Bootstrap percolation on homogeneous trees has 2 phase transitions

We study the threshold theta bootstrap percolation model on the homogeneous tree with degree b + 1, 2 <= theta <= b, and initial density p. It is known that there exists a nontrivial critical value for p, which we call p(f), such that a) for p > p(f), the final bootstrapped configuration is fully occupied for almost every initial configuration, and b) if p < p(f) , then for almost every initial configuration, the final bootstrapped configuration has density of occupied vertices less than 1. In this paper, we establish the existence of a distinct critical value for p, p(c), such that 0 < p(c) < p(f), with the following properties: 1) if p <= p(c), then for almost every initial configuration there is no infinite cluster of occupied vertices in the final bootstrapped configuration; 2) if p > p(c), then for almost every initial configuration there are infinite clusters of occupied vertices in the final bootstrapped configuration. Moreover, we show that 3) for p < p(c), the distribution of the occupied cluster size in the final bootstrapped configuration has an exponential tail; 4) at p = p(c), the expected occupied cluster size in the final bootstrapped configuration is infinite; 5) the probability of percolation of occupied vertices in the final bootstrapped configuration is continuous on [0, p(f)] and analytic on (p(c), p(f) ), admitting an analytic continuation from the right at p (c) and, only in the case theta = b, also from the left at p(f).

The disk-percolation model on graphs

We study a long-range percolation model whose dynamics describe the spreading of an infection on an infinite graph. We obtain a sufficient condition for phase transition and prove all upper bound for the critical parameter of spherically symmetric trees. (C) 2008 Elsevier B.V. All rights reserved.

Effects of subcutaneous methadone, morphine, buprenorphine or saline on thermal and pressure thresholds in cats

This study compared pressure and thermal thresholds after administration of three opioids in eight cats. Pressure stimulation was performed via a bracelet taped around the forearm. Three ball-bearings were advanced against the forearm by inflation of a modified blood pressure bladder. Pressure in the cuff was recorded at the end point (leg shake and head turn). Thermal threshold was tested as previously reported using a heated probe held against the thorax [Dixon et al. (2002) Research in Veterinary Science, 72, 205]. After baseline recordings, each cat received subcutaneous methadone 0.2 mg/kg, morphine 0.2 mg/kg, buprenorphine 0.02 mg/kg or saline 0.3 mL in a four period cross-over study. Measurements were made at 15, 30, 45 min and 1, 2, 3, 4, 8, 12 and 24 h after the injection. Data were analysed by ANOVA (P < 0.05). There were no significant changes in thresholds after saline. Thermal threshold increased at 45 min after buprenorphine (maximum 2.8 +/- 3 degrees C), 1-3 h after methadone (maximum 3.4 +/- 1.9 degrees C) and 45 min to 1 h (maximum 3.4 +/- 2 degrees C) after morphine. Pressure threshold increased 30-45 min (maximum 238 +/- 206 mmHg) after buprenorphine, 45-60 min after methadone (maximum 255 +/- 232 mmHg) and 45-60 min and 3-6 h (maximum 255 +/- 232 mmHg) after morphine. Morphine provided the best analgesia, and methadone appears a promising alternative. Buprenorphines limited effect was probably related to the subcutaneous route of administration. Previously, buprenorphine has produced much greater effects when given by other routes.

Effects of buprenorphine, carprofen and saline on thermal and mechanical nociceptive thresholds in cats

To evaluate a prototype pressure stimulus device for use in the cat and to compare with a known thermal threshold device.Eight healthy adult cats weighing between 3.0 and 4.9 kg.Pressure stimulation was given via a plastic bracelet taped around the forearm. Three 2.4 mm diameter ball bearings, in a 10-mm triangle, were advanced against the craniolateral surface of the antebrachium by manual inflation of a modified blood pressure bladder. Pressure in the cuff was recorded at the end point (leg shake and head turn). Thermal threshold was also tested. Stimuli were stopped if they reached 55 degrees C or 450 mmHg without response. After four pressure and thermal threshold baselines, each cat received SC buprenorphine 0.01 mg kg(-1), carprofen 4 mg kg(-1) or saline 0.3 mL in a three period cross-over study with a 1-week interval. The investigator was blinded to the treatment. Measurements were made at 0.25. 0.5, 0.75, 1, 2, 3, 4, 6, 8, and 24 hours after injection. Data were analyzed by using ANOVA.There were no significant changes in thermal or pressure threshold after administration of saline or carprofen, but thermal threshold increased from 60 minutes until 8 hours after administration of buprenorphine (p < 0.05). The maximum increase in threshold from baseline (Delta T-max) was 3.5 +/- 3.1 degrees C at 2 hours. Pressure threshold increased 2 hours after administration of buprenorphine (p < 0.05) when the increase in threshold above baseline (Delta P-max) was 162 +/- 189 mmHg.This pressure device resulted in thresholds that were affected by analgesic treatment in a similar manner but to a lesser degree than the thermal method. Pressure stimulation may be a useful additional method for analgesic studies in cats.

