Fractal structure of lattice models and applications to equilibrium and non-equilibrium systems
Project/Area Number |
19540400
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Mathematical physics/Fundamental condensed matter physics
|
Research Institution | Nagoya University |
Principal Investigator |
MINAMI Kazuhiko 名古屋大学, 多元数理科学研究科, 准教授 (40271530)
|
Co-Investigator(Kenkyū-buntansha) |
KONISHI Tetsuro 名古屋大学, 理学(系)研究科, 准教授 (30211238)
渡辺 宙志 名古屋大学, 情報科学研究科, 教授 (50377777)
永尾 太郎 名古屋大学, 多元数理科学研究科, 准教授 (10263196)
|
Project Period (FY) |
2007 – 2010
|
Project Status |
Completed (Fiscal Year 2010)
|
Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
Keywords | 可積分系 / 可解格子模型 / IFSフラクタル |
Research Abstract |
It is derived that the two-dimensional cell sorting problem is mathematically equivalent to the one-dimensional random walk with pair creations and annihilations, i. e. the adhesion probabilities in the cell sorting model analytically relate to the expectation values in the random walk problem. This is an example that two completely different biological systems are governed by a common mathematical structure. This result is obtained through the equivalences of these systems with lattice spin models. It is also shown that arbitrary generation operators can be written by the spin operators, and hence all of the biological stochastic problems can in principle be analyzed with the use of the techniques and knowledges already obtained in the area of lattice spin systems.
|
Report
(6 results)
Research Products
(41 results)