Topic
Spherical contact distribution function
About: Spherical contact distribution function is a research topic. Over the lifetime, 20 publications have been published within this topic receiving 410 citations.
Papers
TL;DR: In this paper, the authors describe two algorithms for the generation of random packings of spheres with arbitrary diameter distribution, i.e., the force-biased algorithm of Mościnski and Bargiel and the Jodrey-Tory sedimentation algorithm.
Abstract: This paper describes two algorithms for the generation of random packings of spheres with arbitrary diameter distribution. The first algorithm is the force-biased algorithm of Mościnski and Bargiel. It produces isotropic packings of very high density. The second algorithm is the Jodrey-Tory sedimentation algorithm, which simulates successive packing of a container with spheres following gravitation. It yields packings of a lower density and of weak anisotropy. The results obtained with these algorithms for the cases of log-normal and two-point sphere diameter distributions are analysed statistically, i. e. standard characteristics of spatial statistics such as porosity (or volume fraction), pair correlation function of the system of sphere centres and spherical contact distribution function of the set-theoretical union of all spheres are determined. Furthermore, the mean coordination numbers are analysed. These results are compared for both algorithms and with data from the literature based on other numerical simulations or from experiments with real spheres.
163 citations
TL;DR: A general reconstruction method is described which simulates point patterns possessing prescribed summary characteristics, which are free of explicit model conditions, for instance the intensity, the L-function, the spherical contact distribution function and the kth nearest neighbour distance distributions.
71 citations
TL;DR: An analysis of the downlink coverage of small cells that are modeled with a Matern cluster process (MCP) is presented and a new accurate formula for the probability generating function of an MCP is derived.
Abstract: A cellular network is usually modeled and analyzed as a Poisson point process (PPP). However, small cells are ordinarily clustered around hotspots in urban areas, which cannot be accurately modeled with a PPP. This letter presents an analysis of the downlink coverage of small cells that are modeled with a Matern cluster process (MCP). A new accurate formula for the probability generating function of an MCP is derived. We also propose a new distribution function for the desired distance (i.e., between the user and serving small cell) based on the spherical contact distribution function of the Boolean model. The above two formulas can be used to obtain a closed-form expression for the downlink average coverage probability of small cells. Simulation results confirm the accuracy of our derived formulas. Our derived MCP-based coverage is accurate and can be used to guide the small cell configuration of a cellular network.
63 citations
TL;DR: In this paper, the authors report on spatial-statistical analyses for simulated random packings of spheres with random diameters, and the simulation methods are the force-biased algorithm and the Jodrey-Tory sedimentation algorithm.
Abstract: This paper reports on spatial-statistical analyses for simulated random packings of spheres with random diameters. The simulation methods are the force-biased algorithm and the Jodrey-Tory sedimentation algorithm. The sphere diameters are taken as constant or following a bimodal or lognormal distribution. Standard characteristics of spatial statistics are used to describe these packings statistically, namely volume fraction, pair correlation function of the system of sphere centres and spherical contact distribution function of the set-theoretic union of all spheres. Furthermore, the coordination numbers are analysed.
38 citations
TL;DR: In this paper, the authors provided definitions for the local mean volume and mean surface densities of an inhomogeneous random closed set and provided sufficient conditions on the regularity of the random set involved to satisfy the assumptions of the theorem.
Abstract: In this paper we provide definitions for the local mean volume and mean surface densities of an inhomogeneous random closed set A theorem which relates the local spherical contact distribution function with the local surface and volume density is proven. Sufficient conditions on the regularity of the random set involved to satisfy the assumptions of the theorem are provided, based on Coarea Formula. These conditions are satisfied by a wide class of inhomogeneous random sets, relevant for applications, like some kinds of Boolean Models, for which explicit expressions for the local volume and surface densities are also provided
19 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2017 | 1 |
| 2014 | 3 |
| 2011 | 3 |
| 2010 | 2 |
| 2008 | 1 |