing of stars can be linked to the packing of spheres, corresponding to the loosest packing state.
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•The particle size distributions include continuous gradation, discontinuous gradation and mixture of coarse and fine with large size ratio.•Classical Voronoi, weighted Voronoi and ...two-scale Voronoi algorithms are used to build models with different particle size distributions.•A Repulsion-Displacement method is proposed for the generation of discontinuous gradation particles.
This study presents a novel algorithm to establish a numerical model for the study of mechanical behavior of multi-component material such as particle reinforced metal matrix composites, concrete, particle filled polymers, etc. The algorithm consists of two steps, one is to divide the given region into sub-regions of a specified size distribution, and the other is to fill each sub-region with particles of specified shapes. During the filling process, the contact states between particles can be controlled by the number and positions of reference points. Taking the quasi-static uniaxial tensile simulation of concrete as a verification example, two concrete models with the same particle size distribution but different shapes have been established. Through the comparison of elastoplastic responses of different aggregate shape models in different tensile directions, it is concluded that the models meet the requirements of macroscopic uniformity, meso-scale randomness and statistical rationality. This verifies the feasibility of modeling method and its advantages in precise control of particle shape, distribution and other parameters.
Pick d+1 points uniformly at random on the unit sphere in Rd. What is the expected value of the angle sum of the simplex spanned by these points? Choose n points uniformly at random in the ...d-dimensional ball. What is the expected number of faces of their convex hull? We answer these and some other, seemingly unrelated, questions of stochastic geometry. To this end, we compute expected internal angles of random simplices whose vertices are independent random points sampled from one of the following d-dimensional distributions: (i) the beta distribution with the density proportional to (1−‖x‖2)β, where x is belongs to the unit ball in Rd; (ii) the beta' distribution with the density proportional to (1+‖x‖2)−β on the whole of Rd. These results imply explicit formulae for the expected face numbers of the following random polytopes: (a) the typical Poisson-Voronoi cell; (b) the zero cell of the Poisson hyperplane tessellation; (c) beta and beta' polytopes defined as convex hulls of i.i.d. samples from the corresponding distributions.
•Some cancerous mutations are cooperative; their invasion can be modelled using public goods games.•We simulate evolutionary dynamics in tissues using the Voronoi tessellation model.•This allows us ...to spatially decouple birth and death and capture a dynamic population structure.•We find cooperation is favoured compared to death-birth processes on fixed graphs.•Cooperation prefers local game play but global competition for offspring.
Cancer cells obtain mutations which rely on the production of diffusible growth factors to confer a fitness benefit. These mutations can be considered cooperative, and studied as public goods games within the framework of evolutionary game theory. The population structure, benefit function and update rule all influence the evolutionary success of cooperators. We model the evolution of cooperation in epithelial cells using the Voronoi tessellation model. Unlike traditional evolutionary graph theory, this allows us to implement global updating, for which birth and death events are spatially decoupled. We compare, for a sigmoid benefit function, the conditions for cooperation to be favoured and/or beneficial for well-mixed and structured populations. We find that when population structure is combined with global updating, cooperation is more successful than if there were local updating or the population were well-mixed. Interestingly, the qualitative behaviour for the well-mixed population and the Voronoi tessellation model is remarkably similar, but the latter case requires significantly lower incentives to ensure cooperation.
•Structure accounting for variable strut diameter and solid clustering at nodes.•Geometry based on Voronoi tessellation computed from a random set of points.•Good agreement between geometrical ...properties of reconstructed and real foams.•Complex flow field in real foams effectively reproduced in reconstructed foams.
Open-cell foams are considered a potential candidate as an innovative catalyst support in many processes of the chemical industry. In this respect, a deeper understanding of the transport phenomena in such structures can promote their extensive application. In this contribution, we propose a general procedure to recover a representative open-cell structure starting from some easily obtained information. In particular, we adopt a realistic description of the foam geometry by considering clusters of solid material at nodes and different strut-cross sectional shapes depending on the void fraction. The methodology avoids time-consuming and expensive measuring techniques, such as micro-computed tomography (μCT) or magnetic resonance imaging (MRI). Computational Fluid Dynamics (CFD) could be a powerful instrument to enable accurate analyses of the complex flow field and of the gas-to-solid heat and mass transport. The reconstructed geometry can be easily exploited to generate a suitable computational domain allowing for the detailed investigation of the transport properties on a realistic foam structure by means of CFD simulations. Moreover, the proposed methodology easily allows for parametric sensitivity analysis of the foam performances, thus being an instrument for the advanced design of these structures. The geometrical properties of the reconstructed foams are in good agreement with experimental measurements. The flow field established in complex tridimensional geometries reproduces the real foam behavior as proved by the comparison between numerical simulations and experiments.
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