J. M. Sancho

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.

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.

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.

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.

Nonclassical Kinetics in Constrained Geometries: Initial Distribution Effects

We present a detailed study of the effects of the initial distribution on the kinetic evolution of the irreversible reaction A+B→0 in one dimension. Our analytic as well as numerical work is based on a reaction–diffusion model of this reaction. We focus on the role of initial density fluctuations in the creation of the macroscopic patterns that lead to the well-known kinetic anomalies in this system. In particular, we discuss the role of the long wavelength components of the initial fluctuations in determining the long-time behavior of the system. We note that the frequently studied random initial distribution is but one of a variety of possible distributions leading to interesting anomalous behavior. Our discussion includes an initial distribution with correlated A-B pairs and one in which the initial distribution forms a fractal pattern. The former is an example of a distribution whose long wavelength components are suppressed, while the latter exemplifies one whose long wavelength components are enhanced, relative to those of the random distribution.

Particle separation by external fields on periodic surfaces

Particles moving on perfect periodic surfaces under the influence of external forces may move along directions that deviate from that of the force. We briefly recall previous results for transport of particles on surfaces with periodic traps or periodic obstacles driven by a constant external force, and present new results for particles moving in a harmonic periodic potential. The sorting properties are explored as a function of a number of control parameters, specifically the friction, force amplitude and direction, temperature, and lattice constants.