Novel critical phenomena in optimization driven processes on networks

The work presented in this Ph.D thesis was developed in the context of complex network theory, from a statistical physics standpoint. We examine two distinct problems in this research field, taking a special interest in their respective critical properties. In both cases, the emergence of criticality is driven by a local optimization dynamics. Firstly, a recently introduced class of percolation problems that attracted a significant amount of attention from the scientific community, and was quickly followed up by an abundance of other works. Percolation transitions were believed to be continuous, until, recently, an 'explosive' percolation problem was reported to undergo a discontinuous transition, in [93]. The system's evolution is driven by a metropolis-like algorithm, apparently producing a discontinuous jump on the giant component's size at the percolation threshold. This finding was subsequently supported by number of other experimental studies [96, 97, 98, 99, 100, 101]. However, in [1] we have proved that the explosive percolation transition is actually continuous. The discontinuity which was observed in the evolution of the giant component's relative size is explained by the unusual smallness of the corresponding critical exponent, combined with the finiteness of the systems considered in experiments. Therefore, the size of the jump vanishes as the system's size goes to infinity. Additionally, we provide the complete theoretical description of the critical properties for a generalized version of the explosive percolation model [2], as well as a method [3] for a precise calculation of percolation's critical properties from numerical data (useful when exact results are not available). Secondly, we study a network flow optimization model, where the dynamics consists of consecutive mergings and splittings of currents flowing in the network. The current conservation constraint does not impose any particular criterion for the split of current among channels outgoing nodes, allowing us to introduce an asymmetrical rule, observed in several real systems. We solved analytically the dynamic equations describing this model in the high and low current regimes. The solutions found are compared with numerical results, for the two regimes, showing an excellent agreement. Surprisingly, in the low current regime, this model exhibits some features usually associated with continuous phase transitions.

Thick-microstructures for MPGDs: simulations and experimental studies

Cherenkov Imaging counters require large photosensitive areas, capable of single photon detection, operating at stable high gains under radioactive backgrounds while standing high rates, providing a fast response and a good time resolution, and being insensitive to magnetic fields. The development of photon detectors based in Micro Pattern Gaseous detectors (MPGDs), represent a new generation of gaseous photon detectors. In particular, gaseous detectors based on stacked Thick-Gaseous Electron Multipliers (THGEMs), or THGEM based structures, coupled to a CsI photoconverter coating, seem to fulfil the requirements imposed by Cherenkov imaging counters. This work focus on the study of the THGEM-based detectors response as function of its geometrical parameters and applied voltages and electric fields, aiming a future upgrade of the Cherenkov Imaging counter RICH-1 of the COMPASS experiment at CERN SPS. Further studies to decrease the fraction of ions that reach the photocathode (Ion Back Flow – IBF) to minimize the ageing and maximize the photoelectron extraction are performed. Experimental studies are complemented with simulation results, also perfomed in this work.