Corrugation of Roads

We present a one dimensional model for the development of corrugations in roads subjected to compressive forces from a flux of cars. The cars are modeled as damped harmonic oscillators translating with constant horizontal velocity across the surface, and the road surface is subject to diffusive relaxation. We derive dimensionless coupled equations of motion for the positions of the cars and the road surface H(x,t), which contain two phenomenological variables: an effective diffusion constant Delta(H) that characterizes the relaxation of the road surface, and a function alpha(H) that characterizes the plasticity or erodibility of the road bed. Linear stability analysis shows that corrugations grow if the speed of the cars exceeds a critical value, which decreases if the flux of cars is increased. Modifying the model to enforce the simple fact that the normal force exerted by the road can never be negative seems to lead to restabilized, quasi-steady road shapes, in which the corrugation amplitude and phase velocity remain fixed.Comment: 20 pages, 8 figures, typos correcte

Patterns in hydraulic ripples with binary granular mixtures

An experimental study of a binary granular mixture submitted to a transient shear flow in a cylindrical container is reported. The formation of ripples with a spiral shape is observed. The appearance of phase segregation in those spiral patterns is shown. The relative grain size bewteen sand species is found to be a relevant parameter leading to phase segregation. However, the relative repose angle is an irrelevant parameter. The formation of sedimentary structures is also presented. They result from a ripple climbing process. The ``sub-critical'' or ``super-critical'' character of the lamination patterns is shown to depend on the rotation speed of the container.Comment: 9 pages, 9 figures, LateX (using elsart package), submitted to Phys.

Shear bands in granular flow through a mixing length model

We discuss the advantages and results of using a mixing-length, compressible model to account for shear banding behaviour in granular flow. We formulate a general approach based on two function of the solid fraction to be determined. Studying the vertical chute flow, we show that shear band thickness is always independent from flowrate in the quasistatic limit, for Coulomb wall boundary conditions. The effect of bin width is addressed using the functions developed by Pouliquen and coworkers, predicting a linear dependence of shear band thickness by channel width, while literature reports contrasting data. We also discuss the influence of wall roughness on shear bands. Through a Coulomb wall friction criterion we show that our model correctly predicts the effect of increasing wall roughness on the thickness of shear bands. Then a simple mixing-length approach to steady granular flows can be useful and representative of a number of original features of granular flow.Comment: submitted to EP

The Chalk Garden (April 28-29, 1972)

Program for The Chalk Garden (April 28-29, 1972)

Shear-transformation-zone theory of plastic deformation near the glass transition

The shear-transformation-zone (STZ) theory of plastic deformation in glass-forming materials is reformulated in light of recent progress in understanding the roles played the effective disorder temperature and entropy flow in nonequilibrium situations. A distinction between fast and slow internal state variables reduces the theory to just two coupled equations of motion, one describing the plastic response to applied stresses, and the other the dynamics of the effective temperature. The analysis leading to these equations contains, as a byproduct, a fundamental reinterpretation of the dynamic yield stress in amorphous materials. In order to put all these concepts together in a realistic context, the paper concludes with a reexamination of the experimentally observed rheological behavior of a bulk metallic glass. That reexamination serves as a test of the STZ dynamics, confirming that system parameters obtained from steady-state properties such as the viscosity can be used to predict transient behaviors.Comment: 15 pages, four figure

Granular Elasticity without the Coulomb Condition

An self-contained elastic theory is derived which accounts both for mechanical yield and shear-induced volume dilatancy. Its two essential ingredients are thermodynamic instability and the dependence of the elastic moduli on compression.Comment: 4pages, 2 figure

Calculation of the separation streamlines of barchans and transverse dunes

We use FLUENT to calculate the wind profile over barchans and transverse dunes. The form of the streamlines of flow separation at the lee side of the dunes is determined for a symmetric barchan dune in three dimensions, and for the height profile of a measured transverse dune field in the Len\c{c}\'ois Maranhenses.Comment: 6 pages including 5 figures. Proceedings of PSIS 200

Mean Field Theory of Sandpile Avalanches: from the Intermittent to the Continuous Flow Regime

We model the dynamics of avalanches in granular assemblies in partly filled rotating cylinders using a mean-field approach. We show that, upon varying the cylinder angular velocity $\omega$, the system undergoes a hysteresis cycle between an intermittent and a continuous flow regimes. In the intermittent flow regime, and approaching the transition, the avalanche duration exhibits critical slowing down with a temporal power-law divergence. Upon adding a white noise term, and close to the transition, the distribution of avalanche durations is also a power-law. The hysteresis, as well as the statistics of avalanche durations, are in good qualitative agreement with recent experiments in partly filled rotating cylinders.Comment: 4 pages, RevTeX 3.0, postscript figures 1, 3 and 4 appended

Transverse instability of dunes

The simplest type of dune is the transverse one, which propagates with invariant profile orthogonally to a fixed wind direction. Here we show numerically and with a linear stability analysis that transverse dunes are unstable with respect to along-axis perturbations in their profile and decay on the bedrock into barchan dunes. Any forcing modulation amplifies exponentially with growth rate determined by the dune turnover time. We estimate the distance covered by a transverse dune before fully decaying into barchans and identify the patterns produced by different types of perturbation.Comment: 4 pages, 3 figures; To appear in Physical Review Letter

A simple model for a transverse dune field

We present a simple one-dimensional model to describe the evolution of a transverse dune field. The model is characterized by the distances between the dunes and their heights, which determine the inter-dune sand flux. The model reproduces the observation that the dunes in a given field have approximately all the same height. We find that this result is independent of the initial configuration of the field, as well as of coalescence effects between migrating dunes. The time for the final state to be reached is studied as a function of the relevant phenomenological parameters