  Nucleation is considered near the pseudospinodal in a one-dimensional
$\phi^4$ model with a non-conserved order parameter and long-range
interactions. For a sufficiently large system or a system with slow relaxation
to metastable equilibrium, there is a non-negligible probability of nucleation
occurring before reaching metastable equilibrium. This process is referred to
as transient nucleation. The critical droplet is defined to be the
configuration of maximum likelihood that is dynamically balanced between the
metastable and stable wells. Time-dependent droplet profiles and nucleation
rates are derived, and theoretical results are compared to computer simulation.
The analysis reveals a distribution of nucleation times with a distinct peak
characteristic of a nonstationary nucleation rate. Under the quench conditions
employed, transient critical droplets are more compact than the droplets found
in metastable equilibrium simulations and theoretical predictions.
