We show that the distribution of waiting times between earthquakes occurring in California obeys a simple unified scaling law valid from tens of seconds to tens of years. The short time clustering, commonly referred to as aftershocks, is nothing but the short time limit of the general hierarchical properties of earthquakes. There is no unique operational way of distinguishing between main shock...

Scaling laws for third-order susceptibilities are important in guiding efforts to develop better nonlinear-optical materials. Usually these scaling laws are derived by consideration of simplified model systems chosen for analytic or computational tractability, and they are mostly untested by experiment.'3 Here we derive a scaling law based on an essentially exact solution for the hyperpolarizab...

We consider LDPC codes, transmission over the binary symmetric channel (BSC), and decoding using Gallager’s algorithm A. For those ensembles whose threshold is determined by the behavior of the algorithm at the beginning of the decoding process we derive a scaling law. This scaling law has the same form as the scaling law which was established for the the case of transmission over the binary er...

Many scientists are interested in but puzzled by the various inverse power laws with a negative exponent 1 such as the rank-size rule. The rank-size rule is a very simple scaling law followed by many observations of the ubiquitous empirical patterns in physical and social systems. Where there is a rank-size distribution, there will be a hierarchy with cascade structure. However, the equivalence...

Introduction: Previous studies with numerical collisional models have demonstrated that wave-like departures from traditional, linear power-law equilibrium size distributions can result from a small-size cutoff in the particle population [1–4]. At small sizes, a particle cutoff may result from the rapid removal of bodies by non-gravitational forces such as PoyntingRobertson drag or the Yarkovsk...

BACKGROUND Allometric scaling, which represents the dependence of biological traits or processes on body size, is a long-standing subject in biological science. However, there has been no study to consider heat loss to the ambient and an insulation layer representing mammalian skin and fur for the derivation of the scaling law of metabolism. METHODS A simple heat transfer model is proposed to...

The presence of self-organized criticality in biology is often evidenced by a power-law scaling of event size distributions, which can be measured by linear regression on logarithmic axes. We show here that such a procedure does not necessarily mean that the system exhibits self-organized criticality. We first provide an analysis of multisite local field potential (LFP) recordings of brain acti...

[1] We investigate the physics of multiscale convection in Earth’s mantle, characterized by the coexistence of large-scale mantle circulation associated with plate tectonics and small-scale sublithospheric convection. In this study, conditions for the existence of smallscale convection beneath oceanic lithosphere are investigated by deriving a scaling law for the onset of convection in a fluid ...