# softmatter:Hard Sphere Potential

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The hard sphere potential accounts for excluded volume interactions only. The potential is infinite if particles overlap and zero otherwise. Such potentials are not numerically integrateable and cannot be used in Molecular Dynamics Simulation (MD), Brownian Dynamics Simulation (BD), or Dissipative Particle Dynamics Simulation (DPD). Hard sphere potentials are typically used in Monte Carlo Simulation (MC) methods or in event-based, collision dynamics methods (also called discontinuous MD).

$U_{HS}(r) = \begin{cases} \infty,&r<\sigma\\ 0, & r \geq \sigma \end{cases}$