arXiv subjects

Emilio Hernandez-Garcia

Publications and source records attributed to Emilio Hernandez-Garcia.

At least 55 records · Page 3Linked to original sources

arXiv2004

Mixing structures in the Mediterranean Sea from Finite-Size Lyapunov Exponents

We characterize horizontal mixing and transport structures in the surface circulation of the Mediterranean Sea, as obtained from a primitive equation circulation model. We calculate the Finite Size Lyapunov Exponents (FSLEs) of the velocity data set, which gives a direct measure of the local stirring. By proper election of the FSLE parameters, we focus on the mesoscale structures, locating a number of vortices embedded in an intricate network of high-stretching lines. These lines control transport in the system. At the edge of the vortices, a dense tangle of line intersections appears, identifying strong mixing. The spatial distribution of FSLEs, averaged over one year, allows to classify areas in the Mediterranean basin according by their mixing activity. The space average of FSLEs on selected geographical regions gives a measure for quantifying and comparing the mixing seasonal variability.

nlin.CD↗

arXiv2003

Sustained plankton blooms under open chaotic flows

We consider a predator-prey model of planktonic population dynamics, of excitable character, living in an open and chaotic fluid flow, i.e., a state of fluid motion in which fluid trajectories are unbounded but a chaotic region exists that is restricted to a localized area. Despite that excitability is a transient phenomenon and that fluid trajectories are continuously leaving the system, there is a regime of parameters where the excitation remains permanently in the system, given rise to a persistent plankton bloom. This regime is reached when the time scales associated to fluid stirring become slower than the ones associated to biological growth.

nlin.CD↗

arXiv2003

Clustering, advection and patterns in a model of population dynamics with neighborhood-dependent rates

We introduce a simple model of population dynamics which considers birth and death rates for every individual that depend on the number of particles in its neighborhood. The model shows an inhomogeneous quasistationary pattern with many different clusters of particles. We derive the equation for the macroscopic density of particles, perform a linear stability analysis on it, and show that there is a finite-wavelength instability leading to pattern formation. This is the responsible for the approximate periodicity with which the clusters of particles arrange in the microscopic model. In addition, we consider the population when immersed in a fluid medium and analyze the influence of advection on global properties of the model.

cond-mat↗

arXiv2003

Effective dimensions and percolation in hierarchically structured scale-free networks

We introduce appropriate definitions of dimensions in order to characterize the fractal properties of complex networks. We compute these dimensions in a hierarchically structured network of particular interest. In spite of the nontrivial character of this network that displays scale-free connectivity among other features, it turns out to be approximately one-dimensional. The dimensional characterization is in agreement with the results on statistics of site percolation and other dynamical processes implemented on such a network.

cond-mat↗

arXiv2003

Filament bifurcations in a one-dimensional model of reacting excitable fluid flow

Recently, it has been shown that properties of excitable media stirred by two-dimensional chaotic flows can be properly studied in a one-dimensional framework \cite{excitablePRL,excitablePRE}, describing the transverse profile of the filament-like structures observed in the system. Here, we perform a bifurcation analysis of this one-dimensional approximation as a function of the {\it Damk{ö}hler} number, the ratio between the chemical and the strain rates. Different branches of stable solutions are calculated, and a Hopf bifurcation, leading to an oscillating filament, identified.

nlin.CD↗

arXiv2002

Excitable media in open and closed chaotic flows

We investigate the response of an excitable medium to a localized perturbation in the presence of a two-dimensional smooth chaotic flow. Two distinct types of flows are numerically considered: open and closed. For both of them three distinct regimes are found, depending on the relative strengths of the stirring and the rate of the excitable reaction. In order to clarify and understand the role of the many competing mechanisms present, simplified models of the process are introduced. They are one-dimensional baker-map models for the flow and a one-dimensional approximation for the transverse profile of the filaments.

nlin.CD↗

arXiv2002

The role of diffusion in the chaotic advection of a passive scalar with finite lifetime

We study the influence of diffusion on the scaling properties of the first order structure function, S_1, of a two-dimensional chaotically advected passive scalar with finite lifetime, i.e., with a decaying term in its evolution equation. We obtain an analytical expression for S_1 where the dependence on the diffusivity, the decaying coefficient and the stirring due to the chaotic flow is explicitly stated. We show that the presence of diffusion introduces a crossover length-scale, the diffusion scale (L_d), such that the scaling behaviour for the structure function is analytical for length-scales shorter than L_d, and shows a scaling exponent that depends on the decaying term and the mixing of the flow for larger scales. Therefore, the scaling exponents for scales larger than L_d are not modified with respect to those calculated in the zero diffusion limit. Moreover, L_d turns out to be independent of the decaying coeficient, being its value the same as for the passive scalar with infinite lifetime. Numerical results support our theoretical findings.

nlin.CD↗

arXiv2002

Spatial Patterns in Chemically and Biologically Reacting Flows

We present here a number of processes, inspired by concepts in Nonlinear Dynamics such as chaotic advection and excitability, that can be useful to understand generic behaviors in chemical or biological systems in fluid flows. Emphasis is put on the description of observed plankton patchiness in the sea. The linearly decaying tracer, and excitable kinetics in a chaotic flow are mainly the models described. Finally, some warnings are given about the difficulties in modeling discrete individuals (such as planktonic organisms) in terms of continuous concentration fields.

nlin.CD↗

arXiv2002

Anticipating the dynamics of chaotic maps

We study the regime of anticipated synchronization in unidirectionally coupled chaotic maps such that the slave map has its own output reinjected after a certain delay. For a class of simple maps, we give analytic conditions for the stability of the synchronized solution, and present results of numerical simulations of coupled 1D Bernoulli-like maps and 2D Baker maps, that agree well with the analytic predictions.

