Cyclic Complexity of Some Infinite Words and Generalizations

Cassaigne et al. introduced the cyclic complexity function c_x(n), which gives the number of cyclic conjugacy classes of length-n factors of a word x. We study the behavior of this function for the Fibonacci word f and the Thue–Morse word t. If φ = (1 + √5)/2, we show that lim sup_{n → 1} c_f(n)/n ≥ 2/φ² and conjecture that equality holds. Similarly, we show that lim sup_{n → 1} c_t(n)/n ≥ 2 and conjecture that equality holds. We also propose a generalization of the cyclic complexity function and suggest some directions for further investigation. Most results are obtained by computer proofs using Mousavi’s Walnut software.The first author was supported by an NSERC USRA. The second author was supported by an NSERC Discovery Grant

Peat consumption and carbon loss due to smouldering wildfire in a temperate peatland

Temperate peatlands represent a substantial store of carbon and their degradation is a potentially significant positive feedback to climate change. The ignition of peat deposits can cause smouldering wildfires that have the potential to release substantial amounts of carbon and to cause environmental damage from which ecosystem recovery can be slow. Direct estimates of the loss of carbon due to smouldering wildfires are needed to inform global estimates of the effect of wildfire on carbon dynamics and to aid with national emissions accounting. We surveyed the effect of a severe wildfire that burnt within an afforested peatland in the Scottish Highlands during the summer of 2006. The fire ignited layers of peat which continued to burn as a sub-surface smouldering wildfire for more than a month after the initial surface fire and despite several episodes of heavy rain. The smouldering fire perimeter enclosed an area of 4.1 ha. Analysis of weather records showed that the fire coincided with unusually warm, dry conditions and a period when the Canadian Fire Weather Index system predicted both generally high danger conditions (high Fire Weather Index) and low fuel moisture content in deep organic soil layers (high Drought Code values). Remaining peat layers in the burn area had comparatively low fuel moisture contents of ca. 250% dry weight. Within the smouldering fire’s perimeter, mean depth of burn was estimated at 17.5 ± 2.0 cm but ranged from 1 to 54 cm. Based on field measurements, our estimates suggested that, in total, the smouldering wildfire burnt 773 ± 120 t of organic matter corresponding to 396 ± 63 t of carbon and a carbon loss per unit area burnt of 96 ± 15 t ha−1 (9.6 ± 1.5 kg m−2). This corresponds to between 0.1% and 0.3% of the estimated total amount of carbon sequestered annually by UK peatlands. Our results also provide circumstantial evidence that afforestation of peatland soils, and associated site preparation, may contribute to an increased risk of peat fires. Smouldering fires are difficult to detect using remotely sensing techniques due to their low temperature and low heat release and the fact that the tree canopy remains intact for months afterwards. If similar smouldering fires are underreported in other temperate, boreal and tropical peatland regions then emissions from peatland burning may well be a substantially greater issue than currently assumed

Effects of fire and CO2 on biogeography and primary production in glacial and modern climates

Dynamic global vegetation models (DGVMs) can disentangle causes and effects in the control of vegetation and fire. We used a DGVM to analyse climate, CO2 and fire influences on biome distribution and net primary production (NPP) in last glacial maximum (LGM) and pre-industrial (PI) times. The Land surface Processes and eXchanges (LPX) DGVM was run in a factorial design with fire ‘off’ or ‘on’, CO2 at LGM (185 ppm) or PI (280 ppm) concentrations, and LGM (modelled) or recent climates. Results were analysed by Stein–Alpert decomposition to separate primary effects from synergies. Fire removal causes forests to expand and global NPP to increase slightly. Low CO2 greatly reduces forest area (dramatically in a PI climate; realistically under an LGM climate) and global NPP. NPP under an LGM climate was reduced by a quarter as a result of low CO2. The reduction in global NPP was smaller at low temperatures, but greater in the presence of fire. Global NPP is controlled by climate and CO2 directly through photosynthesis, but also through biome distribution, which is strongly influenced by fire. Future vegetation simulations will need to consider the coupled responses of vegetation and fire to CO2 and climate