The effect of disorder is investigated in granular superconductive materials with strong and weak links. The transition is controlled by the interplay of the emph{tunneling} $g$ and emph{intragrain} $g_{intr}$ conductances, which depend on the streng
th of the intergrain coupling. For $g ll g_{intr}$, the transition involves first the grain boundary, while for $g sim g_{intr}$ the transition occurs into the whole grain. The different intergrain coupling is considered by modelling the superconducting material as a disordered network of Josephson junctions. Numerical simulations show that on increasing the disorder, the resistive transition occurs for lower temperatures and the curve broadens. These features are enhanced in disordered superconductors with strong links. The different behaviour is further checked by estimating the average network resistance for weak and strong links in the framework of the effective medium approximation theory. These results may be relevant to shed light on long standing puzzles as: (i) enhancement of the superconducting transition temperature of many metals in the granular states; (ii) suppression of superconductivity in homogeneously disordered films compared to standard granular systems close to the metal-insulator transition; (iii) enhanced degradation of superconductivity by doping and impurities in strongly linked materials, such as magnesium diboride, compared to weakly-linked superconductors, such as cuprates.
Systems with the coexistence of different stable attractors are widely exploited in systems biology in order to suitably model the differentiating processes arising in living cells. In order to describe genetic regulatory networks several determinist
ic models based on systems of nonlinear ordinary differential equations have been proposed. Few studies have been developed to characterize how either an external input or the coupling can drive systems with different coexisting states. For the sake of simplicity, in this manuscript we focus on systems belonging to the class of radial isochron clocks that exhibits hard excitation, in order to investigate their complex dynamics, local and global bifurcations arising in presence of constant external inputs. In particular the occurrence of saddle node on limit cycle bifurcations is detected.
The relationship between the size and the variance of firm growth rates is known to follow an approximate power-law behavior $sigma(S) sim S^{-beta(S)}$ where $S$ is the firm size and $beta(S)approx 0.2$ is an exponent weakly dependent on $S$. Here w
e show how a model of proportional growth which treats firms as classes composed of various number of units of variable size, can explain this size-variance dependence. In general, the model predicts that $beta(S)$ must exhibit a crossover from $beta(0)=0$ to $beta(infty)=1/2$. For a realistic set of parameters, $beta(S)$ is approximately constant and can vary in the range from 0.14 to 0.2 depending on the average number of units in the firm. We test the model with a unique industry specific database in which firm sales are given in terms of the sum of the sales of all their products. We find that the model is consistent with the empirically observed size-variance relationship.
The resistive transition of granular high-T$_c$ superconductors, characterized by either weak (YBCO-like) or strong (MgB$_2$-like) links, occurs through a series of avalanche-type current density rearrangements. These rearrangements correspond to the
creation of resistive layers, crossing the whole specimen approximately orthogonal to the current density direction, due to the simultaneous transition of a large number of weak-links or grains. The present work shows that exact solution of the Kirchhoff equations for strongly and weakly linked networks of nonlinear resistors, with Josephson junction characteristics, yield the subsequent formation of resistive layers within the superconductive matrix as temperature increases. Furthermore, the voltage noise observed at the transition is related to the resistive layer formation process. The noise intensity is estimated from the superposition of voltage drop elementary events related to the subsequent resistive layers. At the end of the transition, the layers mix-up, the step amplitude decreases and the resistance curve smoothes. This results in the suppression of noise, as experimentally found. Remarkably, a scaling law for the noise intensity with the network size is argued. It allows to extend the results to networks with arbitrary size and, thus, to real specimens.
