Research projects

本研究では、分子動力学法を用いて界面不安定性の分散関係を安定モードを含めて精密に測定する新手法を提案し、その物理機構を解明するとともに制御手法の開発を目指す。従来のホワイトノイズを用いた解析では取得が困難であった減衰モードを、指定波数の変調を与えることで直接評価し、特に粘性の役割を明らかにする。さらに、界面に配置した分子に独立の波数変調を与えることで、不安定波数の選択的成長による制御を試みる。本研究は大規模計算によって初めて得られる精密な分散関係とその制御を通じ、界面不安定性の理解と応用に新たな展開をもたらす。

「富岳」に代表されるように、我が国では大規模な計算資源を保有している一方、その計算能力を十全に活かすには高度な計算機科学の知識が要求され、計算科学との両立が困難であるという背景があった。本研究は、特に大規模分子動力学法に向けたフレームワークを構築することで、数値計算を実行する研究者が自分でコードを開発する環境を提供し、計算機科学と計算科学の分断を緩和しようとするものである。特に、並列計算機を扱うにあたって通信部分と計算部分の密結合を分離することで、研究者が本質的なプログラミングに集中し、研究成果へとつなげることを期待する。具体的な応用例として、高分子や気液混相流への適用を目指す。

The behavior of complex fluids, which contains polymers or bubbles, was investigated by molecular dynamics simulations. We have studied the Kalman vortexes occurring at the rear of the cylinder and found that the vortexes become blurred for fluid with polymers. This phenomenon did not occur when the length of the polymer was short, indicating that the length of the polymer was important. In a flow with bubble formation, the position of the vortex generation shifted to the rear and the reaction from the vortexes on the cylinder disappears. These findings can only be obtained by studying the molecular scale by molecular dynamics methods.

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.

We have studied Ostwald ripening of bubbles by molecular dynamics simulations involving billions of particles. The scaling exponents were estimated from the bubble-size distribution function and the values of them were successfully described by the classical theory of Ostwald ripening, the Lifshitz-Slyozov-Wagner (LSW) theory. This is the first direct confirmation of LSW theory in bubble nuclei. As temperature increases, the crossover of the scaling exponent is observed. This crossover implies that the growth of bubbles changes from interface-limited to diffusion-limited. We also observed the growth rate of the bubbles (the kinetic term) directly for the first time. While the kinetic term is well described by the theory in the scaling region, it has broad distribution in early stage. This behavior shows that the inhomogeneity of the pressure in the system and the inhomogeneity is the reason why the classical theory fails to describe the early stage of the bubble nucleation.

The Nose-Hoover method is studied as a non-Hamilton dynamics system. A stochastic process of the Nose-Hoover method is discussed on the basis of the Markovian approximation. It is proved that the dynamics which achieves Gibbs' canonical distribution must involve non-canonical transformation.