Related papers: Lyapunov modes in three-dimensional Lennard-Jones …
A new method to describe hyperbolic patterns in two dimensional flows is proposed. The method is based on the Covariant Lyapunov Vectors (CLVs), which have the properties to be covariant with the dynamics, and thus being mapped by the…
We study a simplified coupled atmosphere-ocean model using the formalism of covariant Lyapunov vectors (CLVs), which link physically-based directions of perturbations to growth/decay rates. The model is obtained via a severe truncation of…
We compute Lyapunov vectors (LVs) corresponding to the largest Lyapunov exponents in delay-differential equations with large time delay. We find that characteristic LVs, and backward (Gram-Schmidt) LVs, exhibit long-range correlations,…
We investigate theoretically and numerically the effect of polymer additives on two-dimensional turbulence by means of a viscoelastic model. We provide compelling evidence that at vanishingly small concentrations, such that the polymers are…
Long-living coupled transverse and longitudinal phonon modes are explored in dense and regular arrangements of flat microfluidic droplets. The collective oscillations are driven by hydrodynamic interactions between the confined droplets and…
The Navier-Stokes equations generate an infinite set of generalized Lyapunov exponents defined by different ways of measuring the distance between exponentially diverging perturbed and unperturbed solutions. This set is demonstrated to be…
We present a phenomenological analysis of long-period variables (LPVs) in the Large Magellanic Cloud with the aim of detecting pulsation modes associated to different period-luminosity (PL) relations. Among brighter LPVs we discover a group…
We demonstrate that a separation of the velocity field in large and small scales according to a streamwise Fourier decomposition identifies subspaces with stable Lyapunov exponents and allows the dynamics to exhibit properties of an…
Despite the apparent complexity of turbulent flow, identifying a simpler description of the underlying dynamical system remains a fundamental challenge. Capturing how the turbulent flow meanders amongst unstable states (simple invariant…
Three structural populations with distinct average mobility are identified within an equilibrium two-dimensional Lennard-Jones fluid simulated via molecular dynamics at a constant temperature and varying density. Quantifying the structure…
Critical transitions occur in a variety of dynamical systems. Here, we employ quantifiers of chaos to identify changes in the dynamical structure of complex systems preceding critical transitions. As suitable indicator variables for…
Lagrangian transport structures for three-dimensional and time-dependent fluid flows are of great interest in numerous applications, particularly for geophysical or oceanic flows. In such flows, chaotic transport and mixing can play…
Neutrino-neutrino refraction can lead to non-periodic flavor oscillations in dense neutrino gases, and it has been hypothesized that some solutions are chaotic in nature. This is of particular interest in the case of neutrino emission from…
We present numerical simulations of disordered stealthy hyperuniform layered media ranging up to 10,000 thin slabs of high-dielectric constant separated by intervals of low dielectric constant that show no apparent evidence of Anderson…
In a smooth flow, the leading-order response of trajectories to infinitesimal perturbations in their initial conditions is described by the finite-time Lyapunov exponents and associated characteristic directions of stretching. We give a…
The dependence of the Lyapunov exponent on the closeness parameter, $\epsilon$, in tangent bifurcation systems is investigated. We study and illustrate two averaging procedures for defining Lyapunov exponents in such systems. First, we…
In this paper we use the finite size Lyapunov Exponent (FSLE) to characterize Lagrangian coherent structures in three-dimensional (3d) turbulent flows. Lagrangian coherent structures act as the organizers of transport in fluid flows and are…
We consider the relationship between Eulerian modal decompositions and Lagrangian coherent structures (LCSs). The model sensitivity framework developed by Kasz\'as and Haller (2020) is used to express data-driven modal representations of…
Intermolecular forces are modeled by means of a modified Lennard-Jones potential, introducing a distance of minimum approach, and the effect of intermolecular interactions is accounted for with a self consistent field of the Vlasov type. A…
In a dynamical system the first Lyapunov vector (LV) is associated with the largest Lyapunov exponent and indicates ---at some point on the attractor--- the direction of maximal growth in tangent space. The LV corresponding to the second…