Measurements of the electrical response of granular Sn-Ge thin films below the superconducting transition temperature are reported. Addition of an external noise to the magnetic field applied to the sample is found to increase the sample voltage response to a small externally applied ac signal. The gain coefficient for this signal as well as the signal-to-noise ratio displays clear maxima at particular noise levels. We interpret these observations as a stochastic resonance in the percolative Josephson media that occurs close to the percolation threshold.

We present the exact and complete analytical solution of the classical problem of the Josephson tunnel junction of arbitrary length <$E W~symbol <174>~(0,~inf )> in the presence of externally applied magnetic fields and transport currents. Contrary to a wide-spread belief, the exact analytical solution unambiguously proves the absence of any qualitative difference between the so-called "small" (<$E W~<< <<~1>) and "large" junctions (<$E W~>> >>~1>). Another unexpected physical implication of the exact analytical solution is the existence (in the current-carrying state) of unquantized Josephson vortices carrying fractional flux and located near one of the junction's edges. We also refine on the mathematical definition of critical transport current.