Entropy and Long range correlations in literary English

Recently long range correlations were detected in nucleotide sequences and in human writings by several authors. We undertake here a systematic investigation of two books, Moby Dick by H. Melville and Grimm's tales, with respect to the existence of long range correlations. The analysis is based on the calculation of entropy like quantities as the mutual information for pairs of letters and the entropy, the mean uncertainty, per letter. We further estimate the number of different subwords of a given length $n$. Filtering out the contributions due to the effects of the finite length of the texts, we find correlations ranging to a few hundred letters. Scaling laws for the mutual information (decay with a power law), for the entropy per letter (decay with the inverse square root of $n$) and for the word numbers (stretched exponential growth with $n$ and with a power law of the text length) were found.Comment: 8 page

Thermodynamics of hot dense H-plasmas: Path integral Monte Carlo simulations and analytical approximations

This work is devoted to the thermodynamics of high-temperature dense hydrogen plasmas in the pressure region between $10^{-1}$ and $10^2$ Mbar. In particular we present for this region results of extensive calculations based on a recently developed path integral Monte Carlo scheme (direct PIMC). This method allows for a correct treatment of the thermodynamic properties of hot dense Coulomb systems. Calculations were performed in a broad region of the nonideality parameter $\Gamma \lesssim 3$ and degeneracy parameter $n_e \Lambda^3 \lesssim 10$. We give a comparison with a few available results from other path integral calculations (restricted PIMC) and with analytical calculations based on Pade approximations for strongly ionized plasmas. Good agreement between the results obtained from the three independent methods is found.Comment: RevTex file, 21 pages, 5 ps-figures include

Guessing probability distributions from small samples

We propose a new method for the calculation of the statistical properties, as e.g. the entropy, of unknown generators of symbolic sequences. The probability distribution $p(k)$ of the elements $k$ of a population can be approximated by the frequencies $f(k)$ of a sample provided the sample is long enough so that each element $k$ occurs many times. Our method yields an approximation if this precondition does not hold. For a given $f(k)$ we recalculate the Zipf--ordered probability distribution by optimization of the parameters of a guessed distribution. We demonstrate that our method yields reliable results.Comment: 10 pages, uuencoded compressed PostScrip

Star formation in shocked cluster spirals and their tails

Recent observations of ram pressure stripped spiral galaxies in clusters revealed details of the stripping process, i.e., the truncation of all interstellar medium (ISM) phases and of star formation (SF) in the disk, and multiphase star-forming tails. Some stripped galaxies, in particular in merging clusters, develop spectacular star-forming tails, giving them a jellyfish-like appearance. In merging clusters, merger shocks in the intra-cluster medium (ICM) are thought to have overrun these galaxies, enhancing the ambient ICM pressure and thus triggering SF, gas stripping and tail formation. We present idealised hydrodynamical simulations of this scenario, including standard descriptions for SF and stellar feedback. To aid the interpretation of recent and upcoming observations, we focus on particular structures and dynamics in SF patterns in the remaining gas disk and in the near tails, which are easiest to observe. The observed jellyfish morphology is qualitatively reproduced for, both, face-on and edge-on stripping. In edge-on stripping, the interplay between the ICM wind and the disk rotation leads to asymmetries along the ICM wind direction and perpendicular to it. The apparent tail is still part of a highly deformed gaseous and young stellar disk. In both geometries, SF takes place in knots throughout the tail, such that the stars in the tails show no ordered age gradients. Significant SF enhancement in the disk occurs only at radii where the gas will be stripped in due course.Comment: 6 pages, submitted to MNRAS Letter

Mass and Gas Profiles in A1689: Joint X-ray and Lensing Analysis

We carry out a comprehensive joint analysis of high quality HST/ACS and Chandra measurements of A1689, from which we derive mass, temperature, X-ray emission and abundance profiles. The X-ray emission is smooth and symmetric, and the lensing mass is centrally concentrated indicating a relaxed cluster. Assuming hydrostatic equilibrium we deduce a 3D mass profile that agrees simultaneously with both the lensing and X-ray measurements. However, the projected temperature profile predicted with this 3D mass profile exceeds the observed temperature by ~30% at all radii, a level of discrepancy comparable to the level found for other relaxed clusters. This result may support recent suggestions from hydrodynamical simulations that denser, more X-ray luminous small-scale structure can bias observed temperature measurements downward at about the same (~30%) level. We determine the gas entropy at 0.1r_{vir} (where r_{vir} is the virial radius) to be ~800 keV cm^2, as expected for a high temperature cluster, but its profile at >0.1r_{vir} has a power-law form with index ~0.8, considerably shallower than the ~1.1 index advocated by theoretical studies and simulations. Moreover, if a constant entropy ''floor'' exists at all, then it is within a small region in the inner core, r<0.02r_{vir}, in accord with previous theoretical studies of massive clusters.Comment: 18 pages, 20 figures, 7 tables, accepted for publication in MNRAS, minor changes to match published versio

