Complex dynamics in simple systems with periodic parameter oscillations

We study systems with periodically oscillating parameters that can give way to complex periodic or nonperiodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal Lyapunov exponent corresponds to a stable periodic orbit. By this, extremely complicated periodic orbits composed of contracting and expanding phases appear in a natural way. Employing the technique of ϵ-uncertain points, we find that values of the control parameters supporting such periodic motion are densely embedded in a set of values for which the motion is chaotic. When a tiny amount of noise is coupled to the system, dynamics with positive and with negative nontrivial Lyapunov exponents are indistinguishable. We discuss two physical systems, an oscillatory flow inside a duct and a dripping faucet with variable water supply, where such a mechanism seems to be responsible for a complicated alternation of laminar and turbulent phases.

Modelling of control options for an outbreak of Mycoplasma gallisepticum in egg production: a decision support tool

Mycoplasma gallisepticum (MG) is a bacterium that causes respiratory disease in chickens, leading to reduced egg production. A dynamic simulation model was developed that can be used to assess the costs and benefits of control using antimicrobials or vaccination in caged or free range systems. The intended users are veterinarians and egg producers. A user interface is provided for input of flock specific parameters. The economic consequence of an MG outbreak is expressed as a reduction in expected egg output. The model predicts that either vaccination or microbial treatment can approximately halve potential losses from MG in some circumstances. Sensitivity analysis is used to test assumptions about infection rate and timing of an outbreak. Feedback from veterinarians points to the value of the model as a discussion tool with producers.

Synoptic versus orographic control on stationary convective banding

Quasi-stationary convective bands can cause large localised rainfall accumulations and are often anchored by topographic features. Here, the predictability of and mechanisms causing one such band are determined using ensembles of the Met Office Unified Model at convection-permitting resolution (1.5 km grid length). The band was stationary over the UK for 3 h and produced rainfall accumulations of up to 34 mm. The amount and location of the predicted rainfall was highly variable despite only small differences between the large-scale conditions of the ensemble members. Only three of 21 members of the control ensemble produced a stationary rain band; these three had the weakest upstream winds and hence lowest Froude number. Band formation was due to the superposition of two processes: lee-side convergence resulting from flow around an upstream obstacle and thermally forced convergence resulting from elevated heating over the upstream terrain. Both mechanisms were enhanced when the Froude number was lower. By increasing the terrain height (thus reducing the Froude number), the band became more predictable. An ensemble approach is required to successfully predict the possible occurrence of such quasi-stationary convective events because the rainfall variability is largely modulated by small variations of the large-scale flow. However, high-resolution models are required to accurately resolve the small-scale interactions of the flow with the topography upon which the band formation depends. Thus, although topography provides some predictability, the quasi-stationary convective bands anchored by it are likely to remain a forecasting challenge for many years to come.

Ecophysiology of seed dormancy and the control of germination in early spring-flowering Galanthus nivalis and Narcissus pseudonarcissus (Amaryllidaceae)

Seed dormancy induction and alleviation in the winter-flowering moist temperate woodland species Galanthus nivalis and Narcissus pseudonarcissus are complex and poorly understood. Temperature, light and desiccation were investigated to elucidate their role in the germination ecophysiology of these species. Outdoor and laboratory experiments simulating different seasonal temperatures, seasonal durations, and temperature fluctuations; the presence of light during different seasons; and intermittent drying (during the summer period) over several ‘years’ investigated the importance of these factors in germination. Warm summer-like temperatures (20°C) were necessary for germination at subsequent cooler autumn-like temperatures (greatest at 15°C in G. nivalis and 10°C in N. pseudonarcissus). As the warm temperature duration increased so did germination at subsequent cooler temperatures; further germination occurred in subsequent ‘years’ at cooler temperatures following a second, and also third, warm period. Germination was significantly greater in darkness, particularly in G. nivalis. Dormancy increased with seed maturation period in G. nivalis, because seeds extracted from green capsules germinated more readily than those from yellow. Desiccation increased dormancy in an increasing proportion of N. pseudonarcissus seeds the later they were dried in ‘summer’. Seed viability was only slightly reduced by desiccation in N. pseudonarcissus but was poor and variable in G. nivalis. Shoot formation occurred both at the temperature at which germination was greatest and also if 5°C cooler. In summary, continuous hydration of seeds of both species during warm summer-like temperatures results in the gradual release of seed dormancy; thereafter, darkness and cooler temperatures promote germination. Cold temperatures, increased seed maturity (G. nivalis), and desiccation (N. pseudonarcissus) increase dormancy while light inhibits germination.

