A. M. Lacasta

Modeling of spatiotemporal patterns in bacterial colonies.

A diffusion-reaction model for the growth of bacterial colonies is presented. The often observed cooperative behavior developed by bacteria which increases their motility in adverse growth conditions is here introduced as a nonlinear diffusion term. The presence of this mechanism depends on a response which can present hysteresis. By changing only the concentrations of agar and initial nutrient, numerical integration of the proposed model reproduces the different patterns shown by Bacillus subtilis OG-01.

Weak disorder: anomalous transport and diffusion are normal yet again.

We carry out a detailed study of the motion of particles driven by a constant external force over a landscape consisting of a periodic potential corrugated by a small amount of spatial disorder. We observe anomalous behavior in the form of subdiffusion and superdiffusion and even subtransport over very long time scales. Recent studies of transport over slightly random landscapes have focused only on parameters leading to normal behavior, and while enhanced diffusion has been identified when the external force approaches the critical value associated with the transition from locked to running solutions, the regime of anomalous behavior had not been recognized. We provide a qualitative explanation for the origin of these anomalies, and make connections with a continuous time random walk approach.

From subdiffusion to superdiffusion of particles on solid surfaces

We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two-dimensional potential. The potential may be either periodic or random. Depending on the potential and the damping, we observe superdiffusion, large-step diffusion, diffusion, and subdiffusion. Superdiffusive behavior is associated with low damping and is in most cases transient, albeit often long. Subdiffusive behavior is associated with highly damped particles in random potentials. In some cases subdiffusive behavior persists over our entire simulation and may be characterized as metastable. In any case, we stress that this rich variety of behaviors emerges naturally from an ordinary Langevin equation for a system described by ordinary canonical Maxwell-Boltzmann statistics.

Interface roughening in Hele-Shaw flows with quenched disorder: Experimental and theoretical results

We study the forced fluid invasion of an air-filled model porous medium at constant flow rate, in 1+1 dimensions, both experimentally and theoretically. We focus on the nonlocal character of the interface dynamics, due to liquid conservation, and its effect on the scaling properties of the interface upon roughening. Specifically, we study the limit of large flow rates and weak capillary forces. Our theory predicts a roughening behaviour characterized at short times by a growth exponent β1 = 5/6, a roughness exponent α1 = 5/2, and a dynamic exponent z1 = 3, and by β2 = 1/2, α2 = 1/2, and z2 = 1 at long times, before saturation. This theoretical prediction is in good agreement with the experiments at long times. The ensemble of experiments, theory, and simulations provides evidence for a new universality class of interface roughening in 1+1 dimensions.

Dispersionless transport in a washboard potential

We study and characterize a new dynamical regime of underdamped particles in a tilted washboard potential. We find that for small friction in a finite range of forces the particles move essentially nondispersively, that is, coherently, over long intervals of time. The associated distribution of the particle positions moves at an essentially constant velocity and is far from Gaussian-like. This new regime is complementary to, and entirely different from, well-known nonlinear response and large dispersion regimes observed for other values of the external force.

Phase separation driven by external fluctuations

The influence of external fluctuations in phase separation processes is analysed. These fluctuations arise from random variations of an external control parameter. A linear stability analysis of the homogeneous state shows that phase separation dynamics can be induced by external noise. The spatial structure of the noise is found to have a relevant role in this phenomenon. Numerical simulations confirm these results. A comparison with order-disorder noise-induced phase transitions is also made.

Analytical approach to sorting in periodic and random potentials

There has been a recent revolution in the ability to manipulate micrometer-sized objects on surfaces patterned by traps or obstacles of controllable configurations and shapes. One application of this technology is to separate particles driven across such a surface by an external force according to some particle characteristic such as size or index of refraction. The surface features cause the trajectories of particles driven across the surface to deviate from the direction of the force by an amount that depends on the particular characteristic, thus leading to sorting. While models of this behavior have provided a good understanding of these observations, the solutions have so far been primarily numerical. In this paper we provide analytic predictions for the dependence of the angle between the direction of motion and the external force on a number of model parameters for periodic as well as random surfaces. We test these predictions against exact numerical simulations.

Transport and diffusion on crystalline surfaces under external forces

We present a numerical study of classical particles obeying a Langevin equation and moving on a solid crystalline surface under an external force that may either be constant or modulated by periodic oscillations. We focus on the particle drift velocity and diffusion. The roles of friction and equilibrium thermal fluctuations are studied for two nonlinear dynamical regimes corresponding to low and to high but finite friction. We identify a number of resonances and antiresonances, and provide phenomenological interpretations of the observed behaviour.

Numerical study of A+A -> 0 and A+B ->0 reactions with inertia

Using numerical methods the authors study the annihilation reactions A+A-->0 and A+B-->0 in one and two dimensions in the presence of inertial contributions to the motion of the particles. The particles move freely following Langevin dynamics at a fixed temperature. The authors focus on the role of friction.

Phase-field model of Hele-Shaw flows in the high-viscosity contrast regime.

A one-sided phase-field model is proposed to study the dynamics of unstable interfaces of Hele-Shaw flows in the high viscosity contrast regime. The corresponding macroscopic equations are obtained by means of an asymptotic expansion from the phase-field model. Numerical integrations of the phase-field model in a rectangular Hele-Shaw cell reproduce finger competition with the final evolution to a steady-state finger.