The evaluation of Education Maintenance Allowance Pilots: three years' evidence: a quantitative evaluation

This is the third report of the longitudinal quantitative evaluation of Education Maintenance Allowance (EMA) pilots and the first since the government announced that EMA is to be rolled out nationally from 2004. The evaluation was commissioned in 1999, by the Department for Education and Skills (DfES) from a consortium of research organisations, led by the Centre for Research in Social Policy (CRSP) and including the National Centre for Social Research, the Institute for Fiscal Studies (IFS) and the National Institute for Careers Education and Counselling (NICEC). The statistical evaluation design is a longitudinal cohort study involving large random sample surveys of young people (and their parents) in 10 EMA pilot areas and eleven control areas. Two cohorts of young people were selected from Child Benefit records. The first cohort of young people left compulsory schooling in the summer of 1999 and they, and their parents, were interviewed between October 1999 and April 2000 (Year 12 interview). A second interview was carried out with these young people between October 2000 and April 2001 (Year 13 interview). The second cohort left compulsory education the following summer of 2000 and young people, and their parents, were first interviewed between October 2000 and April 2001. The report uses both propensity score matching (PSM) and descriptive techniques, each of which brings their own particular strengths to the analysis

Full capacitance matrix of coupled quantum dot arrays: static and dynamical effects

We numerically calculated the full capacitance matrices for both one-dimensional (1D) and two-dimensional (2D) quantum-dot arrays. We found it is necessary to use the full capacitance matrix in modeling coupled quantum dot arrays due to weaker screening in these systems in comparison with arrays of normal metal tunnel junctions. The static soliton potential distributions in both 1D and 2D arrays are well approximated by the unscreened (1/r) coulomb potential, instead of the exponential fall-off expected from the often used nearest neighbor approximation. The Coulomb potential approximation also provides a simple expression for the full inverse capacitance matrix of uniform quantum dot arrays. In terms of dynamics, we compare the current-voltage (I-V) characteristics of voltage biased 1D arrays using either the full capacitance matrix or its nearest neighbor approximation. The I-V curves show clear differences and the differences become more pronounced when larger arrays are considered.Comment: 8 pages preprint format, 3 PostScript figure

Percolation of satisfiability in finite dimensions

The satisfiability and optimization of finite-dimensional Boolean formulas are studied using percolation theory, rare region arguments, and boundary effects. In contrast with mean-field results, there is no satisfiability transition, though there is a logical connectivity transition. In part of the disconnected phase, rare regions lead to a divergent running time for optimization algorithms. The thermodynamic ground state for the NP-hard two-dimensional maximum-satisfiability problem is typically unique. These results have implications for the computational study of disordered materials.Comment: 4 pages, 4 fig

Dislocations in the ground state of the solid-on-solid model on a disordered substrate

We investigate the effects of topological defects (dislocations) to the ground state of the solid-on-solid (SOS) model on a simple cubic disordered substrate utilizing the min-cost-flow algorithm from combinatorial optimization. The dislocations are found to destabilize and destroy the elastic phase, particularly when the defects are placed only in partially optimized positions. For multi defect pairs their density decreases exponentially with the vortex core energy. Their mean distance has a maximum depending on the vortex core energy and system size, which gives a fractal dimension of $1.27 \pm 0.02$. The maximal mean distances correspond to special vortex core energies for which the scaling behavior of the density of dislocations change from a pure exponential decay to a stretched one. Furthermore, an extra introduced vortex pair is screened due to the disorder-induced defects and its energy is linear in the vortex core energy.Comment: 6 pages RevTeX, eps figures include

Measuring functional renormalization group fixed-point functions for pinned manifolds

Exact numerical minimization of interface energies is used to test the functional renormalization group (FRG) analysis for interfaces pinned by quenched disorder. The fixed-point function R(u) (the correlator of the coarse-grained disorder) is computed. In dimensions D=d+1, a linear cusp in R''(u) is confirmed for random bond (d=1,2,3), random field (d=0,2,3), and periodic (d=2,3) disorders. The functional shocks that lead to this cusp are seen. Small, but significant, deviations from 1-loop FRG results are compared to 2-loop corrections. The cross-correlation for two copies of disorder is compared with a recent FRG study of chaos.Comment: 4 pages, 4 figure

