arXiv subjects

Vladimír Krajňák

Publications and source records attributed to Vladimír Krajňák.

7 recordsLinked to original sources

arXiv2024

Roaming in acetaldehyde

We investigate roaming in the photodissociation of acetaldehyde (CH$_3$CHO), providing insight into the contrasting roaming dynamics observed for this molecule compared to formaldehyde. We carry out trajectory studies for full-dimensional acetaldehyde, supplemented with an analysis of a two degree-of-freedom restricted model and obtain evidence for two distinct roaming pathways. Trajectories exhibit roaming at both shorter (9-11.5 au) and larger (14.5-22.9 au) maximum CH$_3$-HCO separations, characterized by differing amounts of HCO rotation. No roaming trajectories were found in the intervening gap region. The roaming dynamics near 14.5-22.9 au are well-reproduced by the restricted model and involve passage through a centrifugal barrier, analogous to formaldehyde roaming. However, the shorter-range 9-11.5 au roaming appears unique to acetaldehyde, and is likely facilitated by repulsive interactions absent in the simplified models. Phase space analysis reveals that this additional roaming pathway is inaccessible in the reduced dimensionality system. The findings suggest acetaldehyde's increased propensity for roaming compared to formaldehyde may arise from the presence of multiple distinct roaming mechanisms rather than solely the higher roaming fragment mass.

math.DS↗

arXiv2022

Predicting trajectory behaviour via machine-learned invariant manifolds

In this paper, we use support vector machines (SVM) to develop a machine learning framework to discover phase space structures that distinguish between distinct reaction pathways. The SVM model is trained using data from trajectories of Hamilton's equations and works well even with relatively few trajectories. Moreover, this framework is specifically designed to require minimal a priori knowledge of the dynamics in a system. This makes our approach computationally better suited than existing methods for high-dimensional systems and systems where integrating trajectories is expensive. We benchmark our approach on Chesnavich's CH$_4^+$ Hamiltonian.

physics.chem-ph↗

arXiv2021

Support vector machines for learning reactive islands

We develop a machine learning framework that can be applied to data sets derived from the trajectories of Hamilton's equations. The goal is to learn the phase space structures that play the governing role for phase space transport relevant to particular applications. Our focus is on learning reactive islands in two degrees-of-freedom Hamiltonian systems. Reactive islands are constructed from the stable and unstable manifolds of unstable periodic orbits and play the role of quantifying transition dynamics. We show that support vector machines (SVM) is an appropriate machine learning framework for this purpose as it provides an approach for finding the boundaries between qualitatively distinct dynamical behaviors, which is in the spirit of the phase space transport framework. We show how our method allows us to find reactive islands directly in the sense that we do not have to first compute unstable periodic orbits and their stable and unstable manifolds. We apply our approach to the Hénon-Heiles Hamiltonian system, which is a benchmark system in the dynamical systems community. We discuss different sampling and learning approaches and their advantages and disadvantages.

math.DS↗

arXiv2021

Reactive Islands for Three Degrees-of-Freedom Hamiltonian Systems

We develop the geometrical, analytical, and computational framework for reactive island theory for three degrees-of-freedom time-independent Hamiltonian systems. In this setting, the dynamics occurs in a 5-dimensional energy surface in phase space and is governed by four-dimensional stable and unstable manifolds of a three-dimensional normally hyperbolic invariant sphere. The stable and unstable manifolds have the geometrical structure of spherinders and we provide the means to investigate the ways in which these spherinders and their intersections determine the dynamical evolution of trajectories. This geometrical picture is realized through the computational technique of Lagrangian descriptors. In a set of trajectories, Lagrangian descriptors allow us to identify the ones closest to a stable or unstable manifold. Using an approximation of the manifold on a surface of section we are able to calculate the flux between two regions of the energy surface.

nlin.CD↗

arXiv2019

Phase space structures causing the reaction rate decrease in the collinear hydrogen exchange reaction

The collinear hydrogen exchange reaction is a paradigm system for understanding chemical reactions. It is the simplest imaginable atomic system with $2$ degrees of freedom modeling a chemical reaction, yet it exhibits behaviour that is still not well understood - the reaction rate decreases as a function of energy beyond a critical value. Using lobe dynamics we show how invariant manifolds of unstable periodic orbits guide trajectories in phase space. From the structure of the invariant manifolds we deduce that insufficient transfer of energy between the degrees of freedom causes a reaction rate decrease. In physical terms this corresponds to the free hydrogen atom repelling the whole molecule instead of only one atom from the molecule. We further derive upper and lower bounds of the reaction rate, which are desirable for practical reasons.

nlin.CD↗

arXiv2019

Roaming at Constant Kinetic Energy: Chesnavich's Model and the Hamiltonian Isokinetic Thermostat

We consider the roaming mechanism for chemical reactions under the nonholonomic constraint of constant kinetic energy. Our study is carried out in the context of the Hamiltonian isokinetic thermostat applied to Chesnavich's model for an ion-molecule reaction. Through an analysis of phase space structures we show that imposing the nonholonomic constraint does not prevent the system from exhibiting roaming dynamics, and that the origin of the roaming mechanism turns out to be analogous to that found in the previously studied Hamiltonian case.

nlin.CD↗

arXiv2019

Dynamics of the Morse Oscillator: Analytical Expressions for Trajectories, Action-Angle Variables, and Chaotic Dynamics

We consider the one degree-of-freedom Hamiltonian system defined by the Morse potential energy function (the "Morse oscillator"). We use the geometry of the level sets to construct explicit expressions for the trajectories as a function of time, their period for the bounded trajectories, and action-angle variables. We use these trajectories to prove sufficient conditions for chaotic dynamics, in the sense of Smale horseshoes, for the time-periodically perturbed Morse oscillator using a Melnikov type approach.

math.DS↗