The sphere packing problem into bounded containers in three-dimension non-Euclidean space

Казаков, А. Л.; Lempert, A. A.; Ta, The-Anh

doi:10.1016/j.ifacol.2018.11.450

Cited by 7 publications

(2 citation statements)

References 18 publications

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“…In the dynamic approaches, the spheres change their position or their size during the packing process, which is controlled by a shrinking algorithm (Tory & Jodrey, 1986;Torquato & Jiao, 2010;He et al, 2018), compression forces algorithm (Khirevich, et al, 2013;Baranau & Tallarek, 2014) or gravitational algorithm (Shi & Zhang, 2008;Hitti & Bernacki, 2013;Sahu, 2009;Ilina & Bernacki, 2016). In the case of constructive approaches, sphere parameters like size or position are preserved during the packing process, so they are less costly but have difficulties in achieving high-density packing (Evans, 1993;Cui & O'Sullivan, 2003;Kazakov et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Sphere packing algorithm for the generation of digital models of polycrystalline microstructures with heterogeneous grain sizes

Hajder¹,

Madej²

2020

cmms

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Development of the cellular automata (CA) sphere packing algorithm dedicated to the generation of two-and threedimensional digital, synthetic microstructure models with heterogenous grain size distribution is presented within the paper. The synthetic microstructure model is generated in four major steps: generation of 2D/3D cellular automata computational domain, generation of circles/spheres with a required size distribution, close-packed filling of the computational domain with generated circles/spheres, growth of the circles/spheres according to the unconstrained CA growth algorithm. As a result, synthetic microstructure models with prescribed, e.g. uni-or bimodal, grain size distribution are obtained. To reduce the computational complexity and decrease execution time, the rotation of the circles/spheres during the packing stage is based on the vector accounting for the distance from computational domain borders and other spheres. The CA grain growth algorithm is also implemented using threads mechanism, allowing parallel execution of computations to increase its efficiency. The developed algorithm, along with the implementation details as well as a set of exemplary results, are presented within the paper.

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Section: Introductionmentioning

confidence: 99%

Sphere packing algorithm for the generation of digital models of polycrystalline microstructures with heterogeneous grain sizes

Hajder¹,

Madej²

2020

cmms

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“…In this article, we propose an algorithm for solving the sphere packing problem for various bounded multi-connected containers in a three-dimensional non-Euclidean space. Here, as in our previous papers [5,6,22,23], we use a special non-Euclidean metric, which means not the distance between points, but the time that is required to pass this way. Such statements appear in the logistics when one needs to locate a given number of commercial facilities and to maximize the overall service area.…”

Section: Introductionmentioning

confidence: 99%

On the Algorithm for Equal Balls Packing into a Multi-connected Set

Казаков

Lempert

Ta³

2019

Proceedings of the VIth International Workshop 'Critical Infrastructures: Contingency Management, Intelligent, Agent-Based, Clo

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The paper is devoted to the problem of densest packing a given number of equal balls into multi-connected containers. The objective is to find the maximum radius associated with balls. We consider the problem both in three-dimensional Euclidean and one class of non-Euclidean spaces. In this study, the distance between points means the minimum time required to overcome the path between them. The algorithm based on the optical-geometric approach and billiard simulation combination is suggested and implemented. The idea is the following: we initially construct sufficiently small balls and enlarge them step by step as long as all the balls keep inside without overlaps. Computational experiments show the applicability and validity of the method.

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An efficient solution space exploring and descent method for packing equal spheres in a sphere

Zhou,

Ren,

et al. 2024

Computers & Operations Research

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The sphere packing problem into bounded containers in three-dimension non-Euclidean space

Cited by 7 publications

References 18 publications

Sphere packing algorithm for the generation of digital models of polycrystalline microstructures with heterogeneous grain sizes

Sphere packing algorithm for the generation of digital models of polycrystalline microstructures with heterogeneous grain sizes

On the Algorithm for Equal Balls Packing into a Multi-connected Set

An efficient solution space exploring and descent method for packing equal spheres in a sphere

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