Effects of meperidine or saline on thermal, mechanical and electrical nociceptive thresholds in cats

Objective To measure cutaneous electrical nociceptive thresholds in relation to known thermal and mechanical stimulation for nociceptive threshold detection in cats.Study design Prospective, blinded, randomized cross-over study with 1-week washout interval.Animals Eight adult cats [bodyweight 5.1 +/- 1.8 kg (mean + SD)].Methods Mechanical nociceptive thresholds were tested using a step-wise manual inflation of a modified blood pressure bladder attached to the cat's thoracic limb. Thermal nociceptive thresholds were measured by increasing the temperature of a probe placed on the thorax. The electrical nociceptive threshold was tested using an escalating current from a constant current generator passed between electrodes placed on the thoracic region. A positive response (threshold) was recorded when cats displayed any or all of the following behaviors: leg shake, head turn, avoidance, or vocalization. Four baseline readings were performed before intramuscular injection of meperidine (5 mg kg(-1)) or an equal volume of saline. Threshold recordings with each modality were made at 15, 30, 45, 60, 90, and 120 minutes post-injection. Data were analyzed using ANOVA and paired t-tests (significance at p < 0.05).Results There were no significant changes in thermal, mechanical, or electrical thresholds after saline. Thermal thresholds increased at 15-60 minutes (p < 0.01) and mechanical threshold increased at 30 and 45 minutes after meperidine (p < 0.05). Maximum thermal threshold was +4.1 +/- 0.3 degrees C above baseline at 15 minutes while maximum mechanical threshold was 296 +/- 265 mmHg above baseline at 30 minutes after meperidine. Electrical thresholds following meperidine were not significantly different than baseline (p > 0.05). Thermal and electrical thresholds after meperidine were significantly higher than saline at 30 and 45 minutes (p < 0.05), and at 120 minutes (p < 0.05), respectively. Mechanical thresholds were significantly higher than saline treatment at 30 minutes (p <= 0.05).Conclusion and clinical relevance Electrical stimulation did not detect meperidine analgesia whereas both thermal and mechanical thresholds changed after meperidine administration in cats.

Short-time dynamics of percolation observables

We consider the critical short-time evolution of magnetic and droplet-percolation order parameters for the Ising model in two and three dimensions, through Monte Carlo simulations with the (local) heat-bath method. We find qualitatively different dynamic behaviors for the two types of order parameters. More precisely, we find that the percolation order parameter does not have a power-law behavior as encountered for the magnetization, but develops a scale (related to the relaxation time to equilibrium) in the Monte Carlo time. We argue that this difference is due to the difficulty in forming large clusters at the early stages of the evolution. Our results show that, although the descriptions in terms of magnetic and percolation order parameters may be equivalent in the equilibrium regime, greater care must be taken to interpret percolation observables at short times. In particular, this concerns the attempts to describe the dynamics of the deconfinement phase transition in QCD using cluster observables.

Dynamic critical behavior of percolation observables in the 2d Ising model

We present preliminary results of our numerical study of the critical dynamics of percolation observables for the two-dimensional Ising model. We consider the (Monte-Carlo) short-time evolution of the system obtained with a local heat-bath method and with the global Swendsen-Wang algorithm. In both cases, we find qualitatively different dynamic behaviors for the magnetization and Omega, the order parameter of the percolation transition. This may have implications for the recent attempts to describe the dynamics of the QCD phase transition using cluster observables.

Percolation of Monte Carlo clusters

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The Chemical Percolation Devolatilization Model Applied to the Devolatilization of Coal in High Intensity Acoustic Fields

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Electrical percolation during gelation of lithium doped siloxane-poly(oxyethylene) hybrids

Gelation mechanisms of lithium-doped Siloxane-Poly(oxyethylene) (PEO) hybrids containing polymer of two different molecular weight (500 and 1900 g/mol) were investigated through the evolution of the electrical properties during the solgel transition. The results of electrical measurements, performed by in-situ complex impedance spectroscopy, were correlated with the coordination and the dynamical properties of the lithium ions during the process as shown by Li-7 NMR measurements. For both hybrids sols, a decrease of the conductivity is observed at the initial gelation stage, due to the existence of an inverted percolation process consisting of the progressive separation of solvent molecules containing conducting species in isolated islands during the solid network formation. An increase of conductivity occurs at more advanced stages of gelation and aging, attributed to the increasing connectivity between PEO chains promoted by the formation of crosslinks of siloxane particles at their extremities, favoring hopping motions of lithium ions along the chains.

