The theory of finite-size scaling explains how the singular behavior of thermodynamic quantities in the critical point of a phase transition emerges when the size of the system becomes infinite. Usually, this theory is presented in a phenomenological way. Here, we exactly demonstrate the existence of a finite-size scaling law for the Galton-Watson branching processes when the number of offsprin...

The relation between universality and temporal and spatial scaling of structurefunctions and moments of the coarse-grained energy dissipation in turbulence is studied for flows where the Taylor Frozen Flow Hypothesis holds exactly. To account for observed deviations from a strict scaling law, we conclude that non-constant scaling exponents depend on the mean flow U . Furthermore, spatial and te...

We present here a new calculation of the γ-ray spectrum from pp → π in the Galactic ridge environment. The calculation includes the diffractive pp interaction and incorporates the Feynman scaling violation for the first time. Galactic diffuse γ-rays come, predominantly, from π → γγ in the sub-GeV to multi-GeV range. Hunter et al. found, however, an excess in the GeV range (“GeV Excess”) in the ...

Forest fire burn areas in the western Canadian provinces of Alberta and British Columbia have cumulative frequency-area istributions that are well described by a power law or an upper-truncated power law. The power law scaling extends over as any as five orders of magnitude and is observed for different geographical regions and for time intervals ranging from 1 to 40 ears. The observed scaling ...

The capacity scaling law of wireless networks has been considered as one of the most fundamental issues. In this survey, we aim at providing a comprehensive overview of the development in the area of scaling laws for throughput capacity and delay in wireless networks. We begin with background information on the notion of throughput capacity of random networks. Based on the benchmark random netw...

Scaling behaviour has been observed at mesoscopic level irrespective of crystal structure, type of boundary and operative micro-mechanisms like slip and twinning. The presence of scaling at the meso-scale accompanied with that at the nano-scale clearly demonstrates the intrinsic spanning for different deformation processes and a true universal nature of scaling. The origin of a ½ power law in d...

We explore in depth the validity of a recently proposed scaling law for earthquake interevent time distributions in the case of the Southern California, using the waveform cross-correlation catalog of Shearer et al. Two statistical tests are used: on the one hand, the standard two-sample Kolmogorov-Smirnov test is in agreement with the scaling of the distributions. On the other hand, the one-sa...