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Makrina Agaoglou

Publications and source records attributed to Makrina Agaoglou.

12 recordsLinked to original sources
arXiv2025

Using Lagrangian descriptors to reveal the phase space structure of dynamical systems described by fractional differential equations: Application to the Duffing oscillator

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 descriptors method to study the phase space structure of the unforced and undamped Duffing oscillator when its time evolution is governed by fractional-order differential equations. In our study, we implement two types of fractional derivatives, namely the standard Grünwald-Letnikov method, which is a finite difference approximation of the Riemann-Liouville fractional derivative, and a Grünwald-Letnikov method with a correction term that approximates the Caputo fractional derivative. While there is no issue with forward-time integrations needed for the evaluation of Lagrangian descriptors, we discuss in detail ways to perform the non-trivial task of backward-time integrations and implement two methods for this purpose: a `nonlocal implicit inverse' technique and a `time-reverse inverse' approach. We analyze the differences in the Lagrangian descriptors results due to the two backward-time integration approaches, discuss the physical significance of these differences, and eventually argue that the nonlocal implicit inverse implementation of the Grünwald-Letnikov fractional derivative manages to reveal the phase space structure of fractional-order dynamical systems correctly.

nlin.CD↗
arXiv2024

Analysis of the spread of SARS-CoV-2 in a hospital isolation room using CFD and Lagrangian Coherent Structures

This research paper presents an analysis of the propagation of the SARS-CoV-2, or other similar pathogens, in a hospital isolation room using computational fluid dynamics (CFD) and Lagrangian Coherent Structures (LCS). The study investigates the airflow dispersion and droplets in the room under air conditioning vent and sanitizer conditions. The CFD simulation results show that both the air conditioner and sanitizer systems significantly influence the dispersion of the virus in the room. The use of LCS enables acquiring a deep understanding of the dispersion of suspended particles, providing insights into the mechanisms of virus transmission. The findings of this study could help in developing strategies for improving the design and operation of isolation rooms to minimize the likelihood of virus dissemination within hospitals.

physics.flu-dyn↗
arXiv2024

New links between invariant dynamical structures and uncertainty quantification

This paper proposes a new uncertainty measure, appropriate for quantifying the performance of transport models in assessing the origin or source of a given observation. It is found that in a neighbourhood of the observation the proposed uncertainty measure is related to the invariant dynamical structures of the model. The paper illustrates the implementation of the proposed definition to quantify the performance of ocean data sets in the context of a real oil spill event in the Eastern Mediterranean in 2021.

physics.ao-ph↗
arXiv2024

Bifurcation of Dividing Surfaces Constructed from Period-Doubling Bifurcations of Periodic Orbits in a Caldera Potential Energy Surface

In this work we analyze the bifurcation of dividing surfaces that occurs as a result of two period-doubling bifurcations in a 2D caldera-type potential. We study the structure, the range, the minimum and maximum extents of the periodic orbit dividing surfaces before and after a subcritical period-doubling bifurcation of the family of the central minimum of the potential energy surface. Furthermore, we repeat the same study for the case of a supercritical perioddoubling bifurcation of the family of the central minimum of the potential energy surface. We will discuss and compare the results for the two cases of bifurcations of dividing surfaces.

nlin.CD↗
arXiv2024

Periodically Forced Nonlinear Oscillatory Acoustic Vacuum

In this work, we study the in-plane oscillations of a finite lattice of particles coupled by linear springs under distributed harmonic excitation. Melnikov-type analysis is applied for the persistence of periodic oscillations of a reduced system.

math-ph↗
arXiv2022

Global dynamics visualisation from Lagrangian Descriptors. Applications to discrete and continuous systems

