Dynamics of forest fires as a directed percolation model

Percolation theory as a conceptual framework to explain spontaneous atrial fibrillation termination: a pilot study

Atrial fibrillation (AF) strikingly possesses the ability to abruptly transition into more organized electrical activity and spontaneously terminate, even after persisting for long periods. Despite being central to the clinical behavior and treatment of AF, these phenomena remain incompletely understood. In this paper, we hypothesized that the spontaneous termination of AF may represent a type of percolation phase transition, which is more likely to occur when a domain spanning cluster of refractory sites in the atrium are connected (called a 'percolation cluster'). This was assessed in n=50 computational simulations of AF developed using the Aliev-Panfilov (APV) 2-dimensional cell model. In self-terminating simulations of AF, it was found that the average refractory cluster size, χ(p) (median: 647.7), and the largest refractory cluster size, M1 (median: 1702.3), abruptly increased just prior to AF spontaneously terminating, indicating the onset of the formation of a domain spanning percolation cluster. In contrast, simulations of sustained AF did not demonstrate an increase in χ(p) (median: 463.0) and M1 (median: 1448.2). Self-terminating AF simulations also demonstrated hallmark properties characteristic of a percolation phase transition, such as an abrupt increase in χ(p) at the critical occupation probability pc. The cluster size distribution was also shown to obey a power law for various occupation probabilities p, also indicative of a percolation phase transition. Collectively, these properties suggests that the spontaneous termination of AF could be a form of percolation phase transition, which could provide new insights for AF treatment.

Climate Impacts on Fire Risk in Desert Shrublands: A Modeling Study

Fire is recognized to be an important disturbance in many ecosystems worldwide, although desert ecosystems are not generally thought of as being prone to fire, primarily because of the lack of a continuous fuel bed. However, the likelihood of catastrophic fires in some desert systems is increasing due to the spread of exotic species, which can grow in the open. A second factor increasing fire risk may be extreme rainfall events caused by climate warming that can lead to an increase in fuel loads. Our work explores the impact of increased rainfall on fire risk in creosote shrublands that have been invaded by exotic grasses. We take experimental results from creosote (Larrea tridentata) shrublands in the Mojave and Sonoran Deserts of the Southwestern United States and develop spatially explicit simulation models to explore the impact of shifting rainfall regimes on biomass production and fire spread. In doing this, we explore two scales that are important in the spread of fire: (1) the macro-scale which considers the likelihood that fire arriving at one edge of a modeled landscape will successfully reach the opposite edge, leading to spread at a broader scale; and (2) the micro-scale, which considers fire spread within the landscape. We use a very simple model to first explore how changes in the distribution of fuel in the landscape impact the ability of fire to spread across and within the landscape. We then add more realism by including a direct consideration of creosote shrub distributions and biomass levels produced in different vegetation zones associated with distance from creosote. Our models show that the spread of fire at both macro- and micro-scales can be predicted from a knowledge of the statistical distribution of biomass in the field. The only additional information that is needed to predict the extent of fire spread is the amount of biomass at a local site (g m–2) required to ignite standing biomass in adjacent sites. This will depend upon species composition as well as amount of biomass, the hydration status of the vegetation and climatic conditions, such as windspeed and relative humidity.

Irreversible phase transitions driven by an oscillatory parameter in a far-from-equilibrium system

The dynamic response of a forest-fire model to the harmonic variation of an external parameter is studied by means of numerical simulations. Second-order irreversible phase transitions driven by the harmonic input are reported. The location of such transitions depends on both the amplitude and period of the input signal. By means of epidemic studies the relevant critical exponents can be determined, which allow us to place the reported transitions in the universality class of directed percolation. This conclusion is also supported by a field theoretical calculation.