
Francisco González Montoya- PhD
- . at National Autonomous University of Mexico
Francisco González Montoya
- PhD
- . at National Autonomous University of Mexico
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36
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Introduction
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September 2021 - December 2024
January 2016 - January 2018
February 2018 - July 2018
Publications
Publications (36)
We study the classical chaotic scattering of a He atom off a harmonically vibrating Cu surface. The three degree of freedom (3-dof) model is studied by first considering the non-vibrating 2-dof model for different values of the energy. The set of singularities of the scattering functions shows the structure of the tangle between the stable and unst...
We study the phase space objects that control the transport in a classical Hamiltonian model for a chemical reaction. This model has been proposed to study the yield of products in an ultracold exothermic reaction. In this model, two features determine the evolution of the system: a Van der Waals force and a short-range force associated with the ma...
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 strategies to find such surfaces numerically. We can start from index-1 saddles of the effective potential or from a...
We treat a chaotic Hamiltonian scattering system with three degrees of freedom where the chaotic invariant set is of low dimension. Then the chaos and its structure are not visible in scattering functions plotted along one-dimensional lines in the set of asymptotic initial conditions. We show that an asymptotic observer can nevertheless see the str...
We study the decay scenario of a codimension-2 NHIM in a three degrees of freedom Hamiltonian system under increasing perturbation when the NHIM loses its normal hyperbolicity. On one hand, we follow this decay in the Poincar\'e map for the internal dynamics of the NHIM. On the other hand, we also follow the decay in a time delay function calculate...
In our previous studies [Katsanikas & Wiggins, 2021a, 2021b, 2023a, 2023b, 2024a, 2024b, 2024c], we presented two methods for building up dividing surfaces based on either periodic orbits or 2D/3D generating surfaces, specifically for Hamiltonian systems with three or more degrees of freedom. These papers extended these dividing surface constructio...
In our earlier research [Katsanikas & Wiggins, 2021a, 2021b, 2023a, 2023b, 2024a, 2024b, 2024c], we developed two new approaches for building up dividing surfaces in the phase space of Hamiltonian systems with three or more degrees of freedom. These surfaces were derived either from periodic orbits or from 2D or 3D generating surfaces in the phase...
In earlier research, we developed two techniques designed to expand the construction of a periodic orbit dividing surface for Hamiltonian systems with three or more degrees of freedom. Our methodology involved transforming a periodic orbit into a torus or cylinder, thereby elevating it to a higher-dimensional structure within the energy surface (re...
In previous studies, we developed two techniques aimed at expanding the scope of constructing a periodic orbit dividing surface within a Hamiltonian system with three or more degrees of freedom. Our approach involved extending a periodic orbit into a torus or cylinder, thereby elevating it into a higher-dimensional entity within the energy surface...
In prior studies [Katsanikas & Wiggins, 2021a, 2021b, 2023a, 2023b], we introduced two methodologies for constructing Periodic Orbit Dividing Surfaces (PODS) tailored specifically for Hamiltonian systems with three or more degrees of freedom. These approaches, as described in the aforementioned papers, were applied to a quadratic Hamiltonian system...
In prior work [Katsanikas & Wiggins, 2021a, 2021b, 2023c, 2023d], we introduced two methodologies for constructing Periodic Orbit Dividing Surfaces (PODS) tailored for Hamiltonian systems possessing three or more degrees of freedom. The initial approach, outlined in [Katsanikas & Wiggins, 2021a, 2023c], was applied to a quadratic Hamiltonian system...
In this paper, we analyse the classical action as a tool to reveal the phase space structure of Hamiltonian systems simply and intuitively. We construct a scalar field using the values of the action along the trajectories to analyse the phase space. The different behaviours of the trajectories around important geometrical objects like normally hype...
The topic of this article is a dynamical explanation of the sequential decay in rearrangement scattering. The essential observation is the behaviour of trajectories close to the basin boundary of the breakup channel. As a most simplistic example of demonstration, we use a version of the perturbed three particle Calogero-Moser system in a 1-dimensio...
The study of the phase space of multidimensional systems is one of the central open problems in dynamical systems. Being able to distinguish chaoticity from regularity in nonlinear dynamical systems, as well as to determine the subspace of the phase space in which instabilities are expected to occur, is also an important field. To investigate these...
