The shape of pebbles

摘要: A theory of pebble erosion is presented, based on the assumption that rate at a point surface function Vof curvature there. It proved for physically reasonable functions V,the sphere only shape which can maintain its proportions as it wears away. An argument given leads to particular form Vand few qualitative consequences this are indicated. The time tmay be described using spherical polar coordinates θ, Φ by radius r (θ, Φ, t). This highly nonlinear partial differential equation. However, in case deformed sphere, when terms second order or higher deformation neglected, equation becomes linear and version diffusion stability against deformations various harmonic types then easily analyzed.