Study of thresholds to burning in surface grinding process

This work aims at finding out the threshold to burning in surface grinding process. Acoustic emission and electric power signals are acquired from an analog-digital converter and processed through algorithms in order to generate a control signal to inform the operator or interrupt the process in the case of burning occurrence. The thresholds that dictate the situation of burn and non-burn were studied as well as a comparison between the two parameters was carried out. In the experimental work one type of steel (ABNT-1045 annealed) and one type of grinding wheel referred to as TARGA model 3TG80.3-NV were employed. Copyright © 2005 by ABCM.

A multi-agent system with a percolation approach to simulate the driving pattern of Plug-In ELectric Vehicles

A multi-agent system with a percolation approach to simulate the driving pattern of Plug-In Electric Vehicle (PEV), especially suited to simulate the PEVs behavior on any distribution systems, is presented. This tool intends to complement information about the driving patterns database on systems where that kind of information is not available. So, this paper aims to provide a framework that is able to work with any kind of technology and load generated of PEVs. The service zone is divided into several sub-zones, each subzone is considered as an independent agent identified with corresponding load level, and their relationships with the neighboring zones are represented as network probabilities. A percolation approach is used to characterize the autonomy of the battery of the PVEs to move through the city. The methodology is tested with data from a mid-size city real distribution system. The result shows the sub-area where the battery of PEVs will need to be recharge and gives the planners of distribution systems the necessary input for a medium to long term network planning in a smart grid environment. © 2012 IEEE.

Modeling Habitat Split: Landscape and Life History Traits Determine Amphibian Extinction Thresholds

Habitat split is a major force behind the worldwide decline of amphibian populations, causing community change in richness and species composition. In fragmented landscapes, natural remnants, the terrestrial habitat of the adults, are frequently separated from streams, the aquatic habitat of the larvae. An important question is how this landscape configuration affects population levels and if it can drive species to extinction locally. Here, we put forward the first theoretical model on habitat split which is particularly concerned on how split distance - the distance between the two required habitats - affects population size and persistence in isolated fragments. Our diffusive model shows that habitat split alone is able to generate extinction thresholds. Fragments occurring between the aquatic habitat and a given critical split distance are expected to hold viable populations, while fragments located farther away are expected to be unoccupied. Species with higher reproductive success and higher diffusion rate of post-metamorphic youngs are expected to have farther critical split distances. Furthermore, the model indicates that negative effects of habitat split are poorly compensated by positive effects of fragment size. The habitat split model improves our understanding about spatially structured populations and has relevant implications for landscape design for conservation. It puts on a firm theoretical basis the relation between habitat split and the decline of amphibian populations. © 2013 Fonseca et al.

Can savannas become forests? A coupled analysis of nutrient stocks and fire thresholds in central Brazil

Aims: The effects of fire ensure that large areas of the seasonal tropics are maintained as savannas. The advance of forests into these areas depends on shifts in species composition and the presence of sufficient nutrients. Predicting such transitions, however, is difficult due to a poor understanding of the nutrient stocks required for different combinations of species to resist and suppress fires. Methods: We compare the amounts of nutrients required by congeneric savanna and forest trees to reach two thresholds of establishment and maintenance: that of fire resistance, after which individual trees are large enough to survive fires, and that of fire suppression, after which the collective tree canopy is dense enough to minimize understory growth, thereby arresting the spread of fire. We further calculate the arboreal and soil nutrient stocks of savannas, to determine if these are sufficient to support the expansion of forests following initial establishment. Results: Forest species require a larger nutrient supply to resist fires than savanna species, which are better able to reach a fire-resistant size under nutrient limitation. However, forest species require a lower nutrient supply to attain closed canopies and suppress fires; therefore, the ingression of forest trees into savannas facilitates the transition to forest. Savannas have sufficient N, K, and Mg, but require additional P and Ca to build high-biomass forests and allow full forest expansion following establishment. Conclusions: Tradeoffs between nutrient requirements and adaptations to fire reinforce savanna and forest as alternate stable states, explaining the long-term persistence of vegetation mosaics in the seasonal tropics. Low-fertility limits the advance of forests into savannas, but the ingression of forest species favors the formation of non-flammable states, increasing fertility and promoting forest expansion. © 2013 Springer Science+Business Media Dordrecht.

Experimental poverty thresholds for the United States 1990 to 1998

Includes bibliography