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We investigate the flux penetration patterns and matching fields of a long cylindrical wire of circular cross section in the presence of an external magnetic field. For this study we write the London theory for a long cylinder both for the mixed and Meissner state, with boundary conditions appropriate for this geometry. Using the Monte Carlo Simulated Annealing method, the free energy of the mixed state is minimized with respect to the vortex position and we obtain the ground state of thedoi:10.1103/physrevb.58.5789 fatcat:hq43ff5levgo5fl3ohk6fo55nm