Finding NHIM: Identifying high dimensional phase space structures in reaction dynamics using Lagrangian descriptors

  title={Finding NHIM: Identifying high dimensional phase space structures in reaction dynamics using Lagrangian descriptors},
  author={Shibabrat Naik and V. J. Garc{\'i}a-Garrido and Stephen Wiggins},
  journal={Commun. Nonlinear Sci. Numer. Simul.},

Finding normally hyperbolic invariant manifolds in two and three degrees of freedom with Hénon-Heiles-type potential.

This article presents a method based on a Lagrangian descriptor for revealing the high-dimensional phase space structures that are of interest in nonlinear Hamiltonian systems with index-1 saddle, including a normally hyperbolic invariant manifold and its stable and unstable manifolds.

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

This article identifies 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.

Painting the phase space of dissipative systems with Lagrangian descriptors

Edge manifold as a Lagrangian coherent structure in a high-dimensional state space

Dissipative dynamical systems characterised by two basins of attraction are found in many physical systems, notably in hydrodynamics where laminar and turbulent regimes can coexist. The state space

Phase space analysis of the dynamics on a potential energy surface with an entrance channel and two potential wells.

The analysis of the geometrical template of phase space structures that governs transport in a Hamiltonian system described by a potential energy surface with an entrance/exit channel and two wells separated by an index-1 saddle reveals that the stable and unstable manifolds of the two families of unstable periodic orbits (UPOs) are responsible for controlling access to the potential wells of the trajectories that enter the system through the entrance/ exit channel.

Revealing the phase space structure of Hamiltonian systems using the action

In this work, we analyse the properties of the Maupertuis’ action as a tool to reveal the phase space structure for Hamiltonian systems. We construct a scalar field with the action’s values along the

Geometric parametrisation of Lagrangian Descriptors for 1 degree-of-freedom systems

. Lagrangian Descriptors (LDs) are scalar quantities able to reveal separatrices, manifolds of hyperbolic saddles, and chaotic seas of dynamical systems. A popular version of the LDs consists in

Detection of Dynamical Matching in a Caldera Hamiltonian System Using Lagrangian Descriptors

This work explores a stretched Caldera potential by means of Lagrangian descriptors, allowing us to accurately compute the critical value for the stretching parameter for which dynamical matching behavior occurs in the system.

An Extension of Discrete Lagrangian Descriptors for Unbounded Maps

The capability of the Discrete Lagrangian Descriptors technique to reveal the geometrical template of stable and unstable invariant manifolds in phase space, and also the intricate structure of chaotic sets and strange attractors, is illustrated by applying it to unveil the phase space of a well-known discrete time system, the Henon map.

Geometrical models of the phase space structures governing reaction dynamics

Hamiltonian dynamical systems possessing equilibria of saddle × center × ... × center stability type display reaction-type dynamics for energies close to the energy of such equilibria; entrance and

Lagrangian descriptors of driven chemical reaction manifolds.

It is demonstrated that this so-called distinguished trajectory is exact for harmonic barriers in one dimension and this verification gives impetus to the application of Lagrangian descriptor-based methods in diverse classes of chemical reactions.

The role of normally hyperbolic invariant manifolds (NHIMS) in the context of the phase space setting for chemical reaction dynamics

In this paper we give an introduction to the notion of a normally hyperbolic invariant manifold (NHIM) and its role in chemical reaction dynamics.We do this by considering simple examples for one-,

Sampling Phase Space Dividing Surfaces Constructed from Normally Hyperbolic Invariant Manifolds (NHIMs).

It is shown for both 2 and 3 DoF systems that a version of the general sampling procedure provides points on the analytically defined DS with the correct microcanonical density on the constant-energy DS.

The Application of Lagrangian Descriptors to 3D Vector Fields

Since the 1980s, the application of concepts and ideas from dynamical systems theory to analyze phase space structures has provided a fundamental framework to understand long-term evolution of

Deconstructing field-induced ketene isomerization through Lagrangian descriptors.

The time-dependent geometrical separatrices governing state transitions in field-induced ketene isomerization are constructed using the method of Lagrangian descriptors. We obtain the stable and

Lagrangian descriptors for two dimensional, area preserving, autonomous and nonautonomous maps

Lagrangian descriptors in dissipative systems.

A weighting scheme is introduced within the Lagrangian descriptor and it is demonstrated that for thermal Langevin dynamics it preserves the essential phase space structures, while they are lost in the nonweighted case.