  Solving Newtonian steady-state wind equations with accurate weak interaction
rates and magnetic fields (MFs) of young neutron stars considered, we study the
dynamics and nucleosynthesis of neutrino-driven winds (NDWs) from proto neutron
stars (PNSs). For a typical 1.4 M$_{\odot}$ PNS model, we find the
nucleosynthesis products are closely related to the luminosity of neutrinos and
anti-neutrinos. The lower the luminosity is, the larger effect to the NDWs
caused by weak interactions and MFs is. At a high anti-neutrino luminosity of
typically $8\times 10^{51}$ erg s$^{-1}$, neutrinos and anti-neutrinos dominate
the processes in a NDW and the MFs hardly change the wind's properties. While
at a low anti-neutrino luminosity of $10^{51}$ erg s$^{-1}$ at the late stage
of a NDW, the mass of product and nucleosynthesis are changed significantly in
the strong MFs, they are less important than those in the early stage when the
anti-neutrino luminosity is high. Therefore for the most models considered for
the NDWs from PNSs, based on our calculations the influences of MFs and the net
weak interactions on the nucleosynthesis is not significant.
