arXiv subjects

Cristobal Lopez

Publications and source records attributed to Cristobal Lopez.

52 records · Page 3Linked to original sources

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

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

Diffusive transport and self-consistent dynamics in coupled maps

The study of diffusion in Hamiltonian systems has been a problem of interest for a number of years. In this paper we explore the influence of self-consistency on the diffusion properties of systems described by coupled symplectic maps. Self-consistency, i.e. the back-influence of the transported quantity on the velocity field of the driving flow, despite of its critical importance, is usually overlooked in the description of realistic systems, for example in plasma physics. We propose a class of self-consistent models consisting of an ensemble of maps globally coupled through a mean field. Depending on the kind of coupling, two different general types of self-consistent maps are considered: maps coupled to the field only through the phase, and fully coupled maps, i.e. through the phase and the amplitude of the external field. The analogies and differences of the diffusion properties of these two kinds of maps are discussed in detail.

nlin.CD↗

arXiv2002

Sand stirred by chaotic advection

We study the spatial structure of a granular material, N particles subject to inelastic mutual collisions, when it is stirred by a bidimensional smooth chaotic flow. A simple dynamical model is introduced where four different time scales are explicitly considered: i) the Stokes time, accounting for the inertia of the particles, ii) the mean collision time among the grains, iii) the typical time scale of the flow, and iv) the inverse of the Lyapunov exponent of the chaotic flow, which gives a typical time for the separation of two initially close parcels of fluid. Depending on the relative values of these different times a complex scenario appears for the long-time steady spatial distribution of particles, where clusters of particles may or not appear.

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↗

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↗

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

Bulk dynamics for interfacial growth models

We study the influence of the bulk dynamics of a growing cluster of particles on the properties of its interface. First, we define a {\it general bulk growth model} by means of a continuum Master equation for the evolution of the bulk density field. This general model just considers arbitrary addition of particles (though it can be easily generalized to consider substraction) with no other physical restriction. The corresponding Langevin equation for this bulk density field is derived where the influence of the bulk dynamics is explicitly shown. Finally, when it is assumed a well-defined interface for the growing cluster, the Langevin equation for the height field of this interface for some particular bulk dynamics is written. In particular, we obtain the celebrated Kardar-Parisi-Zhang (KPZ) equation. A Monte Carlo simulation illustrates the theoretical results.

cond-mat.stat-mech↗

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↗

arXiv1999

Forecasting the SST space-time variability of the Alboran Sea with genetic algorithms

We propose a nonlinear ocean forecasting technique based on a combination of genetic algorithms and empirical orthogonal function (EOF) analysis. The method is used to forecast the space-time variability of the sea surface temperature (SST) in the Alboran Sea. The genetic algorithm finds the equations that best describe the behaviour of the different temporal amplitude functions in the EOF decomposition and, therefore, enables global forecasting of the future time-variability.

chao-dyn↗

arXiv1999

The multifractal structure of chaotically advected chemical fields

The structure of the concentration field of a decaying substance produced by chemical sources and advected by a smooth incompressible two-dimensional flow is investigated. We focus our attention on the non-uniformities of the Hölder exponent of the resulting filamental chemical field. They appear most evidently in the case of open flows where irregularities of the field exhibit strong spatial intermittency as they are restricted to a fractal manifold. Non-uniformities of the Hölder exponent of the chemical field in closed flows appears as a consequence of the non-uniform stretching of the fluid elements. We study how this affects the scaling exponents of the structure functions, displaying anomalous scaling, and relate the scaling exponents to the distribution of finite-time Lyapunov exponents of the advection dynamics. Theoretical predictions are compared with numerical experiments.

chao-dyn↗

arXiv1999

Chaotic advection of reacting substances: Plankton dynamics on a meandering jet

We study the spatial patterns formed by interacting populations or reacting chemicals under the influence of chaotic flows. In particular, we have considered a three-component model of plankton dynamics advected by a meandering jet. We report general results, stressing the existence of a smooth-filamental transition in the concentration patterns depending on the relative strength of the stirring by the chaotic flow and the relaxation properties of planktonic dynamical system. Patterns obtained in open and closed flows are compared.

chao-dyn↗

arXiv1999

Smooth-filamental transition of active tracer fields stirred by chaotic advection

The spatial distribution of interacting chemical fields is investigated in the non-diffusive limit. The evolution of fluid parcels is described by independent dynamical systems driven by chaotic advection. The distribution can be filamental or smooth depending on the relative strength of the dispersion due to chaotic advection and the stability of the chemical dynamics. We give the condition for the smooth-filamental transition and relate the Hölder exponent of the filamental structure to the Lyapunov exponents. Theoretical findings are illustrated by numerical experiments.

chao-dyn↗