Organic soils promote the efficacy of entomopathogenic nematodes, with different foraging strategies, in the control of a major forest pest: a meta-analysis of field trial data

The large pine weevil, Hylobius abietis, is a serious pest of reforestation in northern Europe. However, weevils developing in stumps of felled trees can be killed by entomopathogenic nematodes applied to soil around the stumps and this method of control has been used at an operational level in the UK and Ireland. We investigated the factors affecting the efficacy of entomopathogenic nematodes in the control of the large pine weevil spanning 10 years of field experiments, by means of a meta-analysis of published studies and previously unpublished data. We investigated two species with different foraging strategies, the ‘ambusher’ Steinernema carpocapsae, the species most often used at an operational level, and the ‘cruiser’ Heterorhabditis downesi. Efficacy was measured both by percentage reduction in numbers of adults emerging relative to untreated controls and by percentage parasitism of developing weevils in the stump. Both measures were significantly higher with H. downesi compared to S. carpocapsae. General linear models were constructed for each nematode species separately, using substrate type (peat versus mineral soil) and tree species (pine versus spruce) as fixed factors, weevil abundance (from the mean of untreated stumps) as a covariate and percentage reduction or percentage parasitism as the response variable. For both nematode species, the most significant and parsimonious models showed that substrate type was consistently, but not always, the most significant variable, whether replicates were at a site or stump level, and that peaty soils significantly promote the efficacy of both species. Efficacy, in terms of percentage parasitism, was not density dependent.

Body-centric modelling, identification, and acceleration tracking control of a quadrotor UAV

This paper presents the mathematical development of a body-centric nonlinear dynamic model of a quadrotor UAV that is suitable for the development of biologically inspired navigation strategies. Analytical approximations are used to find an initial guess of the parameters of the nonlinear model, then parameter estimation methods are used to refine the model parameters using the data obtained from onboard sensors during flight. Due to the unstable nature of the quadrotor model, the identification process is performed with the system in closed-loop control of attitude angles. The obtained model parameters are validated using real unseen experimental data. Based on the identified model, a Linear-Quadratic (LQ) optimal tracker is designed to stabilize the quadrotor and facilitate its translational control by tracking body accelerations. The LQ tracker is tested on an experimental quadrotor UAV and the obtained results are a further means to validate the quality of the estimated model. The unique formulation of the control problem in the body frame makes the controller better suited for bio-inspired navigation and guidance strategies than conventional attitude or position based control systems that can be found in the existing literature.

The potential of flood forecasting using a variable-resolution global Digital Terrain Model and flood extents from Synthetic Aperture Radar images

A basic data requirement of a river flood inundation model is a Digital Terrain Model (DTM) of the reach being studied. The scale at which modeling is required determines the accuracy required of the DTM. For modeling floods in urban areas, a high resolution DTM such as that produced by airborne LiDAR (Light Detection And Ranging) is most useful, and large parts of many developed countries have now been mapped using LiDAR. In remoter areas, it is possible to model flooding on a larger scale using a lower resolution DTM, and in the near future the DTM of choice is likely to be that derived from the TanDEM-X Digital Elevation Model (DEM). A variable-resolution global DTM obtained by combining existing high and low resolution data sets would be useful for modeling flood water dynamics globally, at high resolution wherever possible and at lower resolution over larger rivers in remote areas. A further important data resource used in flood modeling is the flood extent, commonly derived from Synthetic Aperture Radar (SAR) images. Flood extents become more useful if they are intersected with the DTM, when water level observations (WLOs) at the flood boundary can be estimated at various points along the river reach. To illustrate the utility of such a global DTM, two examples of recent research involving WLOs at opposite ends of the spatial scale are discussed. The first requires high resolution spatial data, and involves the assimilation of WLOs from a real sequence of high resolution SAR images into a flood model to update the model state with observations over time, and to estimate river discharge and model parameters, including river bathymetry and friction. The results indicate the feasibility of such an Earth Observation-based flood forecasting system. The second example is at a larger scale, and uses SAR-derived WLOs to improve the lower-resolution TanDEM-X DEM in the area covered by the flood extents. The resulting reduction in random height error is significant.