Long-distance asymptotic behaviour of multi-point correlation functions in massless quantum models

We provide a microscopic model setting that allows us to readily access to the large-distance asymptotic behaviour of multi-point correlation functions in massless, one-dimensional, quantum models. The method of analysis we propose is based on the form factor expansion of the correlation functions and does not build on any field theory reasonings. It constitutes an extension of the restricted sum techniques leading to the large-distance asymptotic behaviour of two-point correlation functions obtained previously.Comment: 25 page

Form factor approach to dynamical correlation functions in critical models

We develop a form factor approach to the study of dynamical correlation functions of quantum integrable models in the critical regime. As an example, we consider the quantum non-linear Schr\"odinger model. We derive long-distance/long-time asymptotic behavior of various two-point functions of this model. We also compute edge exponents and amplitudes characterizing the power-law behavior of dynamical response functions on the particle/hole excitation thresholds. These last results confirm predictions based on the non-linear Luttinger liquid method. Our results rely on a first principles derivation, based on the microscopic analysis of the model, without invoking, at any stage, some correspondence with a continuous field theory. Furthermore, our approach only makes use of certain general properties of the model, so that it should be applicable, with possibly minor modifications, to a wide class of (not necessarily integrable) gapless one dimensional Hamiltonians.Comment: 33 page

Probing of mortality rate by staying alive : the growth‐reproduction trade‐off in a spatially heterogeneous environment

1. In many annual plants, mollusks, crustaceans and ectothermic vertebrates, growth accompanies reproduction. The growth curves of these organisms often exhibit a complex shape, with episodic cessations or accelerations of growth occurring long after maturation. The mixed allocation to growth and reproduction has poorly understood adaptive consequences, and the life‐history theory does not explain if complex growth in short‐lived organisms can be adaptive. 2. We model the trade‐off between growth and reproduction in a short‐lived organism evolving in a metapopulation. Individuals occupy risky or safe sites throughout their lives, but are uncertain regarding the risk of death. Modelled organisms are allowed to grow and produce offspring at specified time points (moults), although we also consider scenarios that approximate continuous growth and reproduction. 3. Certain combinations of risky to safe sites select for strategies with mixed allocation to growth and reproduction that bet‐hedge offspring production in safe and risky sites. Our model shows that spatially heterogeneous environments select for mixed allocation only if safe sites do not become the prevailing source of recruits, for example, when risky sites are frequent. In certain conditions, growth curves are multi‐phasic, with allocation to growth that stops, remains constant or accelerates during adult life. The resulting complex growth curves are more likely to evolve in short‐lived organisms that moult several times per adult life. 4. Our work shows that spatial heterogeneity can select for growth that accompanies reproduction and provides insights into the adaptive significance of complex growth curves. Short‐lived crustaceans are particularly predisposed to exhibit complex growth patterns as an adaptive response to spatially heterogeneous environments. Our results suggest that standard statistical growth models assuming adult growth rate to only decelerate over life are not well suited to approximate growth curves of short‐lived crustaceans

Population response of triploid grass carp to declining levels of hydrilla in the Santee Cooper Reservoirs, South Carolina

Approximately 768,500 triploid grass carp ( Ctenopharyngodon idella Valenciennes) were stocked into the Santee Cooper reservoirs, South Carolina between 1989 and 1996 to control hydrilla ( Hydrilla verticillata (L.f.) Royle). Hydrilla coverage was reduced from a high of 17,272 ha during 1994 to a few ha by 1998. During 1997, 1998 and 1999, at least 98 triploid grass carp were collected yearly for population monitoring. Estimates of age, growth, and mortality, as well as population models, were used in the study to monitor triploid grass carp and predict population trends. Condition declined from that measured during a previous study in 1994. The annual mortality rate was estimated at 28% in 1997, 32% in 1998 and 39% in 1999; however, only the 1999 mortality rate was significantly different. Few (2 out of 98) of the triploid grass carp collected during 1999 were older than age 9. We expect increased mortality due to an aging population and sparse hydrilla coverage. During 1999, we estimated about 63,000 triploid grass carp system wide and project less than 3,000 fish by 2004, assuming no future stocking. management, population size Ctenopharyngodon idella, Hydrill

