| Project/Area Number |
61540274
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
物理学一般
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
SHIINO Masatoshi Department of Applied Physics,Tokyo Institute of Technology, 理学部応用物理学科, 助手 (60134813)
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| Project Period (FY) |
1986 – 1987
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| Project Status |
Completed (Fiscal Year 1987)
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| Budget Amount *help |
¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1987: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1986: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | Nonequilibrium phase transition / H-theorem / Fluctuation-dissipation theorem Nonlinear Fokker-Planck equation / Entropy production / マッキーンプロセス / リヤプノフファンクショナル / 同期 / ひきこみ / 非平衡熱力学 / クリティカル・スローイングダウン / リセプノフ・ファンクショナル |
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| Research Abstract |
The present project aims at studying the possibility of developing the concepts of phase transitions exhibited by nonequilibrium and (or) nonthermodynamic systems from the statistical mechanics point of view.Our research has a potential applicability to investigations of cooperative phenomena observed in systems consisting of active elements such as living cells in biological organizations. In order to make a systematic and rigorous analysis we have employed stochastic models of infinitely many particle systems with mean-field interaction. The systems consist of infinitely many coupled nonlinear oscilltors subjected to the influence of external noise and are described by sets of infinitely many coupled langevin equations. Noting that the stochastic systems reduce to nonlinear Fokker-Planck equations (NFPE) capable of exhibiting bifurcations associated with phase transitions of the systems,we have made full use of the NFPE to get insights into dynamical properties of the systems associa
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ted with the bifurcations.
The NFPE are classified into two categories. The first type is characterized by the potential condition and has a close resemblance to the case of thermodynamic systems. In this case attractors of the NFPE corresponding to the ergodic components are of fixed point type. The second type refers to the case without potential condition in which attractors are allowed to be of limit-cycle or chaos type. For the first type case,we have elucidated asymptotic approach to equilibrium of the system by proving an H-theorem on the NFPE and conducted nonlinear stability analysis with the H-functional being taken as a Lyapunov functional. Dynamical behavior of fluctuations has also been investigated,by employing Fluctuation-Dissipation theorem,to show the appearance of critical slowing down in the vicinity of the bifurcation points as well as to obtain power spectra and correlation functions of the fluctuations. With regard to the second case we obtained a new type of phase transition,in which as external noise power is decreased the system undergoes Hopf-bifurcation and the probability distribution given by the solution to the NFPE begins to rotate with a certain frequency. Less
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