Perturbative analysis of disordered Ising models close to criticality

We consider a two-dimensional Ising model with random i.i.d. nearest-neighbor ferromagnetic couplings and no external magnetic field. We show that, if the probability of supercritical couplings is small enough, the system admits a convergent cluster expansion with probability one. The associated polymers are defined on a sequence of increasing scales; in particular the convergence of the above expansion implies the infinite differentiability of the free energy but not its analyticity. The basic tools in the proof are a general theory of graded cluster expansions and a stochastic domination of the disorder

Competitive nucleation in reversible Probabilistic Cellular Automata

The problem of competitive nucleation in the framework of Probabilistic Cellular Automata is studied from the dynamical point of view. The dependence of the metastability scenario on the self--interaction is discussed. An intermediate metastable phase, made of two flip--flopping chessboard configurations, shows up depending on the ratio between the magnetic field and the self--interaction. A behavior similar to the one of the stochastic Blume--Capel model with Glauber dynamics is found

Metastability and Nucleation for the Blume-Capel Model. Different mechanisms of transition

We study metastability and nucleation for the Blume-Capel model: a ferromagnetic nearest neighbour two-dimensional lattice system with spin variables taking values in -1,0,+1. We consider large but finite volume, small fixed magnetic field h and chemical potential "lambda" in the limit of zero temperature; we analyze the first excursion from the metastable -1 configuration to the stable +1 configuration. We compute the asymptotic behaviour of the transition time and describe the typical tube of trajectories during the transition. We show that, unexpectedly, the mechanism of transition changes abruptly when the line h=2*lambda is crossed.Comment: 96 pages, 44 tex-figures, 7 postscript figure

First in-beam studies of a Resistive-Plate WELL gaseous multiplier

We present the results of the first in-beam studies of a medium size (10$\times$10 cm$^2$) Resistive-Plate WELL (RPWELL): a single-sided THGEM coupled to a pad anode through a resistive layer of high bulk resistivity ($\sim$10$^9 \Omega$cm). The 6.2~mm thick (excluding readout electronics) single-stage detector was studied with 150~GeV muons and pions. Signals were recorded from 1$\times$1 cm$^2$ square copper pads with APV25-SRS readout electronics. The single-element detector was operated in Ne\(5% $\mathrm{CH_{4}}$) at a gas gain of a few times 10$^4$, reaching 99$\%$ detection efficiency at average pad multiplicity of $\sim$1.2. Operation at particle fluxes up to $\sim$10$^4$ Hz/cm$^2$ resulted in $\sim$23$\%$ gain drop leading to $\sim$5$\%$ efficiency loss. The striking feature was the discharge-free operation, also in intense pion beams. These results pave the way towards robust, efficient large-scale detectors for applications requiring economic solutions at moderate spatial and energy resolutions.Comment: Accepted by JINS

Metastability in Interacting Nonlinear Stochastic Differential Equations II: Large-N Behaviour

We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise, in the limit of large N. Each particle is subjected to a bistable local potential, to a linear coupling with its nearest neighbours, and to an independent source of white noise. For strong coupling (of the order N^2), the system synchronises, in the sense that all oscillators assume almost the same position in their respective local potential most of the time. In a previous paper, we showed that the transition from strong to weak coupling involves a sequence of symmetry-breaking bifurcations of the system's stationary configurations, and analysed in particular the behaviour for coupling intensities slightly below the synchronisation threshold, for arbitrary N. Here we describe the behaviour for any positive coupling intensity \gamma of order N^2, provided the particle number N is sufficiently large (as a function of \gamma/N^2). In particular, we determine the transition time between synchronised states, as well as the shape of the "critical droplet", to leading order in 1/N. Our techniques involve the control of the exact number of periodic orbits of a near-integrable twist map, allowing us to give a detailed description of the system's potential landscape, in which the metastable behaviour is encoded

Darwin’s wind hypothesis: does it work for plant dispersal in fragmented habitats?

Using the wind-dispersed plant Mycelis muralis, we examined how landscape fragmentation affects variation in seed traits contributing to dispersal. Inverse terminal velocity (Vt−1) of field-collected achenes was used as a proxy for individual seed dispersal ability. We related this measure to different metrics of landscape connectivity, at two spatial scales: in a detailed analysis of eight landscapes in Spain and along a latitudinal gradient using 29 landscapes across three European regions. In the highly patchy Spanish landscapes, seed Vt−1 increased significantly with increasing connectivity. A common garden experiment suggested that differences in Vt−1 may be in part genetically based. The Vt−1 was also found to increase with landscape occupancy, a coarser measure of connectivity, on a much broader (European) scale. Finally, Vt−1 was found to increase along a south–north latitudinal gradient. Our results for M. muralis are consistent with ‘Darwin’s wind dispersal hypothesis’ that high cost of dispersal may select for lower dispersal ability in fragmented landscapes, as well as with the ‘leading edge hypothesis’ that most recently colonized populations harbour more dispersive phenotypes.

