  The Jeans criterion is one cornerstone in our understanding of gravitational
fragmentation. A critical limitation of the Jeans criterion is that the
background density is assumed to be a constant, which is often not true in
dynamic conditions such as star-forming regions. For example, during the
formation phase of the high-density gas filaments in a molecular cloud, a
density increase rate $\dot \rho$ implies a mass accumulation time of $t_{\rm
acc}= \rho / \dot \rho= - \rho (\nabla \cdot (\rho \vec{v}))^{-1}$. The system
is non-stationary when the mass accumulation time becomes comparable to the
free-fall time $t_{\rm ff} = 1 / \sqrt{G \rho}$. We study fragmentation in
non-stationary settings, and find that accretion can significantly increase in
the characteristic mass of gravitational fragmentation ( $\lambda_{\rm Jeans,\;
aac}= \lambda_{\rm Jeans} (1 + t_{\rm ff} / t_{\rm acc})^{1/3}$, $m_{\rm
Jeans,\, acc} = m_{\rm Jeans} (1 + t_{\rm ff} / t_{\rm acc})$). In massive
star-forming regions, this mechanism of transport-driven super-jeans
fragmentation can contribute to the formation of massive stars by causing
order-of-magnitude increases in the mass of the fragments.
