Related papers: Variational method for finding periodic orbits in …
We undertake a systematic exploration of recurrent patterns in a 1-dimensional Kuramoto-Sivashinsky system. For a small, but already rather turbulent system, the long-time dynamics takes place on a low-dimensional invariant manifold. A set…
A numerical method is proposed for computing time-periodic and relative time-periodic solutions in dissipative wave systems. In such solutions, the temporal period, and possibly other additional internal parameters such as the propagation…
Plasma turbulence is a key challenge in understanding transport phenomena in magnetically confined plasmas. This work presents a novel approach using periodic orbit theory to analyze plasma turbulence, identifying fundamental structures…
We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…
We analyse and compare several algorithms to compute numerically periodic solutions of high-dimensional dynamical systems and investigate their Floquet stability without building the monodromy matrix. The solution and its perturbation are…
We show that a recently proposed numerical technique for the calculation of unstable periodic orbits in chaotic attractors is capable of finding the least unstable periodic orbits of any given order. This is achieved by introducing a…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…
In this work we study the orbital stability of periodic traveling-wave solutions for dispersive models. The study of traveling waves started in the mid-18th century when John S. Russel established that the flow of water waves in a shallow…
We present an efficient method for fast, complete, and accurate detection of unstable periodic orbits in chaotic systems. Our method consists of a new iterative scheme and an effective technique for selecting initial points. The iterative…
Chaotic dynamics can be effectively studied by continuation from an anti-integrable limit. Using the Henon map as an example, we obtain a simple analytical bound on the domain of existence of the horseshoe that is equivalent to the…
We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…
This thesis details an effort to generate astrophysically interesting solutions to the two-body problem in General Relativity. The thesis consists of two main parts. The first part presents an analytical variational principle for describing…
A variational principle is derived for two-dimensional incompressible rotational fluid flow with a free surface in a moving vessel when both the vessel and fluid motion are to be determined. The fluid is represented by a stream function and…
This study analyses the main characteristics of the fully developed laminar pulsatile flow in a toroidal pipe as the governing parameters vary. A novel computational technique is developed to obtain time-periodic solutions of the…
Advancements in computational fluid mechanics have largely relied on Newtonian frameworks, particularly through the direct simulation of Navier-Stokes equations. In this work, we propose an alternative computational framework that employs…
We consider three-dimensional inviscid irrotational flow in a two layer fluid under the effects of gravity and surface tension, where the upper fluid is bounded above by a rigid lid and the lower fluid is bounded below by a flat bottom. We…
The flow of Ree-Eyring and Casson non-Newtonian fluids is investigated using a variational principle to optimize the total stress. The variationally-obtained solutions are compared to the analytical solutions derived from the…
We provide a constructive method designed in order to control the stability of a given periodic orbit of a general completely integrable system. The method consists of a specific type of perturbation, such that the resulting perturbed…
We describe the Hamiltonian structures, including the Poisson brackets and Hamiltonians, for free boundary problems for incompressible fluid flows with vorticity. The Hamiltonian structure is used to obtain variational principles for…