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Chesnavichs model Hamiltonian for the reaction CH$_4^+ rightarrow$ CH$_3^+$ is known to exhibit a range of interesting dynamical phenomena including roaming. The model system consists of two parts: a rigid, symmetric top representing the CH$_3^+$ ion and a free H atom. We study roaming in this model with focus on the evolution of geometrical features of the invariant manifolds in phase space that govern roaming under variations of the mass of the free atom m and a parameter a that couples radial and angular motion. In addition, we establish an upper bound on the prominence of roaming in Chesnavichs model. The bound highlights the intricacy of roaming as a type of dynamics on the verge between isomerisation and nonreactivity as it relies on generous access to the potential wells to allow reactions as well as a prominent area of high potential that aids sufficient transfer of energy between the degrees of freedom to prevent isomerisation.
Complementary to existing applications of Lagrangian descriptors as an exploratory method, we use Lagrangian descriptors to find invariant manifolds in a system where some invariant structures have already been identified. In this case we use the par
Recent studies have found an unusual way of dissociation in formaldehyde. It can be characterized by a hydrogen atom that separates from the molecule, but instead of dissociating immediately it roams around the molecule for a considerable amount of t
We present the capability of Lagrangian descriptors for revealing the high dimensional phase space structures that are of interest in nonlinear Hamiltonian systems with index-1 saddle. These phase space structures include normally hyperbolic invarian
Phase space structures such as dividing surfaces, normally hyperbolic invariant manifolds, their stable and unstable manifolds have been an integral part of computing quantitative results such as transition fraction, stability erosion in multi-stable
The role of the interface potential on the effective mass of charge carriers is elucidated in this work. We develop a new theoretical formalism using a spatially dependent effective mass that is related to the magnitude of the interface potential. Us