Random sequential packing of cubes into torus
| Project/Area Number |
23540177
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | The Institute of Statistical Mathematics |
|---|
Principal Investigator |
ITOH Yoshiaki 統計数理研究所, 大学共同利用機関等の部局等, 名誉教授 (60000212)
|
|---|
| Project Period (FY) |
2011 – 2013
|
| Project Status |
Completed (Fiscal Year 2013)
|
| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
|
|---|
| Keywords | 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 |
|---|
| Research Abstract |
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 problem
random sequential packing of cubes into torus.
|
Report
(4 results)
Research Products
(10 results)
