Initial data sets for the Schwarzschild spacetime

A characterisation of initial data sets for the Schwarzschild spacetime is provided. This characterisation is obtained by performing a 3+1 decomposition of a certain invariant characterisation of the Schwarzschild spacetime given in terms of concomitants of the Weyl tensor. This procedure renders a set of necessary conditions --which can be written in terms of the electric and magnetic parts of the Weyl tensor and their concomitants-- for an initial data set to be a Schwarzschild initial data set. Our approach also provides a formula for a static Killing initial data set candidate --a KID candidate. Sufficient conditions for an initial data set to be a Schwarzschild initial data set are obtained by supplementing the necessary conditions with the requirement that the initial data set possesses a stationary Killing initial data set of the form given by our KID candidate. Thus, we obtain an algorithmic procedure of checking whether a given initial data set is Schwarzschildean or not.Comment: 16 page

"Peeling property" for linearized gravity in null coordinates

A complete description of the linearized gravitational field on a flat background is given in terms of gauge-independent quasilocal quantities. This is an extension of the results from gr-qc/9801068. Asymptotic spherical quasilocal parameterization of the Weyl field and its relation with Einstein equations is presented. The field equations are equivalent to the wave equation. A generalization for Schwarzschild background is developed and the axial part of gravitational field is fully analyzed. In the case of axial degree of freedom for linearized gravitational field the corresponding generalization of the d'Alembert operator is a Regge-Wheeler equation. Finally, the asymptotics at null infinity is investigated and strong peeling property for axial waves is proved.Comment: 27 page

Crossover from Rate-Equation to Diffusion-Controlled Kinetics in Two-Particle Coagulation

We develop an analytical diffusion-equation-type approximation scheme for the one-dimensional coagulation reaction A+A->A with partial reaction probability on particle encounters which are otherwise hard-core. The new approximation describes the crossover from the mean-field rate-equation behavior at short times to the universal, fluctuation-dominated behavior at large times. The approximation becomes quantitatively accurate when the system is initially close to the continuum behavior, i.e., for small initial density and fast reaction. For large initial density and slow reaction, lattice effects are nonnegligible for an extended initial time interval. In such cases our approximation provides the correct description of the initial mean-field as well as the asymptotic large-time, fluctuation-dominated behavior. However, the intermediate-time crossover between the two regimes is described only semiquantitatively.Comment: 21 pages, plain Te

Anisotropic Diffusion-Limited Reactions with Coagulation and Annihilation

One-dimensional reaction-diffusion models A+A -> 0, A+A -> A, and $A+B -> 0, where in the latter case like particles coagulate on encounters and move as clusters, are solved exactly with anisotropic hopping rates and assuming synchronous dynamics. Asymptotic large-time results for particle densities are derived and discussed in the framework of universality.Comment: 13 pages in plain Te

Impact of an Inner-City Smoke-Free Zone on Outdoor Smoking Patterns:A Before-After Study

INTRODUCTION: On September 2, 2019, Rotterdam’s first inner-city outdoor smoke-free zone encompassing the Erasmus MC, a large university hospital in the Netherlands, the Erasmiaans high school, the Rotterdam University of Applied Sciences and the public road in between, was implemented. AIMS AND METHODS: We aimed to assess spatiotemporal patterning of smoking before and after implementation of this outdoor smoke-free zone. We performed a before–after observational field study. We systematically observed the number of smokers, and their locations and characteristics over 37 days before and after implementation of the smoke-free zone. RESULTS: Before implementation of the smoke-free zone, 4098 people smoked in the area every weekday during working hours. After implementation, the daily number of smokers was 2241, a 45% reduction (p = .007). There was an increase of 432 smokers per day near and just outside the borders of the zone. At baseline, 31% of the smokers were categorized as employee, 22% as student and 3% as patient. Following implementation of the smoke-free zone, the largest decreases in smokers were observed among employees (–67%, p value .004) and patients (–70%, p value .049). Before and after implementation, 21 and 20 smokers were visibly addressed and asked to smoke elsewhere. CONCLUSIONS: Implementation of an inner-city smoke-free zone was associated with a substantial decline in the number of smokers in the zone and an overall reduction of smoking in the larger area. Further research should focus on optimizing implementation of and compliance with outdoor smoke-free zones. IMPLICATIONS: A smoke-free outdoor policy has the potential to denormalize and discourage smoking, support smokers who want to quit, and to protect people from secondhand smoke exposure. Implementation of an inner-city smoke-free zone encompassing a large tertiary hospital and two educational institutions was associated with a substantial decline in the number of smokers in the zone, as well as in the larger area. Voluntary outdoor smoke-free zones can help reduce the number of smokers in the area and protect people from secondhand smoke. There is a need to explore effectiveness of additional measures to further improve compliance

Exact Results for Diffusion-Limited Reactions with Synchronous Dynamics

A new method is introduced allowing to solve exactly the reactions A+A->inert and A+A->A on the 1D lattice with synchronous diffusional dynamics (simultaneous hopping of all particles). Exact connections are found relating densities and certain correlation properties of these two reactions at all times. Asymptotic behavior at large times as well as scaling form describing the regime of low initial density, are derived explicitly.Comment: 12 pages in plain Te

Multiparticle Reactions with Spatial Anisotropy

We study the effect of anisotropic diffusion on the one-dimensional annihilation reaction kA->inert with partial reaction probabilities when hard-core particles meet in groups of k nearest neighbors. Based on scaling arguments, mean field approaches and random walk considerations we argue that the spatial anisotropy introduces no appreciable changes as compared to the isotropic case. Our conjectures are supported by numerical simulations for slow reaction rates, for k=2 and 4.Comment: nine pages, plain Te

Smoke and Alcohol Free with EHealth and Rewards (SAFER) pregnancy study:a before-after study protocol

Despite existing interventions, tobacco smoking and alcohol consumption during pregnancy are common. The Smoke and Alcohol Free with EHealth and Rewards (SAFER) pregnancy intervention combines monthly group sessions, access to a web-based platform and incentives upon biochemically validated cessation for a maximum duration of 6 months to promote cessation of smoking and alcohol use before and during pregnancy. To inform development of the SAFER pregnancy intervention, two focus groups with the target population were held beforehand, with results reported here alongside the final SAFER pregnancy study protocol. In a before-after study we aim to include 66 women who are pregnant or have a wish to become pregnant and who smoke and/or consume alcohol (i.e. target population of the SAFER pregnancy intervention). The primary outcome measure is cessation of smoking and/or alcohol use at 34-38 weeks of gestation, or after six group sessions if women did not become pregnant during the study period. Secondary outcomes focus on the barriers and facilitators for implementation of the SAFER pregnancy intervention

Exact Solutions of Anisotropic Diffusion-Limited Reactions with Coagulation and Annihilation

We report exact results for one-dimensional reaction-diffusion models A+A -> inert, A+A -> A, and A+B -> inert, where in the latter case like particles coagulate on encounters and move as clusters. Our study emphasized anisotropy of hopping rates; no changes in universal properties were found, due to anisotropy, in all three reactions. The method of solution employed mapping onto a model of coagulating positive integer charges. The dynamical rules were synchronous, cellular-automaton type. All the asymptotic large-time results for particle densities were consistent, in the framework of universality, with other model results with different dynamical rules, when available in the literature.Comment: 28 pages in plain TeX + 2 PostScript figure