Isaac Llopis

Dynamic regimes of hydrodynamically coupled self-propelling particles

We analyze the collective dynamics of self-propelling particles (spps) which move at small Reynolds numbers including the hydrodynamic coupling to the suspending solvent through numerical simulations. The velocity distribution functions show marked deviations from Gaussian behavior at short times, and the mean-square displacement at long times shows a transition from diffusive to ballistic motion for appropriate driving mechanism at low concentrations. We discuss the structures the spps form at long times and how they correlate to their dynamic behavior.

The structure and rheology of sheared model swimmer suspensions

We analyze the rheological response of a suspension of simple model swimmers subject to a steady Couette flow. We consider the squirmer model as a means to control systematically the interplay between self-propulsion and active stress generation and analyze their relative impact both on the effective viscosity of a suspension and the microstructure the squirmers develop. We show how self-propulsion introduces an intrinsic contribution to the effective viscosity of the active suspension. Accordingly, apolar squirmers show shear thickening while polar ones develop a shear thinning response to the applied shear. We show that the detailed coupling of the squirmers to the bounding walls has a strong influence on the structure of the suspension and the development of shear bands.

Extinction conditions for isolated populations with Allee effect

One of the main ecological phenomenons is the Allee effect [1-3], in which a positive benefit from the presence of conspecifics arises. In this work we describe the dynamical behavior of a population with Allee effect in a finite domain that is surrounded by a completely hostile environment. Using spectral methods to rewrite the local density of habitants we are able to determine the critical patch size and the bifurcation diagram, hence characterizing the stability of possible solutions, for different ways to introduce the Allee effect in the reaction-diffusion equations.

Low Dose Aerosol Fitness at the Innate Phase of Murine Infection Better Predicts Virulence amongst Clinical Strains of Mycobacterium tuberculosis

Background Evaluation of a quick and easy model to determine the intrinsic ability of clinical strains to generate active TB has been set by assuming that this is linked to the fitness of Mycobacterium tuberculosis strain at the innate phase of the infection. Thus, the higher the bacillary load, the greater the possibility of inducting liquefaction, and thus active TB, once the adaptive response is set. Methodology/Principal Findings The virulence of seven clinical Mycobacterium tuberculosis strains isolated in Spain was tested by determining the bacillary concentration in the spleen and lung of mice at weeks 0, 1 and 2 after intravenous (IV) inoculation of 104 CFU, and by determining the growth in vitro until the stationary phase had been reached. Cord distribution automated analysis showed two clear patterns related to the high and low fitness in the lung after IV infection. This pattern was not seen in the in vitro fitness tests, which clearly favored the reference strain (H37Rv). Subsequent determination using a more physiological low-dose aerosol (AER) inoculation with 102 CFU showed a third pattern in which the three best values coincided with the highest dissemination capacity according to epidemiological data. Conclusions/Significance The fitness obtained after low dose aerosol administration in the presence of the innate immune response is the most predictive factor for determining the virulence of clinical strains. This gives support to a mechanism of the induction of active TB derived from the dynamic hypothesis of latent tuberculosis infection.

Sedimentation of pairs of hydrodynamically interacting semiflexible filaments

We describe the effect of hydrodynamic interactions in the sedimentation of a pair of inextensible semiflexible filaments under a uniform constant force at low Reynolds numbers. We have analyzed the different regimes and the morphology of such polymers in simple geometries, which allow us to highlight the peculiarities of the interplay between elastic and hydrodynamic stresses. Cooperative and symmetry breaking effects associated to the geometry of the fibers gives rise to characteristic motion which give them distinct properties from rigid and elastic filaments.

Effect of environmental fluctuations on invasion fronts

We determine the density profile and velocity of invasion fronts in one-dimensional infinite habitats in the presence of environmental fluctuations. The population dynamics is reformulated in terms of a stochastic reaction-diffusion equation and is reduced to a deterministic equation that incorporates the systematic contributions of the noise. We obtain analytical expressions for the front profile and velocity by constructing a variational principle. The effect of the noise differs, depending on whether it affects the density-independent growth rate, the intraspecific competition term or the Allee threshold. Fluctuations in the density-independent growth rate increase the invasion velocity and the population density of the invaded area. Fluctuations in the competition term also change the population density of the invaded area, but modify the invasion velocity only for certain initial conditions. Fluctuations in the Allee threshold can induce pulled or pushed invasion fronts as well as invasion failure. We compare our analytical results with numerical solutions of the stochastic partial differential equations and show that our procedure proves useful in dealing with reaction-diffusion equations with multiplicative noise.

Extinction and Chaotic Patterns in Map Lattices Under Hostile Conditions

Population dynamics in spatially extended systems can be modeled by Coupled Map Lattices (CML). We employ such equations to study the behavior of populations confined to a finite patch surrounded by a completely hostile environment. By means of the Galerkin projection and the normal solution ansatz, we are able to find analytical expressions for the critical patch size and show the existence of chaotic patterns. The analytical solutions provided are shown to fit, under the appropriate approximations, the dynamics of a logistic map. This interesting result, together with our discussion, suggests the existence of a universal class of spatially extended systems directly linked to the well-known characteristics of the logistic map.

Cooperativity and hydrodynamic interactions in externally driven semiflexible filaments

We describe a simple simulation method that describes the hydrodynamics of semiflexible filaments immersed in a low Reynolds number fluid and analyze how multiple body cooperativity emerges due to the presence of hydrodynamic interactions (HI). We study the sedimentation of ensembles of filaments under an external force and also consider the propulsion of filaments subject to simple periodic driving. In both cases the dynamics shows qualitative differences due to the presence of HI. For sedimentation, the effects include cooperative velocity and instabilities that can be understood from the interplay of deformations due to flexibility and hydrodynamic forces. The motion of swimmers is more complex, and shows both positive and negative cooperation depending on distance, frequency of drive, and flexibility.

Extinction conditions for isolated populations affected by environmental stochasticity.

We determine the critical patch size below which extinction occurs for populations living in one-dimensional habitats surrounded by completely hostile environments in the presence of environmental fluctuations. The population dynamics is reformulated in terms of a stochastic reaction-diffusion equation and is reduced to a deterministic equation that incorporates the systematic contributions of the noise. We obtain bifurcation diagrams and relations for the mean population density at the stationary state, the critical patch size, and the mean number of individuals in the habitat. The effect of the noise differs, depending on whether it affects the net growth rate or the intraspecific competition term. Fluctuations in the net growth rate decrease the critical patch size, whereas fluctuations in the competition term do not change the critical patch size. We compare our analytical results with numerical solutions of the stochastic partial differential equations and show that our procedure proves useful in dealing with reaction-diffusion equations with multiplicative noise.