  Despite the fact that Josephson Junction Arrays (JAA) have been actively
studied for decades, they continue to contribute to the variety of intriguing
and peculiar phenomena (both fundamental and important for potential
applications) providing at the same time a useful tool for testing new
theoretical ideas. To give just a few recent examples, it is sufficient to
mention paramagnetic Meissner effect (PME) as well as the recently introduced
thermophase and piezophase effects suggesting, respectively, a direct influence
of a thermal gradient and an applied stress on phase difference between the
adjacent grains. At the same time, an artificially prepared islands of
superconducting grains, well-described by the various models of JJAs, proved
useful in studying the charging effects in these systems, ranging from Coulomb
blockade of Cooper pair tunneling and Bloch oscillations to propagation of
quantum ballistic vortices. The present paper reviews some of the recently
suggested novel effects which should manifest themselves either in
weak-links-bearing superconductors or in artificially prepared JJAs. In Section
2 we consider the appearance of an electric-field induced magnetization (analog
of the so-called magnetoelectric effect) in a model granular superconductor.
The dual effect, that is an appearance of a magnetic field induced electric
polarization is studied in Section 3. Finally, in Section 4 we discuss a
possibility of two other interesting effects which are expected to occur in a
granular material under mechanical loading. Specifically, we predict the
existence of stress induced paramagnetic moment in zero applied magnetic field
(Josephson piezomagnetism) and study its influence on a low-field magnetization
(leading to a mechanically induced PME).
