Speeding chemical reactions by focusing.

We present numerical results for a chemical reaction of colloidal particles which are transported by a laminar fluid and are focused by periodic obstacles in such a way that the two components are well mixed and consequently the chemical reaction is speeded up. The roles of the various system parameters (diffusion coefficients, reaction rate, and obstacles sizes) are studied. We show that focusing speeds up the reaction from the diffusion limited rate ∼t(-1/2) to very close to the perfect mixing rate, ∼t(-1).

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.

Diffusion coefficient in periodic and random potentials.

Transport and diffusion of particles on modulated surfaces is a nonequilibrium problem which is receiving a great deal of attention due to its technological applications, but analytical calculations are scarce. In earlier work, we developed a perturbative approach to begin to provide an analytic platform for predictions about particle trajectories over such surfaces. In some temperature and forcing regimes, we successfully reproduced results for average particle velocities obtained from numerical simulations. In this paper, we extend the perturbation theory to the calculation of higher moments, in particular the diffusion tensor and the skewness. Numerical simulations are used to check the domain of validity of the perturbative approach.

Exported oscillator competition: a concept to analyze complex rhythms.

We study the interaction between two independent nonlinear oscillators competing through a neutral excitable element. The first oscillator, completely deterministic, acts as a normal pacemaker sending pulses to the neutral element which fires when it is excited by these pulses. The second oscillator, endowed with some randomness, though unable to make the excitable element to beat, leads to the occasional suppression of its firing. The missing beats or errors are registered and their statistics analyzed in terms of the noise intensity and the periods of both oscillators. This study is inspired in some complex rhythms such as a particular class of heart arrhythmia.

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.

Physical analysis of a processive molecular motor: the conventional kinesin.

We present a model that allows for the derivation of the experimentally accessible observables: spatial steps, mean velocity, stall force, useful power, efficiency and randomness, etc. as a function of the [adenosine triphosphate] concentration and an external load F. The model presents a minimum of adjustable parameters and the theoretical predictions compare well with the available experimental results.

Coherence and anticoherence resonance tuned by noise.

We present numerical evidence and a theoretical analysis of the appearance of anticoherence resonance induced by noise, not predicted in former analysis of coherence resonance. We have found that this phenomenon occurs for very small values of the intensity of the noise acting on an excitable system, and we claim that this is a universal signature of a nonmonotonous relaxational behavior near its oscillatory regime. Moreover, we demonstrate that this new phenomenon is totally compatible with the standard situation of coherence resonance appearing at intermediate values of noise intensity.

Modelization of surface diffusion of a molecular dimer.

A simple model for a dimer molecular diffusion on a crystalline surface, as a function of temperature, is presented. The dimer is formed by two particles coupled by a quadratic potential. The dimer diffusion is modeled by an overdamped Langevin equation in the presence of a two-dimensional periodic potential. Numerical simulation's results exhibit some dynamical properties observed, for example, in Si2 diffusion on a silicon [100] surface. They can be used to predict the value of the effective friction parameter. Comparison between our model and experimental measurements is presented.

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.

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.

Controlling chaotic transport in two-dimensional periodic potentials.

We uncover and characterize different chaotic transport scenarios in perfect two-dimensional periodic potentials by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect (i.e., with no directed transport by symmetry breaking of zero-mean forces). After identifying relevant symmetries of the equations of motion, analytical estimates in parameter space for the occurrence of different transport scenarios are provided and confirmed by numerical simulations. These scenarios are highly sensitive to variations of the system's asymmetry parameters, including the eccentricity of the two-dimensional periodic potential and the direction of dc and ac forces, which could be useful for particle sorting purposes in those cases where chaos is unavoidable.

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.

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.

Sorting on periodic surfaces.

Particles moving on crystalline surfaces and driven by external forces or flow fields can acquire velocities along directions that deviate from that of the external force. This effect depends upon the characteristics of the particles, most notably particle size or particle index of refraction, and can therefore be (and has been) used to sort different particles. We introduce a simple model for particles subject to thermal fluctuations and moving in appropriate potential landscapes. Numerical results are compared to recent experiments on landscapes produced with holographic optical tweezers and microfabricated technology. Our approach clarifies the relevance of different parameters, the direction and magnitude of the external force, particle size, and temperature.

Diffusion on a solid surface: anomalous is normal.

We present a numerical study of classical particles diffusing on a solid surface. The particles' motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic or a random two-dimensional potential. The model leads to a rich variety of different transport regimes, some of which correspond to anomalous diffusion such as has recently been observed in experiments and Monte Carlo simulations. We show that this anomalous behavior is controlled by the friction coefficient and stress that it emerges naturally in a system described by ordinary canonical Maxwell-Boltzmann statistics.

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.