Power law cumulative number-size distributions are widely used to describe the scaling properties of data sets and to establish scale invariance. We derive the relationships between the scaling exponents of non-cumulative and cumulative number-size distributions for linearly binned and logarithmically binned data. Cumulative number-size distributions for data sets of many natural phenomena exhi...

Magnetic-field-induced phase transitions were studied with a two-dimensional electron AlGaAs/GaAs system. The temperature-driven flow diagram shows the features of the Γ(2) modular symmetry, which includes distorted flowlines and shiftted critical point. The deviation of the critical conductivities is attributed to a small but resolved spin splitting, which reduces the symmetry in Landau quanti...

Conversion efficiency and electron temperature scaling laws are experimentally studied in the wavelength-cubed (l) regime, where a single-wavelength focus allows low energy pulses incident on a Mo target to produce x rays with excellent efficiency and improved spatial coherence. Focused intensity is varied from 2310 to 2310 W/cm. Conversion efficiency and electron temperature are best described...

Recently, by analyzing the measurement data of Nikuradze [NACA Tech. Memo No. 1292 (1950)], it has been proposed [N. Goldenfeld, Phys. Rev. Lett. 96, 044503 (2006)] that the friction factor, f , of rough-pipe flow obeys a scaling law in the turbulent regime. Here, we provide a phenomenological scaling argument to explain this law and demonstrate how intermittency modifies the scaling form, ther...

Motivated by an important discovery on the drag scaling law (the 4/3 power law) of a flexible fibre in a flowing soap film by Alben et al. (Nature vol. 420, 2002, p. 479) at high Reynolds numbers (2000<Re< 40 000), we investigate drag scaling laws at moderate Re for a compliant fibre tethered at the midpoint and submerged in an incompressible viscous flow using the immersed boundary (IB) method...

Computer simulations are used to test whether a recently introduced generalization of Rosenfeld's excess-entropy scaling method for estimating transport coefficients in systems obeying molecular dynamics can be extended to predict long-time diffusivities in fluids of particles undergoing Brownian dynamics in the absence of interparticle hydrodynamic forces. Model fluids with inverse-power-law, ...

The limits of a recently proposed universal scaling law for the probability distributions of earthquake recurrence times are explored. The scaling properties allow to improve the statistics of occurrence of large earthquakes over small areas by mixing rescaled recurrence times for different areas. In this way, the scaling law still holds for events with M≥5.5 at scales of about 20 km, and for M...

In this article, we study transportation network in Minnesota. We show that the system is characterized by Taylor’s power law for fluctuation scaling with nontrivial values of the scaling exponent. We also show that the characteristic exponent does not unequivocally characterize a given road network, as it may differ within the same network if one takes into account location of observation poin...

Recent advances in the theory of turbulent solutions of the Navier-Stokes equations are discussed and the existence of their associated invariant measures. The statistical theory given by the invariant measures is described and associated with historically-known scaling laws. These are Hack’s law in one dimension, the Bachelor-Kraichnan law in two dimensions and the Kolmogorov’s scaling law in ...

We study the sample-size dependence of the strength of disordered materials with a flaw, by numerical simulations of lattice models for fracture. We find a crossover between a regime controlled by the disorder and another controlled by stress concentrations, ruled by continuum fracture mechanics. The results are formulated in terms of a scaling law involving a statistical fracture process zone....