nlin.CD↗

arXiv2001

Small-scale structure of nonlinearly interacting species advected by chaotic flows

We study the spatial patterns formed by interacting biological populations or reacting chemicals under the influence of chaotic flows. Multiple species and nonlinear interactions are explicitly considered, as well as cases of smooth and nonsmooth forcing sources. The small-scale structure can be obtained in terms of characteristic Lyapunov exponents of the flow and of the chemical dynamics. Different kinds of morphological transitions are identified. Numerical results from a three-component plankton dynamics model support the theory, and they serve also to illustrate the influence of asymmetric couplings.

nlin.CD↗

arXiv2001

Analytical and Numerical Studies of Noise-induced Synchronization of Chaotic Systems

We study the effect that the injection of a common source of noise has on the trajectories of chaotic systems, addressing some contradictory results present in the literature. We present particular examples of 1-d maps and the Lorenz system, both in the chaotic region, and give numerical evidence showing that the addition of a common noise to different trajectories, which start from different initial conditions, leads eventually to their perfect synchronization. When synchronization occurs, the largest Lyapunov exponent becomes negative. For a simple map we are able to show this phenomenon analytically. Finally, we analyze the structural stability of the phenomenon.

nlin.CD↗

arXiv2000

The Complex Ginzburg-Landau Equation in the Presence of Walls and Corners

We investigate the influence of walls and corners (with Dirichlet and Neumann boundary conditions) in the evolution of twodimensional autooscillating fields described by the complex Ginzburg-Landau equation. Analytical solutions are found, and arguments provided, to show that Dirichlet walls introduce strong selection mechanisms for the wave pattern. Corners between walls provide additional synchronization mechanisms and associated selection criteria. The numerical results fit well with the theoretical predictions in the parameter range studied.

nlin.CD↗

arXiv2000

Low-dimensional dynamical system model for observed coherent structures in ocean satellite data

The dynamics of coherent structures present in real-world environmental data is analyzed. The method developed in this Paper combines the power of the Proper Orthogonal Decomposition (POD) technique to identify these coherent structures in experimental data sets, and its optimality in providing Galerkin basis for projecting and reducing complex dynamical models. The POD basis used is the one obtained from the experimental data. We apply the procedure to analyze coherent structures in an oceanic setting, the ones arising from instabilities of the Algerian current, in the western Mediterranean Sea. Data are from satellite altimetry providing Sea Surface Height, and the model is a two-layer quasigeostrophic system. A four-dimensional dynamical system is obtained that correctly describe the observed coherent structures (moving eddies). Finally, a bifurcation analysis is performed on the reduced model.

nlin.CD↗

arXiv2000

Population dynamics advected by chaotic flows: a discrete-time map approach

A discrete-time model of reacting evolving fields, transported by a bidimensional chaotic fluid flow, is studied. Our approach is based on the use of a Lagrangian scheme where {\it fluid particles} are advected by a $2d$ symplectic map possibly yielding Lagrangian chaos. Each {\it fluid particle} carries concentrations of active substances which evolve according to its own reaction dynamics. This evolution is also modeled in terms of maps. Motivated by the question, of relevance in marine ecology, of how a localized distribution of nutrients or preys affects the spatial structure of predators transported by a fluid flow, we study a specific model in which the population dynamics is given by a logistic map with space-dependent coefficient, and advection is given by the standard map. Fractal and random patterns in the Eulerian spatial concentration of predators are obtained under different conditions. Exploiting the analogies of this coupled-map (advection plus reaction) system with a random map, some features of these patterns are discussed.

nlin.CD↗

arXiv2000

Dynamics of localized structures in vector waves

Dynamical properties of topological defects in a twodimensional complex vector field are considered. These objects naturally arise in the study of polarized transverse light waves. Dynamics is modeled by a Vector Complex Ginzburg-Landau Equation with parameter values appropriate for linearly polarized laser emission. Creation and annihilation processes, and selforganization of defects in lattice structures, are described. We find "glassy" configurations dominated by vectorial defects and a melting process associated to topological-charge unbinding.

patt-sol↗

arXiv2000

Forecasting confined spatiotemporal chaos with genetic algorithms

A technique to forecast spatiotemporal time series is presented. it uses a Proper Ortogonal or Karhunen-Loève Decomposition to encode large spatiotemporal data sets in a few time-series, and Genetic Algorithms to efficiently extract dynamical rules from the data. The method works very well for confined systems displaying spatiotemporal chaos, as exemplified here by forecasting the evolution of the onedimensional complex Ginzburg-Landau equation in a finite domain.

nlin.CD↗

arXiv2000

On the effect of small-scale oceanic variability on topography-generated currents

Small-scale oceanic motions, in combination with bottom topography, induce mean large-scale along-isobaths flows. The direction of these mean flows is usually found to be anticyclonic (cyclonic) over bumps (depressions). Here we employ a quasigeostrophic model to show that the current direction of these topographically induced large-scale flows can be reversed by the small-scale variability. This result addresses the existence of a new bulk effect from the small-scale activity that could have strong consequences on the circulation of the world's ocean.

physics.ao-ph↗

arXiv2000

Localized structures in coupled Ginzburg-Landau equations

Coupled Complex Ginzburg-Landau equations describe generic features of the dynamics of coupled fields when they are close to a Hopf bifurcation leading to nonlinear oscillations. We study numerically this set of equations and find, within a particular range of parameters, the presence of uniformly propagating localized objects behaving as coherent structures. Some of these localized objects are interpreted in terms of exact analytical solutions.

nlin.CD↗