Velocity alignment
= Velocity alignment
{title2=$\dot{\mathbf v}_i=\sum_jK_{ij}(\mathbf v_j-\mathbf v_i)$}
An interaction making particle <velocities> approach those of their neighbors. Symmetric nonnegative weights $K_{ij}$ conserve total <momentum> for equal particle <masses> and dissipate relative <kinetic energy>. Connectivity and quantitative lower bounds on the interaction matter for eventual consensus; nonnegativity alone permits noninteracting groups.