Integrable Hamiltonian systems defined on the Lie groups SO(3) and SU(2): an application to the attitude control of a spacecraft

This paper considers left-invariant control systems defined on the Lie groups SU(2) and SO(3). Such systems have a number of applications in both classical and quantum control problems. The purpose of this paper is two-fold. Firstly, the optimal control problem for a system varying on these Lie Groups, with cost that is quadratic in control is lifted to their Hamiltonian vector fields through the Maximum principle of optimal control and explicitly solved. Secondly, the control systems are integrated down to the level of the group to give the solutions for the optimal paths corresponding to the optimal controls. In addition it is shown here that integrating these equations on the Lie algebra su(2) gives simpler solutions than when these are integrated on the Lie algebra so(3).

Puroindoline-b mutations control the lipid binding interactions in mixed puroindoline-a: puroindoline-b systems

The interactions have been investigated of puroindoline-a (Pin-a) and mixed protein systems of Pin-a and wild-type puroindoline-b (Pin-b+) or puroindoline-b mutants (G46S mutation (Pin bH) or W44R mutation (Pin-bS)) with condensed phase monolayers of an anionic phospholipid (L-α-dipalmitoylphosphatidyl-dl-glycerol (DPPG)) at the air/water interface. The interactions of the mixed systems were studied at three different concentration ratios of Pin-a:Pin-b, namely 3:1, 1:1 and 1:3 in order to establish any synergism in relation to lipid binding properties. Surface pressure measurements revealed that Pin-a interaction with DPPG monolayers led to an equilibrium surface pressure increase of 8.7 ± 0.6 mN m-1. This was less than was measured for Pin-a:Pin-b+ (9.6 to 13.4 mN m-1), but was significantly more than was measured for Pin-a:Pin-bH (4.0 to 6.2 mN m-1) or Pin-a:Pin-bS (3.8 to 6.3 mN m-1) over the complete range of concentration ratio. Consequently, surface pressure increases were shown to correlate to endosperm hardness phenotype, with puroindolines present in hard-textured wheat varieties yielding lower equilibrium surface pressure changes. Integrated amide I peak areas from corresponding external reflectance Fourier-transform infrared (ER-FTIR) spectra, used to indicate levels of protein adsorption to the lipid monolayers, showed that differences in adsorbed amount were less significant. The data therefore suggest that Pin-b mutants having single residue substitutions within their tryptophan-rich loop that are expressed in some hard-textured wheat varieties influence the degree of penetration of Pin-a and Pin-b into anionic phospholipid films. These findings highlight the key role of the tryptophan-rich loop in puroindoline-lipid interactions.

Genotypic and environmental influences on the performance of wheat root systems

Genetic and environmental factors interact to determine the growth and activity of crop root systems. This paper examines the effects of agronomic management and genotype on wheat root systems in the UK and Australia, and suggests ways in which root limitations to crop performance might be alleviated. In a field study in the UK which examined late-season growth and activity, fungicide maintained the size of the root system during early grain-filling, and there were significant differences between cultivars in root distribution with depth below 0.3 m. Shamrock had a longer root system below 0.3 m than varieties such as Hereward and Consort. Fungicide significantly increased root growth at 0.1-0.2 m in one season. In Australia, a wheat line selected for high shoot vigour had associated root vigour during early seedling growth but the effect on root growth did not persist. The results provide examples of genotypic differences in wheat root growth under field conditions which interact with agronomic management in ways which can be exploited to benefit growth and yield in diverse environments.

