Another analytic view about quantifying social forces

Montroll had considered a Verhulst evolution approach for introducing a notion he called "social force", to describe a jump in some economic output when a new technology or product outcompetes a previous one. In fact, Montroll's adaptation of Verhulst equation is more like an economic field description than a "social force". The empirical Verhulst logistic function and the Gompertz double exponential law are used here in order to present an alternative view, within a similar mechanistic physics framework. As an example, a "social force" modifying the rate in the number of temples constructed by a religious movement, the Antoinist community, between 1910 and 1940 in Belgium is found and quantified. Practically, two temple inauguration regimes are seen to exist over different time spans, separated by a gap attributed to a specific "constraint", a taxation system, but allowing for a different, smooth, evolution rather than a jump. The impulse force duration is also emphasized as being better taken into account within the Gompertz framework. Moreover, a "social force" can be as here, attributed to a change in the limited need/capacity of some population, coupled to some external field, in either Verhulst or Gompertz equation, rather than resulting from already existing but competing goods as imagined by Montroll.Comment: 4 figures, 29 refs., 15 pages; prepared for Advances in Complex System

Correlation amplitude and entanglement entropy in random spin chains

Using strong-disorder renormalization group, numerical exact diagonalization, and quantum Monte Carlo methods, we revisit the random antiferromagnetic XXZ spin-1/2 chain focusing on the long-length and ground-state behavior of the average time-independent spin-spin correlation function C(l)=\upsilon l^{-\eta}. In addition to the well-known universal (disorder-independent) power-law exponent \eta=2, we find interesting universal features displayed by the prefactor \upsilon=\upsilon_o/3, if l is odd, and \upsilon=\upsilon_e/3, otherwise. Although \upsilon_o and \upsilon_e are nonuniversal (disorder dependent) and distinct in magnitude, the combination \upsilon_o + \upsilon_e = -1/4 is universal if C is computed along the symmetric (longitudinal) axis. The origin of the nonuniversalities of the prefactors is discussed in the renormalization-group framework where a solvable toy model is considered. Moreover, we relate the average correlation function with the average entanglement entropy, whose amplitude has been recently shown to be universal. The nonuniversalities of the prefactors are shown to contribute only to surface terms of the entropy. Finally, we discuss the experimental relevance of our results by computing the structure factor whose scaling properties, interestingly, depend on the correlation prefactors.Comment: v1: 16 pages, 15 figures; v2: 17 pages, improved discussions and statistics, references added, published versio

Aperiodic quantum XXZ chains: Renormalization-group results

We report a comprehensive investigation of the low-energy properties of antiferromagnetic quantum XXZ spin chains with aperiodic couplings. We use an adaptation of the Ma-Dasgupta-Hu renormalization-group method to obtain analytical and numerical results for the low-temperature thermodynamics and the ground-state correlations of chains with couplings following several two-letter aperiodic sequences, including the quasiperiodic Fibonacci and other precious-mean sequences, as well as sequences inducing strong geometrical fluctuations. For a given aperiodic sequence, we argue that in the easy-plane anisotropy regime, intermediate between the XX and Heisenberg limits, the general scaling form of the thermodynamic properties is essentially given by the exactly-known XX behavior, providing a classification of the effects of aperiodicity on XXZ chains. We also discuss the nature of the ground-state structures, and their comparison with the random-singlet phase, characteristic of random-bond chains.Comment: Minor corrections; published versio

A Method for Individual Source Brightness Estimation in Single- and Multi-band Data

We present a method of reliably extracting the flux of individual sources from sky maps in the presence of noise and a source population in which number counts are a steeply falling function of flux. The method is an extension of a standard Bayesian procedure in the millimeter/submillimeter literature. As in the standard method, the prior applied to source flux measurements is derived from an estimate of the source counts as a function of flux, dN/dS. The key feature of the new method is that it enables reliable extraction of properties of individual sources, which previous methods in the literature do not. We first present the method for extracting individual source fluxes from data in a single observing band, then we extend the method to multiple bands, including prior information about the spectral behavior of the source population(s). The multi-band estimation technique is particularly relevant for classifying individual sources into populations according to their spectral behavior. We find that proper treatment of the correlated prior information between observing bands is key to avoiding significant biases in estimations of multi-band fluxes and spectral behavior, biases which lead to significant numbers of misclassified sources. We test the single- and multi-band versions of the method using simulated observations with observing parameters similar to that of the South Pole Telescope data used in Vieira, et al. (2010).Comment: 11 emulateapj pages, 3 figures, revised to match published versio

Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice

We investigate the phase diagram of a discrete version of the Maier-Saupe model with the inclusion of additional degrees of freedom to mimic a distribution of rodlike and disklike molecules. Solutions of this problem on a Bethe lattice come from the analysis of the fixed points of a set of nonlinear recursion relations. Besides the fixed points associated with isotropic and uniaxial nematic structures, there is also a fixed point associated with a biaxial nematic structure. Due to the existence of large overlaps of the stability regions, we resorted to a scheme to calculate the free energy of these structures deep in the interior of a large Cayley tree. Both thermodynamic and dynamic-stability analyses rule out the presence of a biaxial phase, in qualitative agreement with previous mean-field results

Electron trapping and acceleration by the plasma wakefield of a self-modulating proton beam

It is shown that co-linear injection of electrons or positrons into the wakefield of the self-modulating particle beam is possible and ensures high energy gain. The witness beam must co-propagate with the tail part of the driver, since the plasma wave phase velocity there can exceed the light velocity, which is necessary for efficient acceleration. If the witness beam is many wakefield periods long, then the trapped charge is limited by beam loading effects. The initial trapping is better for positrons, but at the acceleration stage a considerable fraction of positrons is lost from the wave. For efficient trapping of electrons, the plasma boundary must be sharp, with the density transition region shorter than several centimeters. Positrons are not susceptible to the initial plasma density gradient.Comment: 9 pages, 9 figures, 1 table, 44 reference

Discovery of CH and OH in the -513 km s-1 Ejecta of Eta Carinae

The very massive star, Eta Carinae, is enshrouded in an unusual complex of stellar ejecta, which is highly depleted in C and O, and enriched in He and N. This circumstellar gas gives rise to distinct absorption components corresponding to at least 20 different velocities along the line-of-sight. The velocity component at -513 kms-1 exhibits very low ionization with predominantly neutral species of iron-peak elements. Our statistical equilibrium/photoionization modeling indicates that the low temperature (T = 760 K) and high density (n_H=10^7 cm^-3) of the -513 kms-1 component is conducive to molecule formation including those with the elements C and O. Examination of echelle spectra obtained with the Space Telescope Imaging Spectrograph (STIS) aboard the confirms the model's predictions. The molecules, H_2, CH, and most likely OH, have been identified in the -513 kms-1 absorption spectrum. This paper presents the analysis of the HST/STIS spectra with the deduced column densities for CH, OH and C I, and upper limit for CO. It is quite extraordinary to see molecular species in a cool environment at such a high velocity. The sharp molecular and ionic absorptions in this extensively CNO- processed material offers us a unique environment for studying the chemistry, dust formation processes, and nucleosynthesis in the ejected layers of a highly evolved massive star.Comment: tentatively scheduled for the ApJ 1 September 2005, v630, 1 issu