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 method requires only the knowledge of orbits on finite time windows and is free of the computation of the tangent vector dynamics (i.e., variational equations are not needed). To demonstrate its ability in visualising different dynamical behaviors, in particular for highlighting chaotic regions, several stability maps of classical systems, obtained with different phase space methods, are reproduced. The benchmark examples are rooted in discrete and continuous nearly-integrable dynamical systems, with prominent features played by resonances. These include the Chirikov standard map, higher dimensional symplectic and volume preserving maps, fundamental models of resonances, and a 3 degrees-of-freedom nearly-integrable Hamiltonian system with a dense web of resonances. The indicator thus appears to be relevant for understanding phase space transport mediated by resonances in nearly-integrable system, as ubiquitous in celestial mechanics or astrodynamics.

math.DS↗
arXiv2022

The Influence of a Parameter that Controls the Asymmetry of a Potential Energy Surface with an Entrance Channel and Two Potential Wells

In this paper we study an asymmetric valley-ridge inflection point (VRI) potential, whose energy surface (PES) features two sequential index-1 saddles (the upper and the lower), with one saddle having higher energy than the other and two potential wells separated by the lower index-1 saddle. We show how the depth and the flatness of our potential changes as we modify the parameter that controls the asymmetry as well as how the branching ratio (ratio of the trajectories that enter each well) is changing as we modify the same parameter and its correlation with the area of the lobes as they have formulated by the stable and unstable manifolds that have been extracted from the gradient of the LD scalar fields.

math.DS↗
arXiv2021

The time evolution of the trajectories after the selectivity in a symmetric potential energy surface with a post-transition-state bifurcation

Selectivity is an important phenomenon in chemical reaction dynamics. This can be quantified by the branching ratio of the trajectories that visit one or the other wells to the total number of trajectories in a system with a potential with two sequential index-1 saddles and two wells (top well and bottom well). In our case, the branching ratio is 1:1 because of the symmetry of our potential energy surface. The mechanisms of transport and the behavior of the trajectories in this kind of systems have been studied recently. In this paper we study the time evolution after the selectivity as energy varies using periodic orbit dividing surfaces. We investigate what happens after the first visit of a trajectory to the region of the top or the bottom well for different values of energy. We answer the natural question, what is the destiny of these trajectories?

nlin.CD↗
arXiv2021

Bifurcation of dividing surfaces constructed from a pitchfork bifurcation of periodic orbits in a symmetric potential energy surface with a post-transition-state bifurcation

In this work we analyze the bifurcation of dividing surfaces that occurs as a result of a pitchfork bifurcation of periodic orbits in a two degrees of freedom Hamiltonian System. The potential energy surface of the system that we consider has four critical points: two minima, a high energy saddle and a lower energy saddle separating two wells (minima). In this paper we study the structure, the range, and the minimum and maximum extent of the periodic orbit dividing surfaces of the family of periodic orbits of the lower saddle as a function of the total energy.

nlin.CD↗
arXiv2021

Revealing the phase space structure of Hamiltonian systems using the action

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 stable and unstable manifolds, and KAM islands generate characteristic patterns on the scalar field constructed with the action. Using these different patterns is possible to identify the skeleton of the phase space and understand the dynamics. Also, we present a simple argument based on the conservation of the energy and the behaviour of the trajectories to understand the values of their actions. In order to show how this tool reveals the phase space structures and its effectiveness, we compare the scalar field constructed with the actions with Poincare maps for the same set of initial conditions in the phase space of an open Hamiltonian system with 2 degrees of freedom.

nlin.CD↗
arXiv2020

Exploring Isomerization Dynamics on a Potential Energy Surface with an Index-2 Saddle using Lagrangian Descriptors

In this paper we explore the phase space structures governing isomerization dynamics on a potential energy surface with four wells and an index-2 saddle. For this model, we analyze the influence that coupling both degrees of freedom of the system and breaking the symmetry of the problem have on the geometrical template of phase space structures that characterizes reaction. To achieve this goal we apply the method of Lagrangian descriptors, a technique with the capability of unveiling the key invariant manifolds that determine transport processes in nonlinear dynamical systems. This approach reveals with extraordinary detail the intricate geometry of the isomerization routes interconnecting the different potential wells, and provides us with valuable information to distinguish between initial conditions that undergo sequential and concerted isomerization.

nlin.CD↗