Slow Logarithmic Decay of Magnetization in the Zero Temperature Dynamics of an Ising Spin Chain: Analogy to Granular Compaction

We study the zero temperature coarsening dynamics in an Ising chain in presence of a dynamically induced field that favors locally the `-' phase compared to the `+' phase. At late times, while the `+' domains still coarsen as $t^{1/2}$, the `-' domains coarsen slightly faster as $t^{1/2}\log (t)$. As a result, at late times, the magnetization decays slowly as, $m(t)=-1 +{\rm const.}/{\log (t)}$. We establish this behavior both analytically within an independent interval approximation (IIA) and numerically. In the zero volume fraction limit of the `+' phase, we argue that the IIA becomes asymptotically exact. Our model can be alternately viewed as a simple Ising model for granular compaction. At late times in our model, the system decays into a fully compact state (where all spins are `-') in a slow logarithmic manner $\sim 1/{\log (t)}$, a fact that has been observed in recent experiments on granular systems.Comment: 4 pages Revtex, 3 eps figures, supersedes cond-mat/000221

On universality in aging ferromagnets

This work is a contribution to the study of universality in out-of-equilibrium lattice models undergoing a second-order phase transition at equilibrium. The experimental protocol that we have chosen is the following: the system is prepared in its high-temperature phase and then quenched at the critical temperature $T_c$. We investigated by mean of Monte Carlo simulations two quantities that are believed to take universal values: the exponent $\lambda/z$ obtained from the decay of autocorrelation functions and the asymptotic value $X_\infty$ of the fluctuation-dissipation ratio $X(t,s)$. This protocol was applied to the Ising model, the 3-state clock model and the 4-state Potts model on square, triangular and honeycomb lattices and to the Ashkin-Teller model at the point belonging at equilibrium to the 3-state Potts model universality class and to a multispin Ising model and the Baxter-Wu model both belonging to the 4-state Potts model universality class at equilibrium.Comment: 17 page

Quasi-stationary regime of a branching random walk in presence of an absorbing wall

A branching random walk in presence of an absorbing wall moving at a constant velocity $v$ undergoes a phase transition as the velocity $v$ of the wall varies. Below the critical velocity $v_c$, the population has a non-zero survival probability and when the population survives its size grows exponentially. We investigate the histories of the population conditioned on having a single survivor at some final time $T$. We study the quasi-stationary regime for $v<v_c$ when $T$ is large. To do so, one can construct a modified stochastic process which is equivalent to the original process conditioned on having a single survivor at final time $T$. We then use this construction to show that the properties of the quasi-stationary regime are universal when $v\to v_c$. We also solve exactly a simple version of the problem, the exponential model, for which the study of the quasi-stationary regime can be reduced to the analysis of a single one-dimensional map.Comment: 2 figures, minor corrections, one reference adde

Outbreak size distributions in epidemics with multiple stages

Multiple-type branching processes that model the spread of infectious diseases are investigated. In these stochastic processes, the disease goes through multiple stages before it eventually disappears. We mostly focus on the critical multistage Susceptible-Infected-Recovered (SIR) infection process. In the infinite population limit, we compute the outbreak size distributions and show that asymptotic results apply to more general multiple-type critical branching processes. Finally using heuristic arguments and simulations we establish scaling laws for a multistage SIR model in a finite population.Comment: 7 pages, 2 figures; added references, final versio

Patchiness and Demographic Noise in Three Ecological Examples

Understanding the causes and effects of spatial aggregation is one of the most fundamental problems in ecology. Aggregation is an emergent phenomenon arising from the interactions between the individuals of the population, able to sense only -at most- local densities of their cohorts. Thus, taking into account the individual-level interactions and fluctuations is essential to reach a correct description of the population. Classic deterministic equations are suitable to describe some aspects of the population, but leave out features related to the stochasticity inherent to the discreteness of the individuals. Stochastic equations for the population do account for these fluctuation-generated effects by means of demographic noise terms but, owing to their complexity, they can be difficult (or, at times, impossible) to deal with. Even when they can be written in a simple form, they are still difficult to numerically integrate due to the presence of the "square-root" intrinsic noise. In this paper, we discuss a simple way to add the effect of demographic stochasticity to three classic, deterministic ecological examples where aggregation plays an important role. We study the resulting equations using a recently-introduced integration scheme especially devised to integrate numerically stochastic equations with demographic noise. Aimed at scrutinizing the ability of these stochastic examples to show aggregation, we find that the three systems not only show patchy configurations, but also undergo a phase transition belonging to the directed percolation universality class.Comment: 20 pages, 5 figures. To appear in J. Stat. Phy

The non-equilibrium response of the critical Ising model: Universal scaling properties and Local Scale Invariance

Motivated by recent numerical findings [M. Henkel, T. Enss, and M. Pleimling, J. Phys. A: Math. Gen. 39 (2006) L589] we re-examine via Monte Carlo simulations the linear response function of the two-dimensional Ising model with Glauber dynamics quenched to the critical point. At variance with the results of Henkel et al., we detect discrepancies between the actual scaling behavior of the response function and the prediction of Local Scale Invariance. Such differences are clearly visible in the impulse autoresponse function, whereas they are drastically reduced in integrated response functions. Accordingly, the scaling form predicted on the basis of Local Scale Invariance simply provides an accurate fitting form for some quantities but cannot be considered to be exact.Comment: 25 pages, 4 figure