The study of the phase space of multidimensional systems is one of the central open problems in dynamical systems. Being able to distinguish chaoticity from regularity in nonlinear dynamical systems, as well as to determine the subspace of the phase space in which instabilities are expected to occur, is also an important field. To investigate these...
The topic of this article is the numerical search of codimension 2 normally hyperbolic invariant manifolds in Hamiltonian systems with 3-degrees of freedom and their internal dynamics. We point out relations between different strategies to find such surfaces numerically. We can start from index-1 saddles of the effective potential or from a partial...
In this paper, we explore the dynamics of a Hamiltonian system after a double van der Waals potential energy surface degenerates into a single well. The energy of the system is increased from the bottom of the potential well up to the dissociation energy, which occurs when the system becomes open. In particular, we study the bifurcations of the bas...
This paper explores the phase space structures characterising transport for a double-well van der Waals potential surface. Trajectories are classified as inter-well, intra-well, and escaping-from-a-well to define different dynamical fates. In particular, roaming trajectories, which are a new paradigm in chemical reaction dynamics, are observed. We...
In this paper, we explore the dynamics of a Hamiltonian system after a double van der Waals potential energy surface degenerates into a single well. The energy of the system is increased from the bottom of the potential well up to the dissociation energy, which occurs when the system becomes open. In particular, we study the bifurcations of the bas...
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 trajectories in the phase space. The different behaviour of the trajectories around important phase space objects like unstable periodic orbits, their...
In this paper, we explore the phase space structures characterising transport for a double-well van der Waals potential. Trajectories are classified as inter-well, intra-well, and escaping-from-a-well to define different dynamical fates. In particular, roaming trajectories which are a new paradigm in chemical reaction dynamics are observed. We appl...
This book is a collaborative project between researchers in the CHAMPS (Chemistry and Mathematics in Phase Space) research project https://www.champsproject.com Research in CHAMPS is concerned with discovering the geometrical structures in the phase space of dynamical systems that govern the many and varied mechanisms leading to a chemical reaction...
We study the phase space structures that control the transport in a classical Hamiltonian model for a chemical reaction. This model has been proposed to study the yield of products in an ultracold exothermic reaction [1]. In the considered model, two elements determine the evolution of the system: a Van der Waals force and short-range force associa...
In this paper, we analyse the phase space structure of the roaming dynamics in a 2 degree of freedom potential energy surface consisting of two identical planar Morse potentials separated by a distance. This potential energy surface was previously studied in Carpenter B K et al (2018 Regul. Chaotic Dyn. 23 60–79), and it has two potential wells sur...
In this article, we study the classical chaotic scattering of a He atom off a harmonically vibrating Cu surface. The three degrees of freedom (3- dof) model is studied by first considering the non-vibrating 2-dof model for different values of the energy. We calculate the set of singularities of the scattering functions and study its connection with...
Chemistry is concerned with the transformation of matter. In more detail, it is concerned with the breaking, formation, and rearrangement of bonds in molecules. Fundamentally, these descriptions highlight “changes in time”. Mathematically, the study of systems changing in time is the subject of dynamical systems theory. This book represents an acco...
In this paper, we analyse the phase space structure of the roaming dynamics in a two degree of freedom potential energy surface consisting of two identical planar Morse potentials separated by a distance. This potential energy surface was previously studied in \cite{carpenter2018dynamics}, and it has two potential wells surrounded by an unbounded f...
In this paper we explain how the perturbation of partial integrability can be visualized by the restriction of the Poincaré map to an invariant two-dimensional subset of its full domain. The most appropriate surface is a normally hyperbolic invariant manifold built up by stack construction over the most prominent hyperbolic fixed point of the reduc...
It is explained in which way the ternary symmetric horseshoe can be obtained along a development scenario starting with a binary horseshoe. We explain the case of a complete ternary horseshoe in all detail and then give briefly some further incomplete cases. The key idea is to start with a three degrees of freedom system with a rotational symmetry,...
We study a prototypical three degrees of freedom chaotic scattering system depending on a perturbation parameter. For one limiting case of the parameter, the system has a conserved quantity and can be reduced to a two degrees of freedom system. And for the other limiting case, the chaotic invariant set is completely hyperbolic and forms a dust. For...
We take the scattering of electrons off a perturbed magnetic dipole as an example for demonstrating chaotic scattering systems with three open degrees of freedom. We explain the connection between the chaotic invariant set, the scattering functions and the doubly differential cross section. The most interesting structures in this cross section are...