On the thermodynamic limit of form factors in the massless XXZ Heisenberg chain

We consider the problem of computing form factors of the massless XXZ Heisenberg spin-1/2 chain in a magnetic field in the (thermodynamic) limit where the size M of the chain becomes large. For that purpose, we take the particular example of the matrix element of the third component of spin between the ground state and an excited state with one particle and one hole located at the opposite ends of the Fermi interval (umklapp-type term). We exhibit its power-law decrease in terms of the size of the chain M, and compute the corresponding exponent and amplitude. As a consequence, we show that this form factor is directly related to the amplitude of the leading oscillating term in the long-distance asymptotic expansion of the two-point correlation function of the third component of spin.Comment: 28 page

Evidence of a Metal Rich Galactic Bar from the Vertex Deviation of the Velocity Ellipsoid

We combine radial velocities, proper motions, and low resolution abundances for a sample of 315 K and M giants in the Baade's Window (l,b)=(0.9,-4) Galactic bulge field. The velocity ellipsoid of stars with [Fe/H]>-0.5 dex shows a vertex deviation in the plot of radial versus transverse velocity, consistent with that expected from a population with orbits supporting a bar. We demonstrate that the significance of this vertex deviation using non-parametric rank correlation statistic is >99%. The velocity ellipsoid for the metal poor ([FeH]<-0.5) part of the population shows no vertex deviation and is consistent with an isotropic, oblate rotating population. We find no evidence for kinematic subgroups, but there is a mild tendency for the vertical velocity dispersion sigma_b to decrease with increasing metallicity.Comment: 4 pages, ApJ Letters, submitte

Mini Max Wallpaper

Mini Max company formulated a problem for the automatic calculation of the number of wallpaper rolls necessary for decorating a room with wallpaper. The final goal is the development of a web-based calculator open for use to both Mini Max staff and the general public. We propose an approach for reducing the studied problem to the one-dimensional cutting-stock problem. We show this in details for the case of plain wallpapers as well as for the case of patterned wallpapers with straight match. The one-dimensional cutting-stock problem can be formulated as a linear integer programming problem. We develop an approach for calculating the needed number of wallpapers for relatively small problems, create an algorithm in a suitable graphical interface and make different tests. The tests show the efficiency of the proposed approach compared with the existent (available) wallpapers’ calculators

An ice giant exoplanet interpretation of the anomaly in microlensing event OGLE-2011-BLG-0173

We analyze the microlensing event OGLE-2011-BLG-0173, which shows a small perturbation at the end of the microlensing event caused by the primary lens. We consider both binary lens and binary source models and we explore their degeneracies, some of which have not previously been recognized. There are two families of binary lens solutions, one with a mass ratio $q\approx4\times10^{-4}$ and a separation s~4.6 and the other with q~0.015 and s~0.22, i.e, both have companions in the planetary regime. We search for solutions by using Bayesian analysis that includes planet frequency as a prior and find that the s~4.6 family is the preferred one with ~4 M_Uranus mass planet on an orbit of ~10 AU. The degeneracies arise from a paucity of information on the anomaly, demonstrating that high-cadence observations are essential for characterizing wide-orbit microlensing planets. Hence, we predict that the planned WFIRST microlensing survey will be less prone to these degeneracies than the ongoing ground-based surveys. We discuss the known low-mass, wide-orbit companions and we notice that for the largest projected separations the mass ratios are either high (consistent with brown dwarf companions) or low (consistent with Uranus analogs), but intermediate mass ratios (Jupiter analogs on wide orbits) have not been detected to date, despite the fact that the sensitivity to such planets should be higher than that of Uranus analogs. This is therefore tentative evidence of the existence of a massive ice giant desert at wide separations. On the other hand, given their low intrinsic detection sensitivity, Uranus analogs may be ubiquitous.Comment: AJ accepted, 6 figures, 4 table