Related papers: Finding NHIM: Identifying High Dimensional Phase S…
A model Hamiltonian for the reaction CH$_4^+ \rightarrow$ CH$_3^+$ + H, parametrized to exhibit either early or late inner transition states, is employed to investigate the dynamical characteristics of the roaming mechanism. Tight/loose…
Chemical reactions in multidimensional systems are often described by a rank-1 saddle, whose stable and unstable manifolds intersect in the normally hyperbolic invariant manifold (NHIM). Trajectories started on the NHIM in principle never…
The topic of this article is the numerical search of codimension 2 Normally Hyperbolic Invariant Manifolds (NHIM) in Hamiltonian systems with 3 degrees of freedom and their internal dynamics. We point out relations between different…
In this paper, we apply Lagrangian descriptors to study the invariant manifolds that emerge from the top of two barriers existing in the LiCN<->LiNC isomerization reaction. We demonstrate that the integration times must be large enough…
In this paper we unveil 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.…
In this work, the benefits of the phase fitting technique are embedded in high order discrete Lagrangian integrators. The proposed methodology creates integrators with zero phase lag in a test Lagrangian in a similar way used in phase…
The complexity of arbitrary dynamical systems and chemical reactions, in particular, can often be resolved if only the appropriate periodic orbit - in the form of a limit cycle, dividing surface, instanton trajectories or some other related…
We analyze the classical phase space dynamics of a three degree of freedom Hamiltonian that models multiple bond breaking and forming reactions. The model Hamiltonian, inspired from studies on double proton transfer reactions, allows for…
Recently the phase space structures governing reaction dynamics in Hamiltonian systems have been identified and algorithms for their explicit construction have been developed. These phase space structures are induced by saddle type…
Dynamics between reactants and products are often mediated by a rate-determining barrier and an associated dividing surface leading to the transition state theory rate. This framework is challenged when the barrier is time-dependent because…
We showcase the utility of the Lagrangian descriptors method in qualitatively understanding the underlying dynamical behavior of dynamical systems governed by fractional-order differential equations. In particular, we use the Lagrangian…
Lagrangian descriptors reveal the dynamical skeleton governing transport mechanisms of a generic flow. In doing so, they unveil geometrical structures in the phase space that separate regions with different qualitative behavior. This work…
This paper introduces a new global dynamics and chaos indicator based on the method of Lagrangian Descriptor apt for discriminating ordered and deterministic chaotic motions in multidimensional systems. The selected implementation of this…
In this paper we apply the method of Lagrangian descriptors as an indicator to study the chaotic and regular behavior of trajectories in the phase space of the classical double pendulum system. In order to successfully quantify the degree…
Equilibrium phase transitions are associated with rearrangements of minima of a (Lagrangian) potential. Treatment of non-equilibrium systems requires doubling of degrees of freedom, which may be often interpreted as a transition from the…
We apply the method of Lagrangian Descriptors (LDs) to a symmetric Caldera-type potential energy surface which has three index-1 saddles surrounding a relatively flat region that contains no minimum. Using this method we show the phase…
In this paper we generalize the method of Lagrangian descriptors to two dimensional, area preserving, autonomous and nonautonomous discrete time dynamical systems. We consider four generic model problems--a hyperbolic saddle point for a…
We discuss the dynamics of a particular two-dimensional (2D) physical system in the four dimensional (4D) (non-)commutative phase space by exploiting the consistent Hamiltonian and Lagrangian formalisms based on the symplectic structures…
Chemical selectivity is a phenomenon displayed by potential energy surfaces (PES) that is relevant for many organic chemical reactions whose PES feature a valley-ridge inflection point (VRI) in the region between two sequential index-1…
The rate of a chemical reaction can often be determined by the properties of a rank-1 saddle and the associated transition state separating reactants and products. We have found evidence that such rates can be controlled and even enhanced…