Comparison of the combined phase‐space/trajectory and quasiclassical trajectory methods in the study of reaction dynamics: H + I2and H + Br2

1975 ◽  
Vol 62 (6) ◽  
pp. 2429-2445 ◽  
Author(s):  
R. N. Porter ◽  
D. L. Thompson ◽  
L. M. Raff ◽  
J. M. White
Keyword(s):  
Phase Space ◽  
Reaction Dynamics ◽  
Trajectory Methods ◽  
Phase Space Trajectory

An algorithm for computing phase space structures in chemical reaction dynamics using Voronoi tessellation

2021 ◽  
pp. 133047
Author(s):  
Yuta Mizuno ◽  
Mikoto Takigawa ◽  
Saki Miyashita ◽  
Yutaka Nagahata ◽  
Hiroshi Teramoto ◽  
...  
Keyword(s):  
Phase Space ◽  
Chemical Reaction ◽  
Voronoi Tessellation ◽  
Reaction Dynamics ◽  
Space Structures ◽  
Chemical Reaction Dynamics

scholarly journals Tilting and Squeezing: Phase Space Geometry of Hamiltonian Saddle-Node Bifurcation and its Influence on Chemical Reaction Dynamics

2020 ◽  
Vol 30 (04) ◽  
pp. 2030008 ◽  
Author(s):  
Víctor J. García-Garrido ◽  
Shibabrat Naik ◽  
Stephen Wiggins
Keyword(s):  
Phase Space ◽  
Hamiltonian System ◽  
Potential Energy ◽  
Invariant Manifolds ◽  
Reaction Dynamics ◽  
Potential Energy Function ◽  
Space Structures ◽  
Stable And Unstable Manifolds ◽  
Saddle Node Bifurcation ◽  
Saddle Node

In this article, we present the influence of a Hamiltonian saddle-node bifurcation on the high-dimensional phase space structures that mediate reaction dynamics. To achieve this goal, we identify the phase space invariant manifolds using Lagrangian descriptors, which is a trajectory-based diagnostic suitable for the construction of a complete “phase space tomography” by means of analyzing dynamics on low-dimensional slices. First, we build a Hamiltonian system with one degree-of-freedom (DoF) that models reaction, and study the effect of adding a parameter to the potential energy function that controls the depth of the well. Then, we extend this framework to a saddle-node bifurcation for a two DoF Hamiltonian, constructed by coupling a harmonic oscillator, i.e. a bath mode, to the other reactive DoF in the system. For this problem, we describe the phase space structures associated with the rank-1 saddle equilibrium point in the bottleneck region, which is a Normally Hyperbolic Invariant Manifold (NHIM) and its stable and unstable manifolds. Finally, we address the qualitative changes in the reaction dynamics of the Hamiltonian system due to changes in the well depth of the potential energy surface that gives rise to the saddle-node bifurcation.

Utilizing Recurrence Quantification Analysis for Chatter Detection in Turning

2010 ◽  
Author(s):  
Vazhayil Govindan Rajesh ◽  
V. N. Narayanan Namboothiri
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Nonlinear Dynamical System ◽  
Recurrence Quantification Analysis ◽  
Cutting Process ◽  
Chatter Detection ◽  
Nonlinear Dynamical ◽  
Recurrence Quantification ◽  
Quantification Analysis ◽  
Phase Space Trajectory

Recurrence quantification analysis (RQA) quantifies the number and duration of recurrences of the nonlinear dynamical system presented by its phase space trajectory. The present work analyzes the dynamics of the cutting process in a lathe by studying the recurrent behavior of the system using RQA. It reports the capability of this analysis to detect the transition from chatter free cutting to chatter cutting which occurs due to instability of the cutting process, during the turning operation. The study reveals that the RQA variable, percent determinism is sensitive to this transition. It is found that the value of this variable increases when chatter occurs.

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