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

@article{Naik2019FindingNI, 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.}, year={2019}, volume={79}, pages={104907} }

## 27 Citations

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

- MathematicsPhysical review. E
- 2019

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.

### Visualizing the Phase Space of the HeI2 van der Waals Complex using Lagrangian Descriptors

- Physics
- 2021

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

- MathematicsInt. J. Bifurc. Chaos
- 2020

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

- MathematicsCommunications in Nonlinear Science and Numerical Simulation
- 2022

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

- Physics
- 2020

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.

- PhysicsPhysical review. E
- 2020

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

- Physics, Mathematics
- 2021

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

- Mathematics
- 2021

. 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

- MathematicsInt. J. Bifurc. Chaos
- 2020

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

- MathematicsInt. J. Bifurc. Chaos
- 2020

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.

## 50 References

### Lagrangian descriptors: A method for revealing phase space structures of general time dependent dynamical systems

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- 2013

### Geometrical models of the phase space structures governing reaction dynamics

- Physics
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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.

- PhysicsPhysical review. E
- 2017

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

- Mathematics
- 2016

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).

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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

- MathematicsRegular and Chaotic Dynamics
- 2018

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…

### On the geometry of transport in phase space I. Transport in k -degree-of-freedom Hamiltonian systems, 2≤k≤∞

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### Deconstructing field-induced ketene isomerization through Lagrangian descriptors.

- PhysicsPhysical chemistry chemical physics : PCCP
- 2016

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

- MathematicsCommun. Nonlinear Sci. Numer. Simul.
- 2015

### Lagrangian descriptors in dissipative systems.

- PhysicsPhysical chemistry chemical physics : PCCP
- 2016

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.