Naslov
Random sequential packing of cubes

Autori
Itoh, Yoshiaki ; Dutour Sikirić, Mathieu

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, pp prezentacija, znanstveni

Izvornik
3rd Texas southmost geometry and topology conference / - , 2010

Skup
3rd Texas southmost geometry and topology conference

Mjesto i datum
Brownsville (TX), Sjedinjene Američke Države, 15.04.2010. - 18.04.2010

Vrsta sudjelovanja
Plenarno

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
random packing; cube; simulation; torus

Sažetak
Because of analytical difficulties for higher dimension, one-dimensional random sequential packing has received attention (Renyi (1958)), Itoh (1980)). The one-dimensional model can be extended to the random sequential packing of cubes. Consider the random sequential packing of cubes of edge length 1 in a parallel position in a larger cube of edge length x. It seems to be natural to expect for the d-dimensional extension that the limiting packing density (i) exists and (ii) is equal to βd as x tends to ∞, where β is the limiting packing density for d = 1 given by Renyi (1958), which is called Palasti’s conjecture. The conjecture (i) is shown by Penrose (2001). It is known that the computer simulations do not support the conjecture (ii). Consider the simplest random sequential packing with rigid boundary, i.e. a packing in which cubes of edge length 2 are put sequentially at random into the cube of edge length 4, with a cubic grid with unit edge length, in a parallel position on the grid. Consider the packing density γd of dimension d. The computer simulations up to dimension 11 (Itoh and Ueda (1983), Itoh and solomon (1986)), seems to fit to γd = d-α with an appropriate constant α. The simplest random sequential packing with rigid boundary is already difficult to study analytically. The expected number of decrease of the packing density is shown to be less than (4 3)d at each step of the random sequential packing (Poyarkov (2004, 2007) ), which proves that the expected number of cubes at the saturation is larger than (32)d. Consider the simple random sequential packing with periodic boundary (random sequential packing into torus). The case d = 1, 2 gives the tiling of cubes (100 per cent packing density), while the case 3 ≤ d does not always give the tiling of cubes. We study geometrical structure generated by of packing of cubes (Dutour-Sikiric, Itoh and Poyarkov (2007). Dutour- Sikiric and Itoh (2009)).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA