DPTM simulation of aeolian sand ripple

Aeolian sand ripple and its time evolution are simulated by the discrete particle tracing method (DPTM) presented in this paper. The difference between this method and the current methods is that the former can consider the three main factors relevant to the formation of natural aeolian sand ripples, which are the wind-blown sand flux above the sand bed formed by lots of sand particles with different diameters, the particle-bed collision and after it the rebound and ejection of sand particles in the sand bed, the saltation of high-speed sand particles and the creep of low-speed sand particles, respectively. The simulated aeolian sand ripple is close to the natural sand ripple not only in basic shape and characteristic, particle size segregation and stratigraphy, but also in formation stages. In addition, three important speeds can be obtained by this method, which are the propagation speed of the saturated aeolian sand ripple and the critical frictional wind speeds of emergence and disappearance of sand ripple. Supported by the Key Project of the National Natural Science Foundation of China (Grant No. 10532040)     

Dynamics of aeolian sand ripples

We analyze theoretically the dynamics of aeolian sand ripples. In order to put the study in the context, we first review existing models. This paper is a continuation of two previous papers (Z. Csahók et al., Physica D 128, 87 (1999); A. Valance et al., Eur. Phys. J. B 10, 543 (1999)), the first one is based on symmetries and the second on a hydrodynamical model. We show how the hydrodynamical model may be modified to recover the missing terms that are dictated by symmetries. The symmetry and conservation arguments are powerful in that the form of the equation is model-independent. We then present an extensive numerical and analytical analysis of the generic sand ripple equation. We find that at the initial stage the wavelength of the ripple is that corresponding to the linearly most dangerous mode. At later stages the profile undergoes a coarsening process leading to a significant increase of the wavelength. We find that including the next higher-order nonlinear term in the equation leads naturally to a saturation of the local slope. We analyze both analytically and numerically the coarsening stage, in terms of a dynamical exponent for the mean wavelength increase. We discuss some future lines of investigations. Received 20 January 2000     

A nonlinear model for aeolian sand ripples

Starting from the phenomenological model for sand ripple formation developed in [#!Bouchaud98!#], we proposed a new interpretation in the light of recent experiments. Furthermore, we derive, close to the threshold of ripple instability, a nonlinear equation for the spatio-temporal evolution of the sand bed profile, which to leading order has a quadratic nonlinearity. This equation is identical to that derived recently on the basis of geometry and conservation law [#!Csahok98!#]. Our derivation connects the coefficients of the nonlinear equation to the underlying physical mechanisms (reptation length...). This equation reveals ripple structures which then undergo a coarsening process, as observed in wind tunnel experiment. Small, fast moving ripples are absorbed by larger, slower forms resulting in a growth of the mean wavelength. Received 5 January 1999     

Vegetation against dune mobility

Vegetation is the most common and most reliable stabilizer of loose soil or sand. This ancient technique is for the first time cast into a set of equations of motion describing the competition between aeolian sand transport and vegetation growth. Our set of equations is then applied to study quantitatively the transition between barchans and parabolic dunes driven by the dimensionless fixation index theta which is the ratio between the dune characteristic erosion rate and vegetation growth velocity. We find a fixation index theta(c) below which the dunes are stabilized, characterized by scaling laws.     

Self-organized ordering of nanostructures produced by ion-beam sputtering

We study the self-organized ordering of nanostructures produced by ion-beam sputtering of targets amorphizing under irradiation. By introducing a model akin to models of pattern formation in aeolian sand dunes, we extend consistently the current continuum theory of erosion by IBS. We obtain new nonlinear effects responsible for the in-plane ordering of the structures, whose strength correlates with the degree of ordering found in experiments. Our results highlight the importance of redeposition and surface viscous flow to this nanopattern formation process.     

Use of forecasting signatures to help distinguish periodicity,randomness, and chaos in ripples and other spatial patterns

Forecasting of one-dimensional time series previously has been used to help distinguish periodicity, chaos, and noise. This paper presents two-dimensional generalizations for making such distinctions for spatial patterns. The techniques are evaluated using synthetic spatial patterns and then are applied to a natural example: ripples formed in sand by blowing wind. Tests with the synthetic patterns demonstrate that the forecasting techniques can be applied to two-dimensional spatial patterns, with the same utility and limitations as when applied to one-dimensional time series. One limitation is that some combinations of periodicity and randomness exhibit forecasting signatures that mimic those of chaos. For example, sine waves distorted with correlated phase noise have forecasting errors that increase with forecasting distance, errors that are minimized using nonlinear models at moderate embedding dimensions, and forecasting properties that differ significantly between the original and surrogates. Ripples formed in sand by flowing air or water typically vary in geometry from one to another, even when formed in a flow that is uniform on a large scale; each ripple modifies the local flow or sand-transport field, thereby influencing the geometry of the next ripple downcurrent. Spatial forecasting was used to evaluate the hypothesis that such a deterministic process-rather than randomness or quasiperiodicity-is responsible for the variation between successive ripples. This hypothesis is supported by a forecasting error that increases with forecasting distance, a greater accuracy of nonlinear relative to linear models, and significant differences between forecasts made with the original ripples and those made with surrogate patterns. Forecasting signatures cannot be used to distinguish ripple geometry from sine waves with correlated phase noise, but this kind of structure can be ruled out by two geometric properties of the ripples: Successive ripples are highly correlated in wavelength, and ripple crests display dislocations such as branchings and mergers.     

Long-time behavior of sand ripples induced by water shear flow

The formation of sand ripples under water shear flow in a narrow annular channel and the approach of the ripple pattern towards a steady state were studied experimentally. Four results are obtained: i) The mean amplitude, the average drift velocity and the mean sediment transport rate of the evolving bed shape are strongly related. A quantitative characterization of this relation is given. ii) The ripple pattern reaches a stationary state with a finite ripple amplitude and wavelength. The time needed to reach the state depends on the shear stress and may be several days. iii) The onset of ripple formation is determined by the bed shear stress, but it seems neither to depend on the grain diameter nor on the depth of the water layer. iv) The ripple amplitude, drift velocity and sediment transport in this stationary state depend on the grain size. This dependency is neither captured by the particle Reynolds number nor by the Shields parameter: an empirical scaling law is presented instead.     

Ripple formation in various metals and super-hard tetrahedral amorphous carbon films in consequence of femtosecond laser irradiation

Ripple formation in consequence of ultrashort laser pulse irradiation of materials is a well-known phenomenon. We have investigated the formation of ripples in various metals, i.e. steel, tungsten carbide hard metal, as well as in superhard ta-C films, where we used femtosecond laser pulses of 775 nm and 387 nm mean wavelength and 150 fs pulse duration. The aim was to investigate how the ripple parameters depend on irradiation parameters, and if such ripples have a potentiality for applications. In the paper, we will show that on smooth surfaces the ripple orientation is perpendicular to the electric field vector of the linearly polarized laser beam, as is well-known. Moreover, it will be shown that the ripple period decreases with decreasing laser wavelength and/or increasing angle of incidence of the laser beam on the substrate. By using optimum parameters large areas of the materials and films can be rippled swiftly, which would be important for applications. For instance, the improvement of frictional and wear behavior of tribologically stressed surfaces by ripples was investigated on ta-C coated steel surfaces.     

Interaction quench in the Hubbard model

Motivated by recent experiments in ultracold atomic gases that explore the nonequilibrium dynamics of interacting quantum many-body systems, we investigate the opposite limit of Landau's Fermi-liquid paradigm: We study a Hubbard model with a sudden interaction quench, that is, the interaction is switched on at time t=0. Using the flow equation method, we are able to study the real time dynamics for weak interaction U in a systematic expansion and find three clearly separated time regimes: (i) An initial buildup of correlations where the quasiparticles are formed. (ii) An intermediate quasi-steady regime resembling a zero temperature Fermi liquid with a nonequilibrium quasiparticle distribution function. (iii) The long-time limit described by a quantum Boltzmann equation leading to thermalization of the momentum distribution function with a temperature T proportional, variantU.     

Modelling thin-film dewetting on structured substrates and templates: Bifurcation analysis and numerical simulations

We study the dewetting process of a thin liquid film on a chemically patterned solid substrate (template) by means of a thin-film evolution equation incorporating a space-dependent disjoining pressure. Dewetting of a thin film on a homogeneous substrate leads to fluid patterns with a typical length scale, that increases monotonously in time (coarsening). Conditions are identified for the amplitude and periodicity of the heterogeneity that allow to transfer the template pattern onto the liquid structure ("pinning") emerging from the dewetting process. A bifurcation and stability analysis of the possible liquid ridge solutions on a periodically striped substrate reveal parameter ranges where pinning or coarsening ultimately prevail. We obtain an extended parameter range of multistability of the pinning and coarsening morphologies. In this regime, the selected pattern depends sensitively on the initial conditions and potential finite perturbations (noise) in the system as we illustrate with numerical integrations in time. Finally, we discuss the instability to transversal modes leading to a decay of the ridges into rows of drops and show that it may diminish the size of the parameter range where the pinning of the thin film to the template is successful.Received: 29 January 2003, Published online: 15 July 2003PACS: 68.15.+e Liquid thin films - 81.16.Rf Nanoscale pattern formation - 47.20.Ky Nonlinearity (including bifurcation theory)     

Compositionally modulated ripples induced by sputtering of alloy surfaces

Sputtering of an amorphous or crystalline material by an ion beam often results in the formation of periodic nanoscale ripple patterns on the surface. In this Letter, we show that, in the case of alloy surfaces, the differences in the sputter yields and surface diffusivities of the alloy components will also lead to spontaneous modulations in composition that can be in or out of phase with the ripple topography. The degree of this kinetic alloy decomposition can be altered by varying the flux of the ion beam. In the high-temperature and low-flux regime, the degree of decomposition scales linearly with the ion flux, but it scales inversely with the ion flux in the low-temperature, high-flux regime.     

Slow dynamics in colloidal glasses and porous media as probed by NMR relaxometry: assessment of solvent levy statistics in the strong adsorption regime

Mesoscopic media such as porous materials or colloidal pastes develop large specific surface area which strongly influence the dynamics of the embedded fluid. This fluid confinement can be used either to probe the interfacial geometry (frozen porous media) or the particle dynamics (paste and colloidal glass). In the strong adsorption regime, it was recently proposed that the effective surface diffusion on flat surface is anomalous and exhibits long time pathology (Lévy walks). This phenomena is directly related to the time and space properties of loop trajectories appearing in the bulk between a desorption and a readsorption step. The Lévy statistics extends the time domain of the embedded fluid dynamics toward the low frequency regime. An interesting way to probe such a slow interfacial process is to use field cycling NMR relaxometry. In the first part of this paper, we propose a simple theoretical model of NMR dispersion which only involves elementary time steps of the solvent dynamics near an interface (loops, trains, tails in relation with the confining geometry). In the second part, field cycling NMR relaxometry is used to probe the slow solvent dynamics in two type of interfacial systems: (i) a colloidal glass made of thin and flat particles (ii) two fully saturated porous media, the Vycor glass and MCM48 respectively. Experimental results are critically compared to closed-form analytical expressions and numerical simulations.     

Measuring the kinetic parameters of saltating sand grains using a high-speed digital camera

A high-speed digital camera is used to record the saltation of three sand samples(diameter range:300–500,200–300 and100–125μm).This is followed by an overlapping particle tracking algorithm to reconstruct the saltating trajectory and the differential scheme to abstract the kinetic parameters of saltating grains.The velocity results confirm the propagating feature of saltation in maintaining near-face aeolian sand transport.Moreover,the acceleration of saltating sand grains was obtained directly from the reconstructed trajectory,and the results reveal that the climbing stage of the saltating trajectory represents an critical process of energy transfer while the sand grains travel through air.     

Strain wave evolution equation for nonlinear propagation in materials with mesoscopic mechanical elements

Nonlinear wave propagation in materials, where distribution function of mesoscopic mechanical elements has very different scales of variation along and normally to diagonal of Preisach-Mayergoyz space, is analyzed. An evolution equation for strain wave, which takes into account localization of element distribution near the diagonal and its slow variation along the diagonal, is proposed. The evolution equation provides opportunity to model propagation of elastic waves with strain amplitudes comparable to and even higher than characteristic scale of element localization near Preisach-Mayergoyz space diagonal. Analytical solutions of evolution equation predict nonmonotonous dependence of wave absorption on its amplitude in a particular regime. The regime of self-induced absorption for small-amplitude nonlinear waves is followed by the regime of self-induced transparency for high-amplitude waves. The developed theory might be useful in seismology, in high-pressure nonlinear acoustics, and in nonlinear acoustic diagnostics of damaged and fatigued materials.     

The laser polarization as control parameter in the formation of laser-induced periodic surface structures: Comparison of numerical and experimental results

Considering self-organized surface pattering upon multi-pulse femtosecond laser irradiation, in particularly the strong dependence of ripples orientation on the laser polarization, we present numerical simulations from an adopted surface erosion model and compare the result to our experimental data on laser-induced nanostructures formation. We present the surface morphologies obtained by this model for different polarizations of the incident laser electric field and show good agreement with ripple formation produced by laser ablation experiments. The correlation of ripples orientation with laser polarization can be described within a model where the polarization causes a breaking of symmetry at the surface. Further we discuss a time evolution of pattern formation. Our results support the non-linear self-organization mechanism of pattern formation on the surface of solids.     

Influence of current ripple on the tungsten cathode erosion

The erosion of a thermionic tungsten cathode is studied. Arc burning conditions under which gas–vapor erosion causes cathode mass losses are determined. It is shown that erosion does not depend on the current ripple amplitude and is roughly equal to 2 ng/C. In experiments, the current ripple amplitude ranges from ±1% to ±50%.     

Effects of pair correlation on mean-field theory of BTW sand pile model

We extend the mean-field calculation of BTW sand pile model to one that includes the correlation between pairs of nearest neighbors. Specifically, we derive dynamical equations of both one-site and two-site densities, and solve the equations order by order starting with the mean-field solution. The investigation provides analytical results for both stationary and dynamic states of the sand pile near the critical point, which are valid in the regime where h?ε²?1 (h= incoming rate of sand grains, ε=bulk dissipation rate of sand grains). In the stationary case, we evaluate the pair correlation and the correction to the mean-field single-site densities due to the correlation. The correction is found to be of the same order as the mean-field solution. In the dynamic case, the initial state deviates from the stationary state by a small fluctuation, which subsequently decays exponentially, with the time constant being reduced from the corresponding mean-field value. Again, the correction to the time constant in this case is found comparable to the mean-field value itself.