Discovery of a very X-ray luminous galaxy cluster at z=0.89 in the WARPS survey

We report the discovery of the galaxy cluster ClJ1226.9+3332 in the Wide Angle ROSAT Pointed Survey (WARPS). At z=0.888 and L_X=1.1e45 erg/s (0.5-2.0 keV, h_0=0.5) ClJ1226.9+3332 is the most distant X-ray luminous cluster currently known. The mere existence of this system represents a huge problem for Omega_0=1 world models. At the modest (off-axis) resolution of the ROSAT PSPC observation in which the system was detected, ClJ1226.9+3332 appears relaxed; an off-axis HRI observation confirms this impression and rules out significant contamination from point sources. However, in moderately deep optical images (R and I band) the cluster exhibits signs of substructure in its apparent galaxy distribution. A first crude estimate of the velocity dispersion of the cluster galaxies based on six redshifts yields a high value of 1650 km/s, indicative of a very massive cluster and/or the presence of substructure along the line of sight. While a more accurate assessment of the dynamical state of this system requires much better data at both optical and X-ray wavelengths, the high mass of the cluster has already been unambiguously confirmed by a very strong detection of the Sunyaev-Zel'dovich effect in its direction (Joy et al. 2001). Using ClJ1226.9+3332 and ClJ0152.7-1357 (z=0.835), the second-most distant X-ray luminous cluster currently known and also a WARPS discovery, we obtain a first estimate of the cluster X-ray luminosity function at 0.8<z<1.4 and L_X>5e44 erg/s. Using the best currently available data, we find the comoving space density of very distant, massive clusters to be in excellent agreement with the value measured locally (z<0.3), and conclude that negative evolution is not required at these luminosities out to z~1. (truncated)Comment: accepted for publication in ApJ Letters, 6 pages, 2 figures, uses emulateapj.st

Statistical Mechanics of Canonical-Dissipative Systems and Applications to Swarm Dynamics

We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative systems can be used for an extension of the dynamics, which also includes elements such as the take-up/dissipation of energy. This way, a rather complex dynamics can be mapped to an analytically tractable model, while still covering important features of non-equilibrium systems. In our paper, this approach is used to derive a rather general swarm model that considers (a) the energetic conditions of swarming, i.e. for active motion, (b) interactions between the particles based on global couplings. We derive analytical expressions for the non-equilibrium velocity distribution and the mean squared displacement of the swarm. Further, we investigate the influence of different global couplings on the overall behavior of the swarm by means of particle-based computer simulations and compare them with the analytical estimations.Comment: 14 pages incl. 13 figures. v2: misprints in Eq. (40) corrected, ref. updated. For related work see also: http://summa.physik.hu-berlin.de/~frank/active.htm

Using Chandra to Unveil the High-Energy Properties of the High-Magnetic Field Radio Pulsar J1119-6127

(shortened) PSR J1119-6127 is a high magnetic field (B=4.1E13 Gauss), young (<=1,700 year-old), and slow (P=408 ms) radio pulsar associated with the supernova remnant (SNR) G292.2-0.5. In 2003, Chandra allowed the detection of the X-ray counterpart of the radio pulsar, and provided the first evidence for a compact pulsar wind nebula (PWN). We here present new Chandra observations which allowed for the first time an imaging and spectroscopic study of the pulsar and PWN independently of each other. The PWN is only evident in the hard band and consists of jet-like structures extending to at least 7" from the pulsar, with the southern `jet' being longer than the northern `jet'. The spectrum of the PWN is described by a power law with a photon index~1.1 for the compact PWN and ~1.4 for the southern long jet (at a fixed column density of 1.8E22/cm2), and a total luminosity of 4E32 ergs/s (0.5-7 keV), at a distance of 8.4 kpc. The pulsar's spectrum is clearly softer than the PWN's spectrum. We rule out a single blackbody model for the pulsar, and present the first evidence of non-thermal (presumably magnetospheric) emission that dominates above ~3keV. A two-component model consisting of a power law component (with photon index ~1.5--2.0) plus a thermal component provides the best fit. The thermal component can be fit by either a blackbody model with a temperature kT~0.21 keV, or a neutron star atmospheric model with a temperature kT~0.14 keV. The efficiency of the pulsar in converting its rotational power, Edot, into non-thermal X-ray emission from the pulsar and PWN is ~5E-4, comparable to other rotation-powered pulsars with a similar Edot. We discuss our results in the context of the X-ray manifestation of high-magnetic field radio pulsars in comparison with rotation-powered pulsars and magnetars.Comment: 26 pages including 3 tables and 7 figures. Accepted for publication in Ap