Softsphere

A softsphere is a computational model used in physics and materials science to represent particles that are not perfectly rigid. Unlike hard spheres, which are assumed to have infinitely stiff boundaries and undergo instantaneous collisions, softspheres interact through a continuous potential energy function that depends on the distance between their centers. This potential typically increases sharply as the spheres overlap, mimicking a repulsive force that prevents them from passing through each other.

The mathematical form of the softsphere potential can vary, but common choices include a Lennard-Jones potential or a simpler repulsive power-law potential. The parameters of these potentials determine the "softness" or stiffness of the spheres. When two softspheres approach, their interaction energy rises, leading to a gradual deceleration and repulsion rather than an abrupt bounce. This allows for phenomena like particle compression and deformation, which are not possible with hard spheres.

Softsphere models are particularly useful for simulating systems where particles are not perfectly rigid, such as granular materials, polymers, or even certain biological structures. They can capture a wider range of physical behaviors, including jamming transitions, packing arrangements, and the response of materials to applied stress. The continuous nature of the interaction also simplifies some numerical integration schemes compared to the discrete event simulation often required for hard spheres. Despite their simplifications, softsphere models provide valuable insights into the collective behavior of many-particle systems.