Random sequential packing of cubes into torus

将立方体随机顺序打包成环面

• 批准号: 23540177
• 负责人: ITOH Yoshiaki
• 金额: $ 2.91万
• 依托单位: The Institute of Statistical Mathematics
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23540177/
• 关键词: 確率論; 多次元ランダムパッキング; 立方体; トーラス; 充填率; 漸近挙動

Very simplified models are introduced to understand the random sequential packing models mathematically. The 1-dimensional model is sometimes called the Parking Problem. To obtain a 1-dimensional packing density, distribution of the minimum of gaps, etc., the classical analysis has to be studied. The packing density of the general multi-dimensional random sequential packing of cubes (hypercubes) makes a well-known unsolved problem. The experimental analysis is usually applied to the problem. We introduced simplified multi-dimensional models of cubes and torus, which keep the character of the original general model, and introduced a combinatorial analysis for combinatorial modelings. Here we succeeded in obtaining expected number of cube for a corner preference random sequential packing of cubes into a larger cube mathmeatically without using computer simulations, which will help to solve our original problemrandom sequential packing of cubes into torus.

非常简化的模型被引入到理解随机序列包装模型的数学。一维模型有时被称为停车问题。为了获得一维堆积密度、最小间隙的分布等，必须研究经典分析。一般多维立方体（超立方体）的随机顺序堆积的堆积密度是一个众所周知的未解决的问题。通常采用实验分析的方法来解决这个问题。我们引入了简化的多维立方体和环面模型，它保持了原来的一般模型的特点，并介绍了组合建模的组合分析。在这里，我们成功地获得了角偏好的预期立方体数量，无需使用计算机模拟，通过数学方法将立方体随机顺序包装成更大的立方体，这将有助于解决我们最初的问题将立方体随机顺序包装成环面。

项目成果

Continuum cascade model of directed random graphs: traveling wave analysis

有向随机图的连续级联模型：行波分析

• DOI: 10.1088/1751-8113/45/45/455002
• 发表时间: 2012
• 期刊: JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL
• 作者: Yoshiaki Itoh;Paul Krapivsky
• 通讯作者: Paul Krapivsky

計算アルゴリズムの確率モデルの解析におけるrecursionと非線形波動

计算算法随机模型分析中的递归和非线性波

• 作者: Yoshihiro Abe;Toshimichi Usuba;I. Sato and M. Itoh;和地輝仁.;高石武史;Toshimichi Usuba;伊藤栄明
• 通讯作者: 伊藤栄明

A binomial splitting process in connection with corner parking problems,

与拐角停车问题相关的二项式分裂过程，

• 发表时间: 2014
• 期刊: Journal of Applied Probability
• 影响因子: 1
• 作者: Fuchs;M.;Hwang;HK..;Itoh;Y.;Mahmoud;H.:
• 通讯作者: H.:

Random sequential packing of cubes

立方体的随机顺序堆积

• 发表时间: 2011
• 作者: Itoh;Y.
• 通讯作者: Y.