Micro-simulating child poverty in 2010 and 2020

The 2008 Pre-Budget Report (PBR) said that 'the Government will take stock of progress towards its 2010 and 2020 child poverty target in the [2009] Budget'. As background to that exercise, this paper updates our previous analysis of the prospects for child poverty in the UK in 2010-11 and 2020-21

The development of low temperature curing adhesives

An approach for the development of a practical low temperature (293 K-311 K/68 F-100 F) curing adhesive system based on a family of amide/ester resins was studied and demonstrated. The work was conducted on resin optimization and adhesive compounding studies. An improved preparative method was demonstrated which involved the reaction of an amine-alcohol precursor, in a DMF solution with acid chloride. Experimental studies indicated that an adhesive formulation containing aluminum powder provided the best performance when used in conjunction with a commercial primer

Dynamical Mass Measurements of Contaminated Galaxy Clusters Using Machine Learning

We study dynamical mass measurements of galaxy clusters contaminated by interlopers and show that a modern machine learning (ML) algorithm can predict masses by better than a factor of two compared to a standard scaling relation approach. We create two mock catalogs from Multidark's publicly available $N$-body MDPL1 simulation, one with perfect galaxy cluster membership information and the other where a simple cylindrical cut around the cluster center allows interlopers to contaminate the clusters. In the standard approach, we use a power-law scaling relation to infer cluster mass from galaxy line-of-sight (LOS) velocity dispersion. Assuming perfect membership knowledge, this unrealistic case produces a wide fractional mass error distribution, with a width of $\Delta\epsilon\approx0.87$. Interlopers introduce additional scatter, significantly widening the error distribution further ($\Delta\epsilon\approx2.13$). We employ the support distribution machine (SDM) class of algorithms to learn from distributions of data to predict single values. Applied to distributions of galaxy observables such as LOS velocity and projected distance from the cluster center, SDM yields better than a factor-of-two improvement ($\Delta\epsilon\approx0.67$) for the contaminated case. Remarkably, SDM applied to contaminated clusters is better able to recover masses than even the scaling relation approach applied to uncontaminated clusters. We show that the SDM method more accurately reproduces the cluster mass function, making it a valuable tool for employing cluster observations to evaluate cosmological models.Comment: 18 pages, 12 figures, accepted for publication at Ap

Transport Properties of a One-Dimensional Two-Component Quantum Liquid with Hyperbolic Interactions

We present an investigation of the sinh-cosh (SC) interaction model with twisted boundary conditions. We argue that, when unlike particles repel, the SC model may be usefully viewed as a Heisenberg-Ising fluid with moving Heisenberg-Ising spins. We derive the Luttinger liquid relation for the stiffness and the susceptibility, both from conformal arguments, and directly from the integral equations. Finally, we investigate the opening and closing of the ground state gaps for both SC and Heisenberg-Ising models, as the interaction strength is varied.Comment: 10 REVTeX pages + 4 uuencoded figures, UoU-002029

Exact spin-orbital separation in a solvable model in one dimension

A one-dimensional model of coupled spin-1/2 spins and pseudospin-1/2 orbitals with nearest-neighbor interaction is rigorously shown to exhibit spin-orbital separation by means of a non-local unitary transformation. On an open chain, this transformation completely decouples the spins from the orbitals in such a way that the spins become paramagnetic while the orbitals form the soluble XXZ Heisenberg model. The nature of various correlations is discussed. The more general cases, which allow spin-orbital separation by the same method, are pointed out. A generalization for the orbital pseudospin greater than 1/2 is also discussed. Some qualitative connections are drawn with the recently observed spin-orbital separation in Sr2CuO3.Comment: 5 page

Exact Solution of Heisenberg-liquid models with long-range coupling

We present the exact solution of two Heisenberg-liquid models of particles with arbitrary spin $S$ interacting via a hyperbolic long-range potential. In one model the spin-spin coupling has the simple antiferromagnetic Heisenberg exchange form, while for the other model the interaction is of the ferromagnetic Babujian-Takhatajan type. It is found that the Bethe ansatz equations of these models have a similar structure to that of the Babujian-Takhatajan spin chain. We also conjecture the integrability of a third new spin-lattice model with long-range interaction.Comment: 7pages Revte

Spectral Properties of Statistical Mechanics Models

The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we have found eigenvalue repulsion as for the Gaussian orthogonal ensemble in random matrix theory. By contrast, in integrable regimes we have found eigenvalue independence leading to a Poissonian behavior, and, for some points, level clustering. These first examples from classical statistical mechanics suggest that the conjecture of integrability successfully applied to quantum spin systems also holds for classical systems.Comment: 4 pages, 1 Revtex file and 4 postscript figures tarred, gzipped and uuencode

GAPS IN THE HEISENBERG-ISING MODEL

We report on the closing of gaps in the ground state of the critical Heisenberg-Ising chain at momentum $\pi$. For half-filling, the gap closes at special values of the anisotropy $\Delta= \cos(\pi/Q)$, $Q$ integer. We explain this behavior with the help of the Bethe Ansatz and show that the gap scales as a power of the system size with variable exponent depending on $\Delta$. We use a finite-size analysis to calculate this exponent in the critical region, supplemented by perturbation theory at $\Delta\sim 0$. For rational $1/r$ fillings, the gap is shown to be closed for {\em all} values of $\Delta$ and the corresponding perturbation expansion in $\Delta$ shows a remarkable cancellation of various diagrams.Comment: 12 RevTeX pages + 4 figures upon reques

Quantum WNW_N Algebras and Macdonald Polynomials

We derive a quantum deformation of the $W_N$ algebra and its quantum Miura transformation, whose singular vectors realize the Macdonald polynomials.Comment: LaTeX file, 17-pages, no-figures, a reference adde