Comparing rice production systems: A challenge for agronomic research and for the dissemination of knowledge-intensive farming practices

This article is a commentary on several research studies conducted on the prospects for aerobic rice production systems that aim at reducing the demand for irrigation water which in certain major rice producing areas of the world is becoming increasingly scarce. The research studies considered, as reported in published articles mainly under the aegis of the International Rice Research Institute (IRRI), have a narrow scope in that they test only 3 or 4 rice varieties under different soil moisture treatments obtained with controlled irrigation, but with other agronomic factors of production held as constant. Consequently, these studies do not permit an assessment of the interactions among agronomic factors that will be of critical significance to the performance of any production system. Varying the production factor of "water" will seriously affect also the levels of the other factors required to optimise the performance of a production system. The major weakness in the studies analysed in this article originates from not taking account of the interactions between experimental and non-experimental factors involved in the comparisons between different production systems. This applies to the experimental field design used for the research studies as well as to the subsequent statistical analyses of the results. The existence of such interactions is a serious complicating element that makes meaningful comparisons between different crop production systems difficult. Consequently, the data and conclusions drawn from such research readily become biased towards proposing standardised solutions for possible introduction to farmers through a linear technology transfer process. Yet, the variability and diversity encountered in the real-world farming environment demand more flexible solutions and approaches in the dissemination of knowledge-intensive production practices through "experiential learning" types of processes, such as those employed by farmer field schools. This article illustrates, based on expertise of the 'system of rice intensification' (SRI), that several cost-effective and environment-friendly agronomic solutions to reduce the demand for irrigation water, other than the asserted need for the introduction of new cultivars, are feasible. Further, these agronomic Solutions can offer immediate benefits of reduced water requirements and increased net returns that Would be readily accessible to a wide range of rice producers, particularly the resource poor smallholders. (C) 2009 Elsevier B.V. All rights reserved.

Integrable quadratic Hamiltonians on the Euclidean group of motions

In this paper, we discuss the problem of globally computing sub-Riemannian curves on the Euclidean group of motions SE(3). In particular, we derive a global result for special sub-Riemannian curves whose Hamiltonian satisfies a particular condition. In this paper, sub-Riemannian curves are defined in the context of a constrained optimal control problem. The maximum principle is then applied to this problem to yield an appropriate left-invariant quadratic Hamiltonian. A number of integrable quadratic Hamiltonians are identified. We then proceed to derive convenient expressions for sub-Riemannian curves in SE(3) that correspond to particular extremal curves. These equations are then used to compute sub-Riemannian curves that could potentially be used for motion planning of underwater vehicles.

Equations to predict methane emissions from cows fed at maintenance energy level in pasture-based systems

Ruminant production is a vital part of food industry but it raises environmental concerns, partly due to the associated methane outputs. Efficient methane mitigation and estimation of emissions from ruminants requires accurate prediction tools. Equations recommended by international organizations or scientific studies have been developed with animals fed conserved forages and concentrates and may be used with caution for grazing cattle. The aim of the current study was to develop prediction equations with animals fed fresh grass in order to be more suitable to pasture-based systems and for animals at lower feeding levels. A study with 25 nonpregnant nonlactating cows fed solely fresh-cut grass at maintenance energy level was performed over two consecutive grazing seasons. Grass of broad feeding quality, due to contrasting harvest dates, maturity, fertilisation and grass varieties, from eight swards was offered. Cows were offered the experimental diets for at least 2 weeks before housed in calorimetric chambers over 3 consecutive days with feed intake measurements and total urine and faeces collections performed daily. Methane emissions were measured over the last 2 days. Prediction models were developed from 100 3-day averaged records. Internal validation of these equations, and those recommended in literature, was performed. The existing in greenhouse gas inventories models under-estimated methane emissions from animals fed fresh-cut grass at maintenance while the new models, using the same predictors, improved prediction accuracy. Error in methane outputs prediction was decreased when grass nutrient, metabolisable energy and digestible organic matter concentrations were added as predictors to equations already containing dry matter or energy intakes, possibly because they explain feed digestibility and the type of energy-supplying nutrients more efficiently. Predictions based on readily available farm-level data, such as liveweight and grass nutrient concentrations were also generated and performed satisfactorily. New models may be recommended for predictions of methane emissions from grazing cattle at maintenance or low feeding levels.