Low-Dimensional Projection of Reactive Islands in Chemical Reaction Dynamics Using a Supervised Dimensionality Reduction Method

Transition state theory is a standard framework for predicting the rate of a chemical reaction. Although the transition state theory has been successfully applied to numerous chemical reaction analyses, many experimental and theoretical studies have reported chemical reactions with a reactivity which cannot be explained by the transition state theory due to dynamic effects. Dynamical systems theory provides a theoretical framework for elucidating dynamical mechanisms of such chemical reactions. In particular, reactive islands are essential phase space structures revealing dynamical reaction patterns. However, the numerical computation of reactive islands in a reaction system of many degrees of freedom involves an intrinsic challenge -- the curse of dimensionality. In this paper, we propose a dimensionality reduction algorithm for computing reactive islands in a reaction system of many degrees of freedom. Using the supervised principal component analysis, the proposed algorithm projects reactive islands into a low-dimensional phase space with preserving the dynamical information on reactivity as much as possible. The effectiveness of the proposed algorithm is examined by numerical experiments for H\'enon-Heiles systems extended to many degrees of freedom. The numerical results indicate that our proposed algorithm is effective in terms of the quality of reactivity prediction and the clearness of the boundaries of projected reactive islands. The proposed algorithm is a promising elemental technology for practical applications of dynamical systems analysis to real chemical systems

タンパク質分子の構造ダイナミクス：ウェーブレット変換による解析

要旨あり生体高分子の揺らぎとダイナミクス－シミュレーションと実験の統計解析－研究詳

Time's Arrow Viewed from Chaos : Late Prof. Tasaki's book on foundation of statistical physics(Perspectives of Nonequilibrium Statistical Physics-The Memory of Professor Shuichi Tasaki-)

この論文は国立情報学研究所の電子図書館事業により電子化されました

<Poster Presentation 15>Dynamical Switching of a Reaction Coordinate Triggered by Breakdown of a Normally Hyperbolic Invariant Manifold

[Date] November 28 (Mon) - December 2 (Fri), 2011: [Place] Kyoto University Clock Tower Centennial Hall, Kyoto, JAPA

Dynamical Switching of a Reaction Coordinate to Carry the System through to a Different Product State at High Energies

Questions of how the nature of a reaction coordinate that dominates the reaction ceases to exist and whether some new features emerge as an increase of total energy of systems are investigated for many degrees of freedom Hamiltonian systems. As a model system, a hydrogen atom in crossed electric and magnetic fields is scrutinized. It is shown that, when the total energy increases, the reaction coordinate no longer dominates the reaction as did at the lower energies. In turn, a new reaction coordinate emerges, connecting totally different reactant and product states. Furthermore, depending on which parts of the phase space the system traverses through the saddle, the system nonuniformly experiences the switching of the reaction coordinate leading to the different product state. The universal mechanism of the cessation and the switching of the reaction coordinate at high energy regimes above the saddle is investigated

Geometrical Structure buried in the Phase Space of Stochastic Structural Transition

この論文は国立情報学研究所の電子図書館事業により電子化されました

Chaotic Reaction Dynamics and the Phase Space Geometry of Multi-dimensional Chemical Reaction(4) Quantum chaos and semiclassical theory in molecular science and nuclear theory, Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems)

この論文は国立情報学研究所の電子図書館事業により電子化されました

Dynamically induced conformation depending on excited normal modes of fast oscillation

We present dynamical effects on conformation in a simple bead-spring model consisting of three beads connected by two stiff springs. The conformation defined by the bending angle between the two springs is determined not only by a given potential energy function depending on the bending angle, but also by fast motion of the springs which constructs the effective potential. A conformation corresponding with a local minimum of the effective potential is hence called the dynamically induced conformation. We develop a theory to derive the effective potential using multiple-scale analysis and the averaging method. A remarkable consequence is that the effective potential depends on the excited normal modes of the springs and amount of the spring energy. Efficiency of the obtained effective potential is numerically verified