Related papers: A nonlinear evolution equation for sand ripples ba…

Weakly nonlinear plane waves are considered in hyperelastic crystals. Evolution equations are derived at a quadratically nonlinear level for the amplitudes of quasi-longitudinal and quasi-transverse waves propagating in arbitrary…

We model formation and evolution of transverse dune fields. In the model, only the cross section of the dune is simulated. The only physical variable of relevance is the dune height, from which the dune width and velocity are determined, as…

A new element is proposed to play a role in the evolution of extrasolar planetary systems: the tidal (or elliptical) instability. It comes from a parametric resonance and takes place in any rotating fluid whose streamlines are (even…

It has been observed that the direction in which a sand dune extends its crest line depends on seasonal variation of wind direction; when the variation is small, the crest line develops more or less perpendicularly to the mean wind…

The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions,…

We solve a one-dimensional sandpile problem analytically in a thick flow regime when the pile evolution may be described by a set of linear equations. We demonstrate that, if an income flow is constant, a space periodicity takes place while…

The one-dimensional motion of $N$ particles in the field of many incoherent waves is revisited numerically. When the wave complex amplitudes are independent, with a gaussian distribution, the quasilinear approximation is found to always…

We present a study of the spiral responses in a stable disc galaxy model to co-orbiting perturbing masses that are evenly spaced around rings. The amplitudes of the responses, or wakes, are proportional to the masses of the perturbations,…

An experimental study of a granular surface submitted to a circular fluid motion is presented. The appearance of an instability along the sand-water interface is observed beyond a critical radius $r_c$. This creates ripples with a spiral…

We consider a slowly rotating rectangular billiard with moving boundaries and use the canonical perturbation theory to describe the dynamics of a billiard particle. In the process of slow evolution certain resonance conditions can be…

In zones of loose sand, wind-blown sand dunes emerge due the linear instability of a flat sedimentary bed. This instability has been studied in experiments and numerical models but rarely in the field, due to the large time and length…

We study sandpile models with stochastic toppling rules and having sticky grains so that with a non-zero probability no toppling occurs, even if the local height of pile exceeds the threshold value. Dissipation is introduced by adding a…

We investigate the evolution of non-linear density perturbations by taking into account the effects of deviations from spherical symmetry of a system. Starting from the standard spherical top hat model in which these effects are ignored, we…

Starting with a post-Newtonian description of compact binary systems, we derive a set of equations that describes the evolution of the orbital angular momentum and both spin vectors during inspiral. We find regions of phase space that…

Third-order nonlinear dispersion equations (NDEs) are shown to admit both shock and rarefaction waves (as weak solutions), which are distinguished by a smooth deformation approach. Compacton-type travelling wave solutions are proved to be…

A novel third order nonlinear evolution equation governing the dynamics of high frequency electrostatic drift waves has been derived in the framework of a plasma fluid model in an inhomogeneous magnetized plasma. The linear dispersion…

We study the excitation and damping of tides in close binary systems, accounting for the leading order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct effects: three-mode nonlinear interactions…

Many small bodies in the solar system are believed to be rubble piles, a collection of smaller elements separated by voids. We propose a model for the structure of a self-gravitating rubble pile. Static friction prevents its elements from…

We report here on a laboratory-scale experiment which reproduces a rich variety of natural patterns with few control parameters. In particular, we focus on intriguing rhomboid structures often found on sandy shores and flats. We show that…

Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…