Related papers: Exact Solutions of a Model for Granular Avalanches
A dissipative stochastic sandpile model is constructed and studied on small world networks in one and two dimensions with different shortcut densities $\phi$, where $\phi=0$ represents regular lattice and $\phi=1$ represents random network.…
A simplified kinetic description of rapid granular media leads to a nonlocal Vlasov-type equation with a convolution integral operator that is of the same form as the continuity equations for aggregation-diffusion macroscopic dynamics.…
I have proposed a\textit{non-Abelian}and stochastic self-organized criticality model in which each avalanche contains one stochastic site and all remaining sites in the avalanche are deterministic with a constant threshold $E_{c}^{I}$.…
We consider a classical spring-mass model of human running which is built upon an inverted elastic pendulum. Based on our previous results concerning asymptotic solutions for large spring constant (or small angle of attack), we construct…
Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the…
We study shock formation in vertically oscillated granular layers, using both molecular dynamics simulations and numerical solutions of continuum equations to Navier-Stokes order. A flat layer of grains is thrown up from an oscillating…
We have developed a Monte Carlo technique for self-consistently calculating the hydrodynamic structure of oblique, steady-state shocks, together with the first-order Fermi acceleration process and associated non-thermal particle…
Rayleigh-B\'{e}nard convection in horizontal layers of binary fluid mixtures heated from below with realistic horizontal boundary conditions is studied theoretically using multi-mode Galerkin expansions. For positive separation ratios the…
Explicit numerical finite difference schemes for partial differential equations are well known to be easy to implement but they are particularly problematic for solving equations whose solutions admit shocks, blowups and discontinuities.…
Strong numerical hints exist in favor of a universal blowup scenario in the Sabra shell model, a popular cascade model of 3D turbulence, which features complex velocity variables on a geometric progression of scales $\ell_n \propto \lambda…
In this survey we report on some recent results related to various singular phenomena arising in the study of some classes of nonlinear elliptic equations. We establish qualitative results on the existence, nonexistence or the uniqueness of…
After the introduction of sandpile model a number of different variants have been studied. In most of these models sand particles are indistinguishable. Here we have painted the sand particles using a few distinct colors, and restrict them…
Avalanche behavior of gravitationally-forced granular layers on a rough inclined plane are investigated experimentally for different materials and for a variety of grain shapes ranging from spherical beads to highly anisotropic particles…
Sand pile models are dynamical systems describing the evolution from $N$ stacked grains to a stable configuration. It uses local rules to depict grain moves and iterate it until reaching a fixed configuration from which no rule can be…
We discuss in this work the validity of the theoretical solution of the nonlinear Couette flow for a granular impurity obtained in a recent work [preprint arXiv:0802.0526], in the range of large inelasticity and shear rate. We show there is…
Three regimes of granular avalanches in fluids are put in light depending on the Stokes number St which prescribes the relative importance of grain inertia and fluid viscous effects, and on the grain/fluid density ratio r. In gas (r >> 1…
We propose a nonlinear hydrodynamical model of granular materials. We show how this model describes the formation of a sand pile from a homogeneous distribution of material under gravity, and then discuss a simulation of a rotating sandpile…
The Gradient Scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the Gradient Scheme framework can be adapted to elasticity equations, and…
We numerically solve the propagation of a shock wave in a chain of elastic beads with no restoring forces under traction (no-tension elasticity). We find a sequence of peaks of decreasing amplitude and velocity. Analyzing the main peak at…
This article investigates a mathematical model for bushfire propagation, focusing on the existence and properties of translating solutions. We obtain quantitative bounds on the environmental diffusion coefficient and ignition kernels,…