Depending on the wind regime, sand dunes exhibit linear, crescent-shaped or star-like forms resulting from the interaction between dune morphology and sand transport. Small-scale dunes form by destabilization of the sand bed with a wavelength (a few tens of metres) determined by the sand transport saturation length. The mechanisms controlling the formation of giant dunes, and in particular accounting for their typical time and length scales, have remained unknown. Using a combination of field measurements and aerodynamic calculations, we show here that the growth of aeolian giant dunes, ascribed to the nonlinear interaction between small-scale superimposed dunes, is limited by the confinement of the flow within the atmospheric boundary layer. Aeolian giant dunes and river dunes form by similar processes, with the thermal inversion layer that caps the convective boundary layer in the atmosphere acting analogously to the water surface in rivers. In both cases, the bed topography excites surface waves on the interface that in turn modify the near-bed flow velocity. This mechanism is a stabilizing process that prevents the scale of the pattern from coarsening beyond the resonant condition. Our results can explain the mean spacing of aeolian giant dunes ranging from 300 m in coastal terrestrial deserts to 3.5 km. We propose that our findings could serve as a starting point for the modelling of long-term evolution of desert landscapes under specific wind regimes.

In this work, we study the diffusion of solute particles in the limit of infinite dilution in a solvent. An estimate is made of the solute concentration below which this limit is attained. We determine the range of the size and mass values of the solute particles where the solute diffusion coefficient is well estimated from the Stokes-Einstein formula. For these aims, extensive molecular-dynamics simulations are carried out for a model tracer-solvent system made up of 5324 molecules including solvent and tracer molecules interacting through Lennard-Jones potentials. The values of the viscosity coefficient, corrected for long time tail contributions, and the diffusion coefficients are obtained with high precision. Positive deviations from the Stokes-Einstein formula are observed as the size ratio or the mass ratio of the tracer to solvent molecules is lowered. For equal solvent and tracer molecular masses, the crossover to the hydrodynamics regime is found to occur when the size ratio is approximately 4. The results show a strong coupling between the size and mass effects on the tracer diffusivity, with the latter being predominant. An analysis of the molecular-dynamics data in the hydrodynamic regime shows that the Stokes-Einstein formula holds for this system with slip boundary conditions and the hydrodynamic radius equal to the cross radius between the tracer-solvent molecules. The friction coefficient is evaluated from the computed autocorrelation function of the force exerted by the fluid on the tracer molecule, following a scheme proposed by Lagar'kov and Sergeev; it is found that the latter criterion gives the correct diffusion coefficient only in the limits of high sizes and high masses.

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The diffusion process of a single spherical nanoparticle immersed in a fluid solvent is studied by molecular dynamics simulations. When the nanoparticle mass stays constant, it is shown that, at short times, the decay of the nanoparticle velocity autocorrelation function is strongly modified when the particle diameter increases. It is also shown that, at large times, the characteristic algebraic decay induced by the hydrodynamic correlations between the solvated particle and the solvent presents a scaling behavior depending on the particle diameter.