Population history from the Neolithic to present on the Mediterranean island of Sardinia: an ancient DNA perspective

Recent ancient DNA studies of western Eurasia have revealed a dynamic history of admixture, with evidence for major migrations during the Neolithic and Bronze Age. The population of the Mediterranean island of Sardinia has been notable in these studies –} Neolithic individuals from mainland Europe cluster more closely with Sardinian individuals than with all other present-day Europeans. The current model to explain this result is that Sardinia received an initial influx of Neolithic ancestry and then remained relatively isolated from expansions in the later Neolithic and Bronze Age that took place in continental Europe. To test this model, we generated genome-wide capture data (approximately 1.2 million variants) for 43 ancient Sardinian individuals spanning the Neolithic through the Bronze Age, including individuals from Sardinia{’}s Nuragic culture, which is known for the construction of numerous large stone towers throughout the island. We analyze these new samples in the context of previously generated genome-wide ancient DNA data from 972 ancient individuals across western Eurasia and whole-genome sequence data from approximately 1,500 modern individuals from Sardinia. The ancient Sardinian individuals show a strong affinity to western Mediterranean Neolithic populations and we infer a high degree of genetic continuity on the island from the Neolithic (around fifth millennium BCE) through the Nuragic period (second millennium BCE). In particular, during the Bronze Age in Sardinia, we do not find significant levels of the {“}Steppe{” ancestry that was spreading in many other parts of Europe at that time. We also characterize subsequent genetic influx between the Nuragic period and the present. We detect novel, modest signals of admixture between 1,000 BCE and present-day, from ancestry sources in the eastern and northern Mediterranean. Within Sardinia, we confirm that populations from the more geographically isolated mountainous provinces have experienced elevated levels of genetic drift and that northern and southwestern regions of the island received more gene flow from outside Sardinia. Overall, our genetic analysis sheds new light on the origin of Neolithic settlement on Sardinia, reinforces models of genetic continuity on the island, and provides enhanced power to detect post-Bronze-Age gene flow. Together, these findings offer a refined demographic model for future medical genetic studies in Sardinia

Critical droplets in Metastable States of Probabilistic Cellular Automata

We consider the problem of metastability in a probabilistic cellular automaton (PCA) with a parallel updating rule which is reversible with respect to a Gibbs measure. The dynamical rules contain two parameters $\beta$ and $h$ which resemble, but are not identical to, the inverse temperature and external magnetic field in a ferromagnetic Ising model; in particular, the phase diagram of the system has two stable phases when $\beta$ is large enough and $h$ is zero, and a unique phase when $h$ is nonzero. When the system evolves, at small positive values of $h$, from an initial state with all spins down, the PCA dynamics give rise to a transition from a metastable to a stable phase when a droplet of the favored $+$ phase inside the metastable $-$ phase reaches a critical size. We give heuristic arguments to estimate the critical size in the limit of zero ``temperature'' ($\beta\to\infty$), as well as estimates of the time required for the formation of such a droplet in a finite system. Monte Carlo simulations give results in good agreement with the theoretical predictions.Comment: 5 LaTeX picture

Abrupt Convergence and Escape Behavior for Birth and Death Chains

We link two phenomena concerning the asymptotical behavior of stochastic processes: (i) abrupt convergence or cut-off phenomenon, and (ii) the escape behavior usually associated to exit from metastability. The former is characterized by convergence at asymptotically deterministic times, while the convergence times for the latter are exponentially distributed. We compare and study both phenomena for discrete-time birth-and-death chains on Z with drift towards zero. In particular, this includes energy-driven evolutions with energy functions in the form of a single well. Under suitable drift hypotheses, we show that there is both an abrupt convergence towards zero and escape behavior in the other direction. Furthermore, as the evolutions are reversible, the law of the final escape trajectory coincides with the time reverse of the law of cut-off paths. Thus, for evolutions defined by one-dimensional energy wells with sufficiently steep walls, cut-off and escape behavior are related by time inversion.Comment: 2 figure