  Nanostructuring of superconducting materials to form dense arrays of thin
parallel nanowires with significantly large transverse Josephson coupling has
proven to be an effective way to increase the upper critical field of
superconducting elements by as much as two orders of magnitude as compared to
the corresponding bulk materials and, in addition, may cause considerable
enhancements in their critical temperatures. Such materials have been realized
in the linear pores of mesoporous substrates or exist intrinsically in the form
of various quasi-1D crystalline materials. The transverse coupling between the
superconducting nanowires is determined by the size-dependent coherence length
E0. In order to obtain E0 over the Langer-Ambegaokar- McCumber-Halperin (LAMH)
theory, extensive experimental fitting parameters have been required over the
last 40 years. We propose a novel Monte Carlo algorithm for determining E0 of
the multi-Cooper pair system in the 1D limit. The concepts of uncertainty
principle, Pauli-limit, spin flip mechanism, electrostatic interaction, thermal
perturbation and co-rotating of electrons are considered in the model. We use
Pb nanowires as an example to monitor the size effect of E0 as a result of the
modified electron-electron interaction without the need for experimental
fitting parameters. We investigate how the coherence length determines the
transverse coupling of nanowires in dense arrays. This determines whether or
not a global phase-coherent state with zero resistance can be formed in such
arrays. Our Monte Carlo results are in very good agreement with experimental
data from various types of superconducting nanowire arrays
