Biomedical subjects

Cristóbal López

Publications and source records attributed to Cristóbal López.

9 recordsLinked to original sources

PubMed2006

Macroscopic description of particle systems with nonlocal density-dependent diffusivity.

In this paper we study macroscopic density equations in which the diffusion coefficient depends on a weighted spatial average of the density itself. We show that large differences (not present in the local density-dependence case) appear between the density equations that are derived from different representations of the Langevin equation describing a system of interacting Brownian particles. Linear stability analysis demonstrates that under some circumstances the density equation interpreted with the Ito calculus has pattern solutions that never appear for the kinetic interpretation, which is the other one typically appearing in the context of nonlinear diffusion processes. We also introduce a discrete-time microscopic model of particles that confirms the results obtained at the macroscopic density level.

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PubMed2005

Self-propelled nonlinearly diffusing particles: Aggregation and continuum description.

We introduce a model of self-propelled particles carrying out a Brownian motion with a diffusion coefficient which depends on the local density of particles within a certain finite radius. Numerical simulations show that in a range of parameters the long-time spatial distribution of particles is nonhomogeneous, and clusters can be observed. A number density equation, which explains the emergence of the aggregates and indicates the values of the parameters for which they appear, is derived. Numerical results of this continuum density equation are also shown.

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PubMed2004

Clustering transition in a system of particles self-consistently driven by a shear flow.

We introduce a simple model of active transport for an ensemble of particles driven by an external shear flow. Active refers to the fact that the flow of the particles is modified by the distribution of particles itself. The model consists in that the effective velocity of every particle is given by the average of the external flow velocities felt by the particles located at a distance less than a typical radius, R. Numerical analysis reveals the existence of a transition to clustering depending on the parameters of the external flow and on R. A continuum description in terms of the number density of particles is derived, and a linear stability analysis of the density equation is performed in order to characterize the transitions observed in the model of interacting particles.

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PubMed2004

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

We introduce a simple model of population dynamics which considers reproducing individuals or particles with birth and death rates depending on the number of other individuals in their neighborhood. The model shows an inhomogeneous quasistationary pattern with many different clusters of particles arranged periodically in space. 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 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, such as the average number of individuals.

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PubMed2004

Continuum description of finite-size particles advected by external flows: the effect of collisions.

The equation of the density field of an assembly of macroscopic particles advected by a hydro-dynamic flow is derived from the microscopic description of the system. This equation allows one to recognize the role and the relative importance of the different microscopic processes implicit in the model: the driving of the external flow, the inertia of the particles, and the collisions among them. The validity of the density description is confirmed by comparisons of numerical studies of the continuum equation with direct simulation Monte Carlo simulations of hard disks advected by a chaotic flow. We show that the collisions have two competing roles: a dispersinglike effect and a clustering effect (even for elastic collisions). An unexpected feature is also observed in the system: the presence of collisions can reverse the effect of inertia, so that grains with lower inertia are more clusterized.

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PubMed2003

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 may not appear.

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PubMed2003

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 backinfluence 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.

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PubMed2002

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 observed in the concentration patterns.

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PubMed2002

Spatial structure of passive particles with inertia transported by a chaotic flow.

We study the spatial patterns formed by inertial particles suspended on the surface of a smooth chaotic flow. In addition to the well-known phenomenon of clustering, we show that, in the presence of diffusion and when a steady space-dependent source of particles is considered, the density of particles may show smooth or fractal features in the low density areas. The conditions needed for the appearance of these structures and their characterization with the first order structure function are also calculated.

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