Position #95 – Nonlinear dynamics, geometry, and statistical mechanics of complex systems

Host institution
JP - Waseda University (早稲田大学)
Lab or research department name
Department of Applied Mechanics and Aerospace Engineering
Mechanical Engineering
Type of mobility
Duration (months)
From 1 to 3 months


Our group has broad interests in nonlinear dynamics, geometry, and statistical mechanics of complex systems in nature. Nature consists of the hierarchy of self-organized systems, ranging from microscopic molecules to the macroscopic universe. It is remarkable that life systems including human beings exist within this hierarchy of nature in a harmonious way. Our research centers on understanding how nature self-organizes such hierarchical structures and how we can utilize the ability of nature to self-organize such harmonious systems. So far, we are conducting research on the following subjects.

(1) At the microscopic level, we focus on understanding and controlling conformational transitions of complex molecular systems, including atomic/molecular clusters, fullerenes, and clathrate hydrates. Recently, we have identified a dynamical driving force that originates from molecular vibrations and is responsible for the spontaneous symmetry breaking of molecular conformations. We expect that this dynamical force can play a crucial role in a wide class of molecular reactions, in which molecules change their structural symmetry in a significant way. We have also been developing a method for rovibrational mode analysis that makes it possible to scrutinize energy transfer among the vibrational and rotational modes of a molecule. Based on this novel mode analysis, we aim at controlling molecular reactions by controlling intramolecular energy flow.

(2) At the macroscopic level, celestial mechanics and space mission design are the subjects of our significant interest, where nonlinear dynamics plays the central role. Recently, the methods of the restricted three-body problem have opened new avenues in this field. In particular, the Lagrange points, halo orbits, and associated invariant manifold “tubes” have great potential for fuel-efficient space missions. Our challenge is to produce new techniques for future space missions and to discover fundamental principles for the order and harmony of planetary systems.

(3) Biological systems are also of our great interest. Biological molecules such as proteins and DNA are designed in an elaborate manner so that they can achieve their functions even in thermal (noisy) environments. Biomolecules are thereby often referred to as “molecular machines” because of the robustness of their functions. We explore the fundamental designing principles and the dynamics of biomolecules based on theoretical and numerical analysis. Recently we have been paying special attention to the roles of the helical chirality or “handedness” of biomolecules in the organization of their high-order structures. We expect that chirality is crucial for the self-‐organization and mutual recognitions of biomolecules.

(4) Recently, it has become evident that fluctuations in many complex systems in nature, such as fluid turbulence, earthquakes, and economic systems, obey statistical laws that are qualitatively different from those known in conventional statistical mechanics. It is thereby an important challenge to elucidate the dynamical mechanisms for these unconventional fluctuations in nature in a unified manner for better predictions and safer lives. Our mission is to achieve this goal by applying the methods of nonlinear dynamics and statistical mechanics.

From January 2016
Maximum available positions
For detailed activity, please use the following link (to be copied in a new browser window)

Tomohiro Yanao <yanao@waseda.jp>