Study on the mechanisms for collective motions of molecular and astronomical systems based the methods of many-body problems

2017 Fiscal Year Final Research Report

• Project/Area Number: 26800207
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Waseda University
• Principal Investigator: Yanao Tomohiro 早稲田大学, 理工学術院, 准教授 (40444450)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 多体問題 / 集団運動 / 分子モーター / DNA / クラスター / 共鳴 / 三体問題 / 重力アシスト

Outline of Final Research Achievements

Understanding the fundamental mechanisms for collective motions of many-body systems, ranging from the microscopic molecular systems to macroscopic astronomical systems, is a significant challenge in modern science and technology. In this study, we have tackled this issue utilizing the methodologies of nonlinear dynamics, statistical mechanics, and differential geometry. As a result, we have developed novel dynamical models for the rotary motions of biological molecular motors and the formation of higher-order structures of DNA. We have also uncovered a dynamical mechanism for driving the dissociation of atomic clusters in terms of the competition between collective internal forces. As to the macroscopic astronomical systems, we have designed fuel-efficient transfer trajectories for space missions between the Earth and the Moon by using resonant gravity assists and invariant manifolds of periodic orbits.

Free Research Field

統計力学、非線形力学、応用数学