  The information about the current-carrying ability of a type-II
superconductor can be obtained by studying the flux relaxation and vortex
penetration phenomena in the superconductor. In early studies, the infinite
series models of the flux relaxation and vortex penetration phenomena were
constructed at a vanishing current density and vanishing internal field,
respectively. However, this is not the only possibility. Here it is shown that
one can reconstruct the theoretical models at the critical points. The new
polynomial model of the flux relaxation (vortex penetration) phenomenon was
constructed by expanding the vortex activation energy as an infinite series of
the current density (internal field) about the critical current density
(equilibrium internal field). The unification of the polynomial models was
proposed. The inverse model of the flux relaxation (vortex penetration)
phenomenon was also constructed by expanding the vortex activation energy as an
infinite series of the inverse current density (inverse internal field) about
the critical current density (equilibrium internal field).
