Optimal steady motions for oriented vehicles

Motivated by the motion planning problem for oriented vehicles travelling in a 3-Dimensional space; Euclidean space E3, the sphere S3 and Hyperboloid H3. For such problems the orientation of the vehicle is naturally represented by an orthonormal frame over a point in the underlying manifold. The orthonormal frame bundles of the space forms R3,S3 and H3 correspond with their isometry groups and are the Euclidean group of motion SE(3), the rotation group SO(4) and the Lorentzian group SO(1; 3) respectively. Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to left-invariant control systems defined on Lie groups. In this paper a method for integrating these systems is given where the controls are time-independent. For constant twist motions or helical motions, the corresponding curves g(t) 2 SE(3) are given in closed form by using the well known Rodrigues’ formula. However, this formula is only applicable to the Euclidean case. This paper gives a method for computing the non-Euclidean screw/helical motions in closed form. This involves decoupling the system into two lower dimensional systems using the double cover properties of Lie groups, then the lower dimensional systems are solved explicitly in closed form.

Thermospheric Control of the Auroral Source of O+Ions for the Magnetosphere

Linear theory, model ion-density profiles and MSIS neutral thermospheric predictions are used to investigate the stability of the auroral, topside ionosphere to oxygen cyclotron waves: variations of the critical height, above which the plasma is unstable, with field-aligned current, thermal ion density and exospheric temperature are considered. In addition, probabilities are assessed that interactions with neutral atomic gases prevent O+ ions from escaping into the magnetosphere after they have been transversely accelerated by these waves. The two studies are combined to give a rough estimate of the total O+ escape flux as a function of the field-aligned current density for an assumed rise in the perpendicular ion temperature. Charge exchange with neutral oxygen, not hydrogen, is shown to be the principle limitation to the escape of O+ ions, which occurs when the waves are driven unstable down to low altitudes. It is found that the largest observed field-aligned current densities can heat a maximum of about 5×1014 O+ ions m−2 to a threshold above which they are subsequently able to escape into the magnetosphere in the following 500s. Averaged over this period, this would constitute a flux of 1012 m−2 s−1 and in steady-state the peak outflow would then be limited to about 1013 m−2 s−1 by frictional drag on thermal O+ at lower altitudes. Maximum escape is at low plasma density unless the O+ scale height is very large. The outflow decreases with decreasing field-aligned current density and, to a lesser extent, with increasing exospheric temperature. Upward flowing ion events are evaluated as a source of O+ ions for the magnetosphere and as an explanation of the observed solar cycle variation of ring current O+ abundance.

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.

Investigating music tempo as a feedback mechanism for closed-loop BCI control

The feedback mechanism used in a brain-computer interface (BCI) forms an integral part of the closed-loop learning process required for successful operation of a BCI. However, ultimate success of the BCI may be dependent upon the modality of the feedback used. This study explores the use of music tempo as a feedback mechanism in BCI and compares it to the more commonly used visual feedback mechanism. Three different feedback modalities are compared for a kinaesthetic motor imagery BCI: visual, auditory via music tempo, and a combined visual and auditory feedback modality. Visual feedback is provided via the position, on the y-axis, of a moving ball. In the music feedback condition, the tempo of a piece of continuously generated music is dynamically adjusted via a novel music-generation method. All the feedback mechanisms allowed users to learn to control the BCI. However, users were not able to maintain as stable control with the music tempo feedback condition as they could in the visual feedback and combined conditions. Additionally, the combined condition exhibited significantly less inter-user variability, suggesting that multi-modal feedback may lead to more robust results. Finally, common spatial patterns are used to identify participant-specific spatial filters for each of the feedback modalities. The mean optimal spatial filter obtained for the music feedback condition is observed to be more diffuse and weaker than the mean spatial filters obtained for the visual and combined feedback conditions.

Optimal infinity-quasiconformal immersions

For a Hamiltonian K ∈ C2(RN × n) and a map u:Ω ⊆ Rn − → RN, we consider the supremal functional (1) The “Euler−Lagrange” PDE associated to (1)is the quasilinear system (2) Here KP is the derivative and [ KP ] ⊥ is the projection on its nullspace. (1)and (2)are the fundamental objects of vector-valued Calculus of Variations in L∞ and first arose in recent work of the author [N. Katzourakis, J. Differ. Eqs. 253 (2012) 2123–2139; Commun. Partial Differ. Eqs. 39 (2014) 2091–2124]. Herein we apply our results to Geometric Analysis by choosing as K the dilation function which measures the deviation of u from being conformal. Our main result is that appropriately defined minimisers of (1)solve (2). Hence, PDE methods can be used to study optimised quasiconformal maps. Nonconvexity of K and appearance of interfaces where [ KP ] ⊥ is discontinuous cause extra difficulties. When n = N, this approach has previously been followed by Capogna−Raich ? and relates to Teichmüller’s theory. In particular, we disprove a conjecture appearing therein.

Optimising mirid control on cocoa farms through complementary monitoring systems

Mirids (Sahlbergella singularis and Distantiella theobroma) are the most important insect pests affecting cocoa production across West Africa. Understanding the population dynamics of mirids is key to their management, however, the current recommended hand-height assessment method is labour intensive. The objective of the study was to compare recently developed mirid sex pheromone trapping and visual hand-height assessment methods as monitoring tools on cocoa farms and to consider implications for a decision support system. Ten farms from the Eastern and Ashanti regions of Ghana were used for the study. Mirid numbers and damage were assessed fortnightly on twenty trees per farm, using both methods, from January 2012 to April 2013. The mirid population increased rapidly in June, reached a peak in September and began to decline in October. There was a significant linear relationship between numbers of mirids sampled to hand-height and mirid damage. High numbers of male mirids were recorded in pheromone traps between January and April 2012 after which there was a gradual decline. There was a significant inverse relationship between numbers of trapped adult mirids and mirids sampled to hand-height (predominantly nymphs). Higher temperatures and lower relative humidities in the first half of the year were associated with fewer mirids at hand-height but larger numbers of adult males were caught in pheromone traps. The study showed that relying solely on one method is not sufficient to provide accurate information on mirid population dynamics and a combination of the two methods is necessary.

Optimal power management strategy for energy storage with stochastic loads

In this paper, a power management strategy (PMS) has been developed for the control of energy storage in a system subjected to loads of random duration. The PMS minimises the costs associated with the energy consumption of specific systems powered by a primary energy source and equipped with energy storage, under the assumption that the statistical distribution of load durations is known. By including the variability of the load in the cost function, it was possible to define the optimality criteria for the power flow of the storage. Numerical calculations have been performed obtaining the control strategies associated with the global minimum in energy costs, for a wide range of initial conditions of the system. The results of the calculations have been tested on a MATLAB/Simulink model of a rubber tyre gantry (RTG) crane equipped with a flywheel energy storage system (FESS) and subjected to a test cycle, which corresponds to the real operation of a crane in the Port of Felixstowe. The results of the model show increased energy savings and reduced peak power demand with respect to existing control strategies, indicating considerable potential savings for port operators in terms of energy and maintenance costs.