The high-order statistics of fluctuations in velocity gradients in the crossover range from the inertial to the Kolmogorov and sub-Kolmogorov scales are studied by direct numerical simulations (DNS) of homogeneous isotropic turbulence with vastly improved resolution. The derivative moments for orders 0 ≤ n ≤ 8 are represented well as powers of the Reynolds number, Re, in the range 380 ≤ Re ≤ 22...

In this paper, we address the logarithmic corrections to the leading power laws that govern thermodynamic quantities as a second-order phase transition point is approached. For phase transitions of spin systems on d-dimensional lattices, such corrections appear at some marginal values of the order parameter or space dimension. We present scaling relations for these exponents. We also consider a...

We have to go back to the late eighties[1,2] to find the first evidence for the existence of a phase transition separating the crumpled and smooth regimes in mathematical models of surfaces defined on a mesh with fixed connectivity. However, the actual values of the critical exponents associated to this phase transition remain largely unknown. Their determination is crucial to identify which ty...

The renowned general epidemic process describes the stochastic evolution of a population of individuals which are either susceptible, infected or dead. A second order phase transition belonging to the universality class of dynamic isotropic percolation lies between endemic or pandemic behavior of the process. We generalize the general epidemic process by introducing a fourth kind of individuals...

Generalized multifractality characterizes scaling of eigenstate observables at Anderson-localization critical points. We explore generalized in 2D systems, with the main focus on spin quantum Hall (SQH) transition superconductors symmetry class C. Relations and differences conventional integer (IQH) are also studied. Using field-theoretical formalism non-linear sigma-model, we derive pure-scali...

The temporal dynamics of complex networks such as the Internet are characterized by a power scaling between the temporal mean and dispersion of signals at each network node. Here we tested the hypothesis that the temporal dynamics of the brain networks are characterized by a similar power law. This realization could be useful to assess the effects of randomness and external modulators on the br...

The scaling of metabolic rates to body size is widely considered to be of great biological and ecological importance, and much attention has been devoted to determining its theoretical and empirical value. Most debate centers on whether the underlying power law describing metabolic rates is 2/3 (as predicted by scaling of surface area/volume relationships) or 3/4 ("Kleiber's law"). Although rec...

The scaling behavior of self-avoiding walks (SAWs) on the backbone of percolation clusters in two, three and four dimensions is studied by Monte Carlo simulations. We apply the pruned-enriched Rosenbluth chain-growth method (PERM). Our numerical results bring about the estimates of critical exponents, governing the scaling laws of disorder averages of the end-to-end distance of SAW configuratio...

We investigate the breakdown of disordered networks under the action of an increasing external-mechanical or electrical-force. We perform a mean-field analysis and estimate scaling exponents for the approach to the instability. By simulating two-dimensional models of electric breakdown and fracture we observe that the breakdown is preceded by avalanche events. The avalanches can be described by...