The unified scaling law for earthquakes, proposed by Bak, Christensen, Danon and Scanlon, is shown to hold worldwide, as well as for areas as diverse as Japan, New Zealand, Spain or New Madrid. The scaling functions that account for the rescaled recurrence-time probability densities show a power-law behavior for long times, with a universal exponent about (minus) 2.2. Another decreasing power l...

We make an experimental characterization of the effect that static disorder has on the shape of a normal Saffman-Taylor finger. We find that static noise induces a small amplitude and long wavelength instability on the sides of the finger. Fluctuations on the finger sides have a dominant wavelength, indicating that the system acts as a selective amplifier of static noise. The dominant wavelengt...

We present a GRANAT/SIGMA observation of the soft gamma-ray afterglow immediately after GRB 920723. The main burst is very bright. After ∼ 6 s, the burst light curve makes a smooth transition into an afterglow where flux decays as t −0.7. The power-law decay lasts for at least 1000 s; beyond this time, the afterglow emission is lost in the background fluctuations. At least ∼20% of main burst en...

Zipf’s law of word frequencies for language discourses is established with statistical rigor. Data show a departure from Zipf’s power law term at low frequencies. This is accounted by a modifying exponential term. Both arise naturally in a model for word frequencies based on Information Theory, algorithmic coding of a text preserving the symbol sequence, concepts from quantum statistical physic...

We have studied an ultra-luminous X-ray source (ULX) in the dwarf galaxy NGC 5408 with a series of XMM-Newton observations, between 2001 July and 2003 January. We find that its X-ray spectrum is best fitted with a power law of photon index Γ ≈ 2.6–2.9 and a thermal component with blackbody temperature kT bb ≈ 0.12–0.14 keV. These spectral features, and the inferred luminosity ≈ 10 40 erg s −1 i...

All articles available through Birkbeck ePrints are protected by intellectual property law, including copyright law. Any use made of the contents should comply with the relevant law. Copyright © 2003 Taylor & Francis. This is an electronic version of an article published in Philosophical Psychology. Philosophical Psychology is available online at: http://www.informaworld.com/ The final version ...

We investigate the statistics of extinction sizes and the taxonomy in a trophic model of evolution recently proposed [Phys. Rev. Lett. 82, 652 (1999)]. By further exploring the parameters of this model, we find that the distribution of extinction sizes N(s) shows typically a characteristic maximum before developing the power-law behavior N(s) approximately s(-alpha) with alpha approximately 2, ...

The well-known Sachs and Taylor bounds provide easy inner and outer estimates for the effective yield set of a polycrystal. It is natural to ask whether they can be improved. We examine this question for two model problems, involving 3D gradients and divergence-free vector fields. For 3D gradients the Taylor bound is far from optimal: we derive an improved estimate which scales differently when...

We study the dynamic and kinematic collision statistics of cloud droplets for a range of flow Taylor microscale Reynolds numbers (up to 500), using a highly scalable hybrid direct numerical simulation approach. Accurate results of radial relative velocity (RRV) and radial distribution function (RDF) at contact have been obtained by taking advantage of their power-law scaling at short separation...

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.