Area-Preserving Structure of Massless Matter-Gravity Fields in 1+1 Dimensions

We derive anomalous Ward identities in two different approaches to the quantization of massless matter-gravity fields in 1+1 dimensions.Comment: 5 pages, LaTex. (Contribution to the Proceedings of the XXXIV Internationale Universit\"atswochen f\"ur Kern- und Teilchenphysik.

Coronavirus (COVID-19) in the United Kingdom: A personality-based perspective on concerns and intention to self-isolate

Objectives Public behaviour change is necessary to contain the spread of coronavirus (COVID‐19). Based on the reinforcement sensitivity theory (RST) framework, this study presents an examination of individual differences in some relevant psychological factors. Design Cross‐sectional psychometric. Methods UK respondents (N = 202) completed a personality questionnaire (RST‐PQ), measures of illness attitudes, concerns about the impact of coronavirus on health services and socio‐economic infrastructures, personal safety, and likelihood of voluntary self‐isolation. Results Respondents most concerned were older, had negative illness attitudes, and scored higher on reward reactivity (RR), indicating the motivation to take positive approach action despite prevailing worry/anxiety. Personal safety concerns were highest in those with negative illness attitudes and higher fight–flight–freeze system (FFFS, reflecting fear/avoidance) scores. Results suggest people are experiencing psychological conflict: between the urge to stay safe (FFFF‐related) and the desire to maintain a normal, pleasurable (RR‐related) life. Ways of ameliorating conflict may include maladaptive behaviours (panic buying), reflecting reward‐related displacement activity. Intended self‐isolation related to FFFS, but also low behavioural inhibition system (related to anxiety) scores. Older people reported themselves less likely to self‐isolate. Conclusions Interventions need to consider individual differences in psychological factors in behaviour change, and we discuss relevant literature to inform policy makers and communicators

An adaptive, fully implicit multigrid phase-field model for the quantitative simulation of non-isothermal binary alloy solidification

Using state-of-the-art numerical techniques, such as mesh adaptivity, implicit time-stepping and a non-linear multi-grid solver, the phase-field equations for the non-isothermal solidification of a dilute binary alloy have been solved. Using the quantitative, thin-interface formulation of the problem we have found that at high Lewis number a minimum in the dendrite tip radius is predicted with increasing undercooling, as predicted by marginal stability theory. Over the dimensionless undercooling range 0.2–0.8 the radius selection parameter, σ*, was observed to vary by over a factor of 2 and in a non-monotonic fashion, despite the anisotropy strength being constant

Advanced numerical methods for the simulation of alloy solidification with high Lewis number

A fully-implicit numerical method based upon adaptively refined meshes for the thermal-solutal simulation of alloy solidification in 2D is presented. In addition we combine an unconditional stable second-order fully-implicit time discretisation scheme with variable step size control to obtain an adaptive time and space discretisation method, where a robust and fast multigrid solver for systems of non-linear algebraic equations is used to solve the intermediate approximations per time step. For the isothermal case, the superiority of this method, compared to widely used fully-explicit methods, with respect to CPU time and accuracy, has been demonstrated and published previously. Here, the new proposed method has been applied to the thermalsolutal case with high Lewis number, where stability issues and time step restrictions have been major constraints in previous research

Ergodicity for SDEs and approximations: Locally Lipschitz vector fields and degenerate noise

The ergodic properties of SDEs, and various time discretizations for SDEs, are studied. The ergodicity of SDEs is established by using techniques from the theory of Markov chains on general state spaces, such as that expounded by Meyn-Tweedie. Application of these Markov chain results leads to straightforward proofs of geometric ergodicity for a variety of SDEs, including problems with degenerate noise and for problems with locally Lipschitz vector fields. Applications where this theory can be usefully applied include damped-driven Hamiltonian problems (the Langevin equation), the Lorenz equation with degenerate noise and gradient systems. The same Markov chain theory is then used to study time-discrete approximations of these SDEs. The two primary ingredients for ergodicity are a minorization condition and a Lyapunov condition. It is shown that the minorization condition is robust under approximation. For globally Lipschitz vector fields this is also true of the Lyapunov condition. However in the locally Lipschitz case the Lyapunov condition fails for explicit methods such as Euler-Maruyama; for pathwise approximations it is, in general, only inherited by specially constructed implicit discretizations. Examples of such discretization based on backward Euler methods are given, and approximation of the Langevin equation studied in some detail

