Influence of the boundary conditions on the current flow pattern along a superconducting wire

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We study the patterns at which the current flow stabilizes in a 1D superconducting wire, for various experimentally reasonable boundary conditions, for small fixed current densities and temperatures close to $T_c$. We pay special attention to the possible existence of a stationary regime. If the contacts are superconducting, truly stationary or normal regimes do not exist, but can be approached as a limit. In the case of weak superconducting contacts, a rich phase diagram is found, with several periodic regimes that involve two phase slip centers. For some of these regimes, the density of Cooper pairs does not have mirror symmetry. If the contacts are normal, the stationary regime is possible.