Surface Covering of Downed Logs: Drivers of a Neglected Process in Dead Wood Ecology

Many species use coarse woody debris (CWD) and are disadvantaged by the forestry-induced loss of this resource. A neglected process affecting CWD is the covering of the surfaces of downed logs caused by sinking into the ground (increasing soil contact, mostly covering the underside of the log), and dense overgrowth by ground vegetation. Such cover is likely to profoundly influence the quality and accessibility of CWD for wood-inhabiting organisms, but the factors affecting covering are largely unknown. In a five-year experiment we determined predictors of covering rate of fresh logs in boreal forests and clear-cuts. Logs with branches were little covered because they had low longitudinal ground contact. For branchless logs, longitudinal ground contact was most strongly related to estimated peat depth (positive relation). The strongest predictor for total cover of branchless logs was longitudinal ground contact. To evaluate the effect on cover of factors other than longitudinal ground contact, we separately analyzed data from only those log sections that were in contact with the ground. Four factors were prominent predictors of percentage cover of such log sections: estimated peat depth, canopy shade (both increasing cover), potential solar radiation calculated from slope and slope aspect, and diameter of the log (both reducing cover). Peat increased cover directly through its low resistance, which allowed logs to sink and soil contact to increase. High moisture and low temperatures in pole-ward facing slopes and under a canopy favor peat formation through lowered decomposition and enhanced growth of peat-forming mosses, which also proved to rapidly overgrow logs. We found that in some boreal forests, peat and fast-growing mosses can rapidly cover logs lying on the ground. When actively introducing CWD for conservation purposes, we recommend that such rapid covering is avoided, thereby most likely improving the CWD's longevity as habitat for many species

Where are we now with European forest multi-taxon biodiversity and where can we head to?

The European biodiversity and forest strategies rely on forest sustainable management (SFM) to conserve forest biodiversity. However, current sustainability assessments hardly account for direct biodiversity indicators. We focused on forest multi-taxon biodiversity to: i) gather and map the existing information; ii) identify knowledge and research gaps; iii) discuss its research potential. We established a research network to fit data on species, standing trees, lying deadwood and sampling unit description from 34 local datasets across 3591 sampling units. A total of 8724 species were represented, with the share of common and rare species varying across taxonomic classes: some included many species with several rare ones (e.g., Insecta); others (e.g., Bryopsida) were represented by few common species. Tree-related structural attributes were sampled in a subset of sampling units (2889; 2356; 2309 and 1388 respectively for diameter, height, deadwood and microhabitats). Overall, multi-taxon studies are biased towards mature forests and may underrepresent the species related to other developmental phases. European forest compositional categories were all represented, but beech forests were over-represented as compared to thermophilous and boreal forests. Most sampling units (94%) were referred to a habitat type of conservation concern. Existing information may support European conservation and SFM strategies in: (i) methodological harmonization and coordinated monitoring; (ii) definition and testing of SFM indicators and thresholds; (iii) data-driven assessment of the effects of environmental and management drivers on multi-taxon forest biological and functional diversity, (iv) multi-scale forest monitoring integrating in-situ and remotely sensed information

General anaesthetic and airway management practice for obstetric surgery in England: a prospective, multicentre observational study

There are no current descriptions of general anaesthesia characteristics for obstetric surgery, despite recent changes to patient baseline characteristics and airway management guidelines. This analysis of data from the direct reporting of awareness in maternity patients’ (DREAMY) study of accidental awareness during obstetric anaesthesia aimed to describe practice for obstetric general anaesthesia in England and compare with earlier surveys and best-practice recommendations. Consenting patients who received general anaesthesia for obstetric surgery in 72 hospitals from May 2017 to August 2018 were included. Baseline characteristics, airway management, anaesthetic techniques and major complications were collected. Descriptive analysis, binary logistic regression modelling and comparisons with earlier data were conducted. Data were collected from 3117 procedures, including 2554 (81.9%) caesarean deliveries. Thiopental was the induction drug in 1649 (52.9%) patients, compared with propofol in 1419 (45.5%). Suxamethonium was the neuromuscular blocking drug for tracheal intubation in 2631 (86.1%), compared with rocuronium in 367 (11.8%). Difficult tracheal intubation was reported in 1 in 19 (95%CI 1 in 16–22) and failed intubation in 1 in 312 (95%CI 1 in 169–667). Obese patients were over-represented compared with national baselines and associated with difficult, but not failed intubation. There was more evidence of change in practice for induction drugs (increased use of propofol) than neuromuscular blocking drugs (suxamethonium remains the most popular). There was evidence of improvement in practice, with increased monitoring and reversal of neuromuscular blockade (although this remains suboptimal). Despite a high risk of difficult intubation in this population, videolaryngoscopy was rarely used (1.9%)