The RANLUX generator: resonances in a random walk test

Using a recently proposed directed random walk test, we systematically investigate the popular random number generator RANLUX developed by Luescher and implemented by James. We confirm the good quality of this generator with the recommended luxury level. At a smaller luxury level (for instance equal to 1) resonances are observed in the random walk test. We also find that the lagged Fibonacci and Subtract-with-Carry recipes exhibit similar failures in the random walk test. A revised analysis of the corresponding dynamical systems leads to the observation of resonances in the eigenvalues of Jacobi matrix.Comment: 18 pages with 14 figures, Essential addings in the Abstract onl

A new integrable generalization of the Korteweg - de Vries equation

A new integrable sixth-order nonlinear wave equation is discovered by means of the Painleve analysis, which is equivalent to the Korteweg - de Vries equation with a source. A Lax representation and a Backlund self-transformation are found of the new equation, and its travelling wave solutions and generalized symmetries are studied.Comment: 13 pages, 2 figure

Dispersion and collapse of wave maps

We study numerically the Cauchy problem for equivariant wave maps from 3+1 Minkowski spacetime into the 3-sphere. On the basis of numerical evidence combined with stability analysis of self-similar solutions we formulate two conjectures. The first conjecture states that singularities which are produced in the evolution of sufficiently large initial data are approached in a universal manner given by the profile of a stable self-similar solution. The second conjecture states that the codimension-one stable manifold of a self-similar solution with exactly one instability determines the threshold of singularity formation for a large class of initial data. Our results can be considered as a toy-model for some aspects of the critical behavior in formation of black holes.Comment: 14 pages, Latex, 9 eps figures included, typos correcte

A deep Chandra observation of the Perseus cluster: shocks and ripples

We present preliminary results from a deep observation lasting almost 200 ks, of the centre of the Perseus cluster of galaxies around NGC 1275. The X-ray surface brightness of the intracluster gas beyond the inner 20 kpc, which contains the inner radio bubbles, is very smooth apart from some low amplitude quasi-periodic ripples. A clear density jump at a radius of 24 kpc to the NE, about 10 kpc out from the bubble rim, appears to be due to a weak shock driven by the northern radio bubble. A similar front may exist round both inner bubbles but is masked elsewhere by rim emission from bright cooler gas. The continuous blowing of bubbles by the central radio source, leading to the propagation of weak shocks and viscously-dissipating sound waves seen as the observed fronts and ripples, gives a rate of working which balances the radiative cooling within the inner 50 kpc of the cluster core.Comment: Accepted for publication in MNRAS (minor changes) Higher picture quality available from http://www-xray.ast.cam.ac.uk/papers/per_200ks.pd

Star Formation, Radio Sources, Cooling X-ray Gas, and Galaxy Interactions in the Brightest Cluster Galaxy in 2A0335+096

We present deep emission-line imaging taken with the SOAR Optical Imaging Camera of the brightest cluster galaxy (BCG) in the nearby (z=0.035) X-ray cluster 2A0335+096. We analyze long-slit optical spectroscopy, archival VLA, Chandra X-ray, and XMM UV data. 2A0335+096 is a bright, cool-core X-ray cluster, once known as a cooling flow. Within the highly disturbed core revealed by Chandra X-ray observations, 2A0335+096 hosts a highly structured optical emission-line system. The redshift of the companion is within 100 km/s of the BCG and has certainly interacted with the BCG, and is likely bound to it. The comparison of optical and radio images shows curved filaments in H-alpha emission surrounding the resolved radio source. The velocity structure of the emission-line bar between the BCG nucleus and the companion galaxy provides strong evidence for an interaction between the two in the last ~50 Myrs. The age of the radio source is similar to the interaction time, so this interaction may have provoked an episode of radio activity. We estimate a star formation rate of >7 solar mass/yr based on the Halpha and archival UV data, a rate similar to, but somewhat lower than, the revised X-ray cooling rate of 10-30 solar masses/year estimated from XMM spectra by Peterson & workers. The Halpha nebula is limited to a region of high X-ray surface brightness and cool X-ray temperature. The detailed structures of H-alpha and X-ray gas differ. The peak of the X-ray emission is not the peak of H-alpha emission, nor does it lie in the BCG. The estimated age of the radio lobes and their interaction with the optical emission-line gas, the estimated timescale for depletion and accumulation of cold gas, and the dynamical time in the system are all similar, suggesting a common trigger mechanism.Comment: Accepted AJ, July 2007 publication. Vol 134, p. 14-2