### Abstract

In many structural models atoms appear as hard monosized spheres. The properties of nanostructured porous matrix filled by adsorbed substance strongly depend on the density of atoms in nanochannels, those can be interpreted as cylinders. The problem of densest packing of monosized spheres in a cylindrical container is considered. It belongs to the optimization problems of Computational Geometry and is known to be NP-hard, i.e. its exact solution cannot be obtained in a polynomial time. Some approaches of the problem, which are applicable for modeling of nanoporous structures, are discussed. The classifications of packing models and known maximal densities are given. Three approaches represent different approximations in the modeling of packing's. Those are: i) the numerical simulation, based on the geometrical properties, wall effects, and determination of stable position of spheres under gravity; ii) the Voronoi-Delaunay network, which models the channel structure in 3D space; and iii) the non-linear mathematical programming methods employed for densest packing search through cylinder height minimizing. These methods can be used for diverse nanoporous structure designs.

Original language | English |
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Title of host publication | Proceedings - 2012 7th International Forum on Strategic Technology, IFOST 2012 |

DOIs | |

Publication status | Published - 2012 |

Event | 2012 7th International Forum on Strategic Technology, IFOST 2012 - Tomsk, Russian Federation Duration: 18 Sep 2012 → 21 Sep 2012 |

### Other

Other | 2012 7th International Forum on Strategic Technology, IFOST 2012 |
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Country | Russian Federation |

City | Tomsk |

Period | 18.9.12 → 21.9.12 |

### Fingerprint

### Keywords

- cylinder
- modeling
- monosized sphere packing
- nanochannel
- nanoporous structure
- optimization

### ASJC Scopus subject areas

- Management of Technology and Innovation

### Cite this

*Proceedings - 2012 7th International Forum on Strategic Technology, IFOST 2012*[6357573] https://doi.org/10.1109/IFOST.2012.6357573

**Monosized sphere packing approach in the nanoporous structure modeling.** / Burtseva, Larysa; Pestryakov, Alexey; Petranovskii, Vitalii.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - 2012 7th International Forum on Strategic Technology, IFOST 2012.*, 6357573, 2012 7th International Forum on Strategic Technology, IFOST 2012, Tomsk, Russian Federation, 18.9.12. https://doi.org/10.1109/IFOST.2012.6357573

}

TY - GEN

T1 - Monosized sphere packing approach in the nanoporous structure modeling

AU - Burtseva, Larysa

AU - Pestryakov, Alexey

AU - Petranovskii, Vitalii

PY - 2012

Y1 - 2012

N2 - In many structural models atoms appear as hard monosized spheres. The properties of nanostructured porous matrix filled by adsorbed substance strongly depend on the density of atoms in nanochannels, those can be interpreted as cylinders. The problem of densest packing of monosized spheres in a cylindrical container is considered. It belongs to the optimization problems of Computational Geometry and is known to be NP-hard, i.e. its exact solution cannot be obtained in a polynomial time. Some approaches of the problem, which are applicable for modeling of nanoporous structures, are discussed. The classifications of packing models and known maximal densities are given. Three approaches represent different approximations in the modeling of packing's. Those are: i) the numerical simulation, based on the geometrical properties, wall effects, and determination of stable position of spheres under gravity; ii) the Voronoi-Delaunay network, which models the channel structure in 3D space; and iii) the non-linear mathematical programming methods employed for densest packing search through cylinder height minimizing. These methods can be used for diverse nanoporous structure designs.

AB - In many structural models atoms appear as hard monosized spheres. The properties of nanostructured porous matrix filled by adsorbed substance strongly depend on the density of atoms in nanochannels, those can be interpreted as cylinders. The problem of densest packing of monosized spheres in a cylindrical container is considered. It belongs to the optimization problems of Computational Geometry and is known to be NP-hard, i.e. its exact solution cannot be obtained in a polynomial time. Some approaches of the problem, which are applicable for modeling of nanoporous structures, are discussed. The classifications of packing models and known maximal densities are given. Three approaches represent different approximations in the modeling of packing's. Those are: i) the numerical simulation, based on the geometrical properties, wall effects, and determination of stable position of spheres under gravity; ii) the Voronoi-Delaunay network, which models the channel structure in 3D space; and iii) the non-linear mathematical programming methods employed for densest packing search through cylinder height minimizing. These methods can be used for diverse nanoporous structure designs.

KW - cylinder

KW - modeling

KW - monosized sphere packing

KW - nanochannel

KW - nanoporous structure

KW - optimization

UR - http://www.scopus.com/inward/record.url?scp=84871840406&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871840406&partnerID=8YFLogxK

U2 - 10.1109/IFOST.2012.6357573

DO - 10.1109/IFOST.2012.6357573

M3 - Conference contribution

SN - 9781467317702

BT - Proceedings - 2012 7th International Forum on Strategic Technology, IFOST 2012

ER -