Simulation of the Zero Temperature Behavior of a 3-Dimensional Elastic Medium

We have performed numerical simulation of a 3-dimensional elastic medium, with scalar displacements, subject to quenched disorder. We applied an efficient combinatorial optimization algorithm to generate exact ground states for an interface representation. Our results indicate that this Bragg glass is characterized by power law divergences in the structure factor $S(k)\sim A k^{-3}$. We have found numerically consistent values of the coefficient $A$ for two lattice discretizations of the medium, supporting universality for $A$ in the isotropic systems considered here. We also examine the response of the ground state to the change in boundary conditions that corresponds to introducing a single dislocation loop encircling the system. Our results indicate that the domain walls formed by this change are highly convoluted, with a fractal dimension $d_f=2.60(5)$. We also discuss the implications of the domain wall energetics for the stability of the Bragg glass phase. As in other disordered systems, perturbations of relative strength $\delta$ introduce a new length scale $L^* \sim \delta^{-1/\zeta}$ beyond which the perturbed ground state becomes uncorrelated with the reference (unperturbed) ground state. We have performed scaling analysis of the response of the ground state to the perturbations and obtain $\zeta = 0.385(40)$. This value is consistent with the scaling relation $\zeta=d_f/2- \theta$, where $\theta$ characterizes the scaling of the energy fluctuations of low energy excitations.Comment: 20 pages, 13 figure

Einstein Gravity on a Brane in 5D Non-compact Flat Spacetime -DGP model revisited-

We revisit the 5D gravity model by Dvali, Gabadadze, and Porrati (DGP). Within their framework it was shown that even in 5D non-compact Minkowski space $(x^\mu,z)$, the Newtonian gravity can emerge on a brane at short distances by introducing a brane-localized 4D Einstein-Hilbert term $\delta(z)M_4^2\sqrt{|\bar{g}_4|}\bar{R}_4$ in the action. Based on this idea, we construct simple setups in which graviton standing waves can arise, and we introduce brane-localized $z$ derivative terms as a correction to $\delta(z)M_4^2\sqrt{|\bar{g}_4|}\bar{R}_4$. We show that the gravity potential of brane matter becomes $-\frac{1}{r}$ at {\it long} distances, because the brane-localized $z$ derivative terms allow only a smooth graviton wave function near the brane. Since the bulk gravity coupling may be arbitrarily small, strongly interacting modes from the 5D graviton do not appear. We note that the brane metric utilized to construct $\delta(z)M_4^2\sqrt{|\bar{g}_4|}\bar{R}_4$ can be relatively different from the bulk metric by a conformal factor, and show that the graviton tensor structure that the 4D Einstein gravity predicts are reproduced in DGP type models.Comment: 1+12 pages, no figure, to appear in JHE

Avalanches and the Renormalization Group for Pinned Charge-Density Waves

The critical behavior of charge-density waves (CDWs) in the pinned phase is studied for applied fields increasing toward the threshold field, using recently developed renormalization group techniques and simulations of automaton models. Despite the existence of many metastable states in the pinned state of the CDW, the renormalization group treatment can be used successfully to find the divergences in the polarization and the correlation length, and, to first order in an $\epsilon = 4-d$ expansion, the diverging time scale. The automaton models studied are a charge-density wave model and a ``sandpile'' model with periodic boundary conditions; these models are found to have the same critical behavior, associated with diverging avalanche sizes. The numerical results for the polarization and the diverging length and time scales in dimensions $d=2,3$ are in agreement with the analytical treatment. These results clarify the connections between the behaviour above and below threshold: the characteristic correlation lengths on both sides of the transition diverge with different exponents. The scaling of the distribution of avalanches on the approach to threshold is found to be different for automaton and continuous-variable models.Comment: 29 pages, 11 postscript figures included, REVTEX v3.0 (dvi and PS files also available by anonymous ftp from external.nj.nec.com in directory /pub/alan/cdwfigs

Critical slowing down in polynomial time algorithms

Combinatorial optimization algorithms which compute exact ground state configurations in disordered magnets are seen to exhibit critical slowing down at zero temperature phase transitions. Using arguments based on the physical picture of the model, including vanishing stiffness on scales beyond the correlation length and the ground state degeneracy, the number of operations carried out by one such algorithm, the push-relabel algorithm for the random field Ising model, can be estimated. Some scaling can also be predicted for the 2D spin glass.Comment: 4 pp., 3 fig

Computational Complexity of Determining the Barriers to Interface Motion in Random Systems

The low-temperature driven or thermally activated motion of several condensed matter systems is often modeled by the dynamics of interfaces (co-dimension-1 elastic manifolds) subject to a random potential. Two characteristic quantitative features of the energy landscape of such a many-degree-of-freedom system are the ground-state energy and the magnitude of the energy barriers between given configurations. While the numerical determination of the former can be accomplished in time polynomial in the system size, it is shown here that the problem of determining the latter quantity is NP-complete. Exact computation of barriers is therefore (almost certainly) much more difficult than determining the exact ground states of interfaces.Comment: 8 pages, figures included, to appear in Phys. Rev.