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J. An constructed analytic hypervirial models of stellar systems with N. W. Evans. Their 2005 family combines explicit gravitational potentials, cusped density profiles and simple phase-space distribution functions, with the special property that a local virial relation holds at every radius.^[ref]

Such models provide controlled examples for relating density cusps and velocity anisotropy. The phase-space distribution function must remain integrable and nonnegative; an attractive density formula alone does not guarantee a physical stellar system.

N. W. Evans developed analytic models of galaxies and dark haloes with J. An. Their hypervirial distribution function has the form $f\propto L^{p-2}{\mathcal{E}}^{(3p+1)/2}$, where $L$ is specific angular momentum and $\mathcal{E}$ is relative binding energy.^[ref]

The resulting hypervirial models connect an adjustable central density cusp to an explicit dynamical population, extending useful features of the Plummer model beyond its finite-density core.