The Fractal Dimension of the Apollonian Sphere Packing

Borkovec, Michal; Paris, W. De; Peikert, Ronald

doi:10.1142/s0218348x94000739

Cited by 98 publications

(99 citation statements)

References 9 publications

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“…The apollonian packing of spheres has as a limit a fractal with dimension 2 . 47 (Borkovec et al, 1994). Such value is very close to those usually quoted for the limit GSD of fully fragmented soils Minh & Cheng, 2013).…”

Section: Particle Splitting and Lost Masssupporting

confidence: 86%

An approach to enhance efficiency of DEM modelling of soils with crushable grains

Ciantia¹,

Arroyo²,

Calvetti³

et al. 2015

Géotechnique

164

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In this study oedometric compression tests of hydrocarbon coke, Fontainebleau sand and silica sand are simulated in three dimensions using breakable particles. The method adapts a rigorous breakage criterion for elasto-brittle spheres to represent failure of grains isolated between platens or within granular masses. The breakage criterion allows for the effect of particle bulk and contact properties to be treated separately. A discrete fragmentation multigenerational approach is applied as a spawning procedure. The number of particles quickly increases during the simulation, but is kept manageable by systematic fine exclusion and upscaling. Fine exclusion leads to mass losses between generations, but that loss is accounted for outside the mechanical model. Sensitivity analysis shows that it is enough to keep 53% of the crushed particle mass within the mechanical model to correctly reproduce experimental macroscopic behaviour. Practical upscaling rules are proposed for (a) contact stiffness, (b) breakage criteria and (c) grain size distribution, and validated simulating the same test, reducing by half the initial number of particles. The results are promising as both the mechanical and grading evolution are well captured with two orders of magnitude savings in computing efficiency.

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Section: Particle Splitting and Lost Masssupporting

confidence: 86%

An approach to enhance efficiency of DEM modelling of soils with crushable grains

Ciantia¹,

Arroyo²,

Calvetti³

et al. 2015

Géotechnique

164

View full text Add to dashboard Cite

show abstract

“…The Apollonian packing has d F = 2.4739 [68], and the values for space-filling bearings are again larger [59].…”

Section: Spatial Propertiesmentioning

confidence: 99%

Self-similar disk packings as model spatial scale-free networks

Doye¹,

Massen²

2005

Phys. Rev. E

140

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The network of contacts in space-filling disk packings, such as the Apollonian packing, are examined. These networks provide an interesting example of spatial scale-free networks, where the topology reflects the broad distribution of disk areas. A wide variety of topological and spatial properties of these systems are characterized. Their potential as models for networks of connected minima on energy landscapes is discussed.

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“…[3,4]). Peikert et al [4] use a quite efficient method called inversion algorithm to produce this three dimensional Apollonian packing.…”

Section: Introductionmentioning

confidence: 99%