On the size distribution of Poisson Voronoi cells

Járai-Szabó, Ferenc; Néda, Zoltán

doi:10.1016/j.physa.2007.07.063

Cited by 517 publications

(374 citation statements)

References 25 publications

(29 reference statements)

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“…In addition, the variance of this distribution, 3π/8−1, is not consistent with the exact results of Gilbert [17] and Brakke [18]. Ferenc and Néda [25], motivated by a known result of one-dimensional Poisson-Voronoi structures, and based on the study of 18,000,000 three-dimensional PoissonVoronoi cells, proposed…”

Section: A Distribution Of Volumesmentioning

confidence: 74%

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Statistical topology of three-dimensional Poisson-Voronoi cells and cell boundary networks

et al. 2013

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Voronoi tessellations of Poisson point processes are widely used for modeling many types of physical and biological systems. In this paper, we analyze simulated Poisson-Voronoi structures containing a total of 250,000,000 cells to provide topological and geometrical statistics of this important class of networks. We also report correlations between some of these topological and geometrical measures. Using these results, we are able to corroborate several conjectures regarding the properties of three-dimensional Poisson-Voronoi networks and refute others. In many cases, we provide accurate fits to these data to aid further analysis. We also demonstrate that topological measures represent powerful tools for describing cellular networks and for distinguishing among different types of networks.

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Section: A Distribution Of Volumesmentioning

confidence: 74%

“…Tanemura [24] later used a substantially larger data set of 5,000,000 cells to obtain more precise data for the distributions of volumes, surfaces areas, and faces, as well as volumes for cells with fixed numbers of faces. Ferenc and Néda [25] later used a data set with 18,000,000 cells to calculate the distribution of cell volumes.…”

Section: Introductionmentioning

confidence: 99%

Statistical topology of three-dimensional Poisson-Voronoi cells and cell boundary networks

et al. 2013

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“…One has to define the threshold above which the concentration is high. To this end, following Monchaux et al (2010Monchaux et al ( , 2012, we compare the probability density function of the logarithm of the Voronoï cell volume, P(v), obtained from the set of particles to be analysed with the semi-analytic distribution corresponding to a random homogeneous particle distribution P r (v) (Ferenc & Néda 2007). The two curves present two intersections at v c and v v : P(v c ) = P r (v c ) and…”

Section: A1 Reference Statementioning

confidence: 99%

Turbulent thermal convection driven by heated inertial particles

et al. 2016

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This is an author-deposited version published in: http://oatao.univ-toulouse.fr/ Eprints ID: 18470Open Archive Toulouse Archive Ouverte (OATAO) OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. The heating of particles in a dilute suspension, for instance by radiation, chemical reactions or radioactivity, leads to local temperature fluctuations in the fluid due to the non-uniformity of the disperse phase. In the presence of a gravity field, the fluid is set in motion by the resulting buoyancy forces. When the particle density is different than that of the fluid, the fluid motion alters the spatial distribution of the particles and possibly strengthens their concentration inhomogeneities. This in turn causes more intense local heating. Direct numerical simulations in the Boussinesq limit show this feedback loop. Various regimes are identified depending on the particle inertia. For very small particle inertia, the macroscopic behaviour of the system is the result of many thermal plumes that are generated independently of each other. For significant particle inertia, clusters of particles are observed and their dynamics controls the flow. The emergence of very intermittent turbulent fluctuations shows that the flow is influenced by the larger structures (turbulent convection) as well as by the small-scale dynamics that affect particle segregation and thus the flow forcing. Assuming thermal equilibrium between the particles and the fluid (i.e. infinitely fast thermal relaxation of the particle), we investigate the evolution of statistical observables with the change of the main control parameters (namely the particle number density, the particle inertia and the domain size), and propose a scaling argument for these trends. Concerning the energy density in the spectral space, it is observed that the turbulent energy and temperature spectra follow a power law, the exponent of which varies continuously with the Stokes number. Furthermore, the study of the spectra of the temperature and momentum forcing (and thus of the concentration/temperature and velocity/temperature correlations) gives strong support to the proposed feedback loop mechanism. We then discuss the intermittency of the flow, and analyse the effect of relaxing some of the simplifying assumptions, thus assessing the relevance of the original studied configuration. To cite this version:

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“…For randomly distributed bubbles, since there is no analytical solution available, the probability density function (PDF) of the Voronoï areas/ volumes normalized by the mean value is usually described with a Γ -distribution (Monchaux et al 2010). Ferenc and Néda (2007) provided an approximation for the threedimensional case of the random PDF using the following equation:…”

Section: Voronoï Diagrams and Clusteringmentioning

confidence: 99%

“…The random distribution is approximated with Eq. 1 (Ferenc and Néda 2007). The resulting plots are shown in Fig.…”

Section: Effect Of Column Heightmentioning

confidence: 99%