Related papers: A nonlinear evolution equation for sand ripples ba…
An outstanding problem in Earth science is understanding the method of transport of magma in the Earth's mantle. Models for this process, transport in a viscously deformable porous media, give rise to scalar degenerate, dispersive,…
The coarsening of an array of vortex ripples prepared in an unstable state is discussed within the framework of a simple mass transfer model first introduced by K.H. Andersen et al. [Phys. Rev. E 63, 066308 (2001)]. Two scenarios for the…
Turbulent flows over wavy surfaces give rise to the formation of ripples, dunes and other natural bedforms. To predict how much sediment these flows transport, research has focused mainly on basal shear stress, which peaks upstream of the…
We derive the Whitham modulation equations for the nonlinear Schr\"odinger equation in the plane (2d NLS) with small dispersion. The modulation equations are derived in terms of both physical and Riemann variables; the latter yields…
A new description of the dynamics of warped accretion discs is presented. A theory of fully nonlinear, slowly varying bending waves is developed, involving a proper treatment of viscous fluid dynamics but neglecting self-gravitation. The…
Coastal erosion describes the displacement of land caused by destructive sea waves, currents or tides. Major efforts have been made to mitigate these effects using groins, breakwaters and various other structures. We try to address this…
When submitted to the repeated passages of vehicles unpaved roads made of sand or gravel can develop a ripply pattern known as washboard or corrugated road. We propose a stability analysis based on experimental measurements of the force…
We present a fully nonlinear hydrodynamic 'shallow water' model of the solar tachocline. The model consists of a global spherical shell of differentially rotating fluid, which has a deformable top, thus allowing motions in radial directions…
We introduce and study a new directed sandpile model with threshold dynamics and stochastic toppling rules. We show that particle conservation law and the directed percolation-like local evolution of avalanches lead to the formation of a…
We consider evolution of wave pulses with formation of dispersive shock waves in framework of fully nonlinear shallow-water equations. Situations of initial elevations or initial dips on the water surface are treated and motion of the…
The manner in which warps in accretion disks evolve depends on the magnitude of the viscosity. For small viscosity $(\alpha < H/R)$ the warp evolves in a wave-like manner; for large viscosity $H/R<\alpha \ll 1$ it evolves diffusively. Here…
We consider an evolution system describing the phenomenon of marble sulphation of a monument, accounting of the surface rugosity. We first prove a local in time well posedness result. Then, stronger assumptions on the data allow us to…
We numerically study a one-dimensional conserved growth equation with competing linear (Ehrlich-Schwoebel) and nonlinear instabilities. As a control parameter is varied, this model exhibits a non-equilibrium phase transition between two…
Stellar oscillation under the combined influences of incident gravitational wave and radiation loss is studied in a simple toy model. The star is approximated as a uniform density ellipsoid in the Newtonian gravity including radiation…
When wind blows over water, ripples are generated on the water surface. These ripples can be regarded as perturbations of the wind field, which is modelled as a parallel inviscid flow. For a given wavenumber $k$, the perturbed…
Of particular interest for radio and hard X-ray diagnostics of accelerated electrons during solar flares is the understanding of the basic non-linear mechanisms regulating the relaxation of electron beams propagating in turbulent plasmas.…
We analyze the survival probability of unstable particles in the context of quantum field theory. After introducing the spectral function of resonances, we show that deviations from the exponential decay law occur at short times after the…
Starting from the physics on the grain scale, we develop a simple continuum description of aeolian sand transport. Beyond popular mean-field models, but without sacrificing their computational efficiency, it accounts for both dominant grain…
We calculate the evolution of planets undergoing a strong tidal encounter using smoothed particle hydrodynamics (SPH), for a range of periastron separations. We find that outside the Roche limit, the evolution of the planet is…
We consider a strictly hyperbolic, genuinely nonlinear system of conservation laws in one space dimension. A sharp decay estimate is proved for the positive waves in an entropy weak solution. The result is stated in terms of a partial…