Overhead and noise threshold of fault-tolerant quantum error correction

Fault tolerant quantum error correction (QEC) networks are studied by a combination of numerical and approximate analytical treatments. The probability of failure of the recovery operation is calculated for a variety of CSS codes, including large block codes and concatenated codes. Recent insights into the syndrome extraction process, which render the whole process more efficient and more noise-tolerant, are incorporated. The average number of recoveries which can be completed without failure is thus estimated as a function of various parameters. The main parameters are the gate (gamma) and memory (epsilon) failure rates, the physical scale-up of the computer size, and the time t_m required for measurements and classical processing. The achievable computation size is given as a surface in parameter space. This indicates the noise threshold as well as other information. It is found that concatenated codes based on the [[23,1,7]] Golay code give higher thresholds than those based on the [[7,1,3]] Hamming code under most conditions. The threshold gate noise gamma_0 is a function of epsilon/gamma and t_m; example values are {epsilon/gamma, t_m, gamma_0} = {1, 1, 0.001}, {0.01, 1, 0.003}, {1, 100, 0.0001}, {0.01, 100, 0.002}, assuming zero cost for information transport. This represents an order of magnitude increase in tolerated memory noise, compared with previous calculations, which is made possible by recent insights into the fault-tolerant QEC process.Comment: 21 pages, 12 figures, minor mistakes corrected and layout improved, ref added; v4: clarification of assumption re logic gate

Socialism without liberation: Land Reclamation Projects in Guinea-Bissau

One of the outstanding aims of most liberation movements has been to increase the economic well-being of their people, Guinea-Bissau being no exception in this respect. How far has the new Nation State succeeded in fulfilling this aim? A comparative analysis of the implementation of land reclamation projects during colonial and post-colonial times reveals astonishing similarities: especially the centralization of development efforts in the hands of administrators disconnected from the grassroots, lack of target group analysis and misconceptions about the aims and needs, as well as the resources, of the population involved in the development efforts, on the part of the administration. The effects of this negative conditioning process of 'development' over many years on the chances of cooperation between peasants and the administration are still largely unknown. Any development planner who wants to encourage the local population to take their future into their own hands, would have to take account of this negative conditioning process

Sick of work or too sick to work? Evidence on health shocks and early retirement from the BHPS

We follow individuals as they retire using discrete-time hazard models applied to a stock sample from 12 waves of the British Household Panel Survey. Results confirm that health shocks are a determinant of retirement age and are quantitatively more important than pension entitlement. This is the case for both men and women and is observed for both a measure of health limitations and a measure of latent health status obtained from a generalized ordered probit model. Further, our results provide evidence that, for women, the health status of their partner impacts on their retirement decisions; an effect that is not evident for men

Recursive algorithms for the elimination of redundant paths in spatial lag operators

Recursive algorithms for the elimination of redundant paths in spatial lag operators are introduced. It is shown that these algorithms have superior computational properties in comparison with the cumbersome procedure proposed by Ross and Harary (1952). A rigorous definition of spatial lag operators is given, while a number of mathematical results and properties are derived. Theoretical and empirical results regarding the performance of the proposed algorithms are presented

Homotopy Lie Superalgebra in Yang-Mills Theory

The Yang-Mills equations are formulated in the form of generalized Maurer-Cartan equations, such that the corresponding algebraic operations are shown to satisfy the defining relations of homotopy Lie superalgebra.Comment: LaTeX2e, 10 page