We analyze the distribution of income and income tax of individuals in Japan for the fiscal year 1998. From the rank-size plots we find that the accumulated probability distribution of both data obey a power law with a Pareto exponent very close to −2. We also present an analysis of the distribution of the debts owed by bankrupt companies from 1997 to March, 2000, which is consistent with a pow...

We investigate numerically the failure process when two elastic media, one hard and one soft that have been glued together thus forming a common interface, are pulled apart. We present three main results: (1) The area distribution of simultaneously failing glue (bursts) follows a power law consistent with the theoretically expected exponent 2.5, (2) the maximum load and displacement before cata...

We study domain coarsening of two-dimensional stripe patterns by numerically solving the Swift-Hohenberg model of Rayleigh-Bénard convection. Near the bifurcation threshold, the evolution of disordered configurations is dominated by grain-boundary motion through a background of largely immobile curved stripes. A numerical study of the distribution of local stripe curvatures, of the structure fa...

Two separate statistical tests are described and developed in order to test unbinned data sets for adherence to the power-law form. The first test employs the TP-statistic, a function defined to deviate from zero when the sample deviates from the power-law form, regardless of the value of the power index. The second test employs a likelihood ratio test to reject a power-law background in favor ...

When investigating the dynamical properties of complex multiple-component physical and physiological systems, it is often the case that the measurable system's output does not directly represent the quantity we want to probe in order to understand the underlying mechanisms. Instead, the output signal is often a linear or nonlinear function of the quantity of interest. Here, we investigate how v...

An exact solution is presented to a model that mimics the crowding effect in financial markets which arises when groups of agents share information. We show that the size distribution of groups of agents has a power law tail with an exponential cut-off. As the size of these groups determines the supply and demand balance, this implies heavy tails in the distribution of price variation. The mome...

Power law distribution seems to be an important characteristic of web graphs. Several existing web graph models generate power law graphs by adding new vertices and non-uniform edge connectivities to existing graphs. Researchers have conjectured that preferential connectivity and incremental growth are both required for the power law distribution. In this paper, we propose a different web graph...

“Our analysis finds Earth’s lakes are power-law distributed for lakes ≥ 8.5 km2 (Fig. 2). Lakes < 8.5 km2 deviate from the power-law distribution such that there are fewer of these small lakes than expected if small lakes conformed to the same power-law distribution as large lakes. Across the range of lake sizes conforming to a power-law distribution, the tail exponent is τ = 1.97 (+ /− 0.01), ...

Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an explanation of how it can arise from a more basic underlying mechanism of competition between opposing forces. We introduce a family of one-dimensional geometri...

We trace the rank size distribution of notes in harmonic music, which on previous works we suggested was much better represented by the Two-parameter, first class Beta distribution than the customary power law, to the ranked mixing of distributions dictated by the harmonic and instrumental nature of the piece. The same representation is shown to arise in other fields by the same type of ranked ...