Final Activity Report Summary - CFNANOSC (Controlling the Critical Parameters and Flux Motion in Nanostructured Superconductors) One of the main objectives of applied superconductivity is a considerable increase of the superconducting critical parameters, i.e. the maximum values of temperature, magnetic field and current the material can sustain without deterioration of its superconducting properties. In principle, all of the critical parameters can be improved by reducing the dimensions of superconductors or through their nano-patterning. Thus the critical current can be enhanced by introducing non-superconducting inclusions which can trap magnetic flux preventing its motion and, consequently, the energy dissipation. Effective trap and control of the motion of magnetic flux lines, or vortices, in mesoscopic and nano-patterned superconductors involving a complex interplay of many interactions is an important fundamental problem. On the other hand, this opens wide prospective for 'new functionalities' and device concepts, e.g. guided flux motion, ratchet effect, fluxonics, fluxon optics and computing. In this study we addressed several important related problems. Formation of vortex shells in mesoscopic superconducting disks and symmetric polygons. Recent experiments revealed vortex shells in micrometer-sized Nb disks. We studied the formation and size-dependence of vortex shells in disks and pillars, and we explained the experimental results and discrepancies with previous theoretical studies. We showed that the filling rules for vortices in symmetric polygons can also be formulated in terms of formation of vortex 'shells' and analysed the stability of the vortex configurations. Pinning-induced formation of vortex clusters and giant vortices in mesoscopic superconducting disks. We revealed a new, disorder-induced, mechanism of clustering and giant-vortex formation in mesoscopic disks. It is related to the selective enhancement of pinning strength in disks and results in a pronounced diamagnetic response, as confirmed by Bitter-decoration experiments. Unconventional vortex dynamics in mesoscopic superconducting Corbino disks. We found that the interplay between the (in)commensurability effects, the vortex-vortex interaction and the gradient Lorentz force in a mesoscopic Corbino disk can result in: (i) unconventional angular melting that first occurs near the boundary where the shear stress is minimum; (ii) unconventional shell dynamics when a shell that experiences a weaker Lorentz force moves faster than the adjacent shell driven by a stronger Lorentz force. Collective vortex phases in periodic plus random pinning potential. We studied the simultaneous effect of regular and random pinning potentials on the vortex lattice structure. We identified different kinds of defects and found that the disordering of the vortex lattice can occur in two steps: (i) appearance of elastic chains of depinned vortices and their percolation via fractal-like structures; (ii) nucleation of domains of depinned vortices. We demonstrated that under applied driving force, vortex transfer is controlled by kinks and antikinks and revealed different dynamical phases of the vortex motion. Guidance of (anti)vortices and in a superconductor with an array of magnetic dipoles. The interplay between the attractive vortex-antivortex interaction and the Lorentz force leads either to separation and moving (anti)vortices in opposite directions, or to their annihilation. We found that the direction of the motion of v-av does not coincide with the direction of the Lorents force. This guidance effect can be controlled by tuning the current and the magnetization of the magnetic dipoles. We also addressed related interdisciplinary topics: (i) The dynamics of colloids in a narrow channel. We found that the transition from elastic to plastic mode is either monotonic, or it contains an NDR-type part (a drop of mobility vs. driving force). This unusual 'solidification' is related to the dynamically-induced increase of the friction. (ii) Single file diffusion of interacting particles in a one-dimensional channel. We found that contrary to previous findings, SFD depends on the inter-particle interaction and could become slower than in theoretical 1D sub-diffusive regime.