2010 Fiscal Year Final Research Report
Fractal structure of lattice models and applications to equilibrium and non-equilibrium systems
| Project/Area Number |
19540400
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Nagoya University |
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Principal Investigator |
MINAMI Kazuhiko 名古屋大学, 多元数理科学研究科, 准教授 (40271530)
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| Co-Investigator(Kenkyū-buntansha) |
KONISHI Tetsuro (30211238)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 可積分系 / 可解格子模型 / IFSフラクタル |
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| 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.
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