Phase description approach to synchronization of oscillatory convection

2015 Fiscal Year Final Research Report

• Project/Area Number: 25800222
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Japan Agency for Marine-Earth Science and Technology
• Principal Investigator: KAWAMURA Yoji 国立研究開発法人海洋研究開発機構, 数理科学・先端技術研究分野, 研究員 (90455494)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 同期現象 / 振動現象 / 位相縮約 / 位相記述 / 振動対流 / 集団振動 / 最適化 / 進行振動解

Outline of Final Research Achievements

We have formulated a theory for the phase description of oscillatory convection in Hele-Shaw cells. The theory can be considered as a phase reduction method for limit-cycle solutions in infinite-dimensional dynamical systems, namely, limit-cycle solutions to partial differential equations representing oscillatory convection. Furthermore, we have also formulated a theory for the phase description of oscillatory convection in a cylindrical Hele-Shaw cell that is laterally periodic. Oscillatory convection in this system is described by a limit-torus solution that possesses two phase modes; one is a spatial phase and the other is a temporal phase. The theory can be considered as a phase reduction method for limit-torus solutions in infinite-dimensional dynamical systems, namely, limit-torus solutions to partial differential equations representing oscillatory convection with a spatially translational mode.

Free Research Field

非線形動力学