Singularities of optimal control problems on some 6-D lie groups

This paper considers the motion planning problem for oriented vehicles travelling at unit speed in a 3-D space. A Lie group formulation arises naturally and the vehicles are modeled as kinematic control systems with drift defined on the orthonormal frame bundles of particular Riemannian manifolds, specifically, the 3-D space forms Euclidean space E-3, the sphere S-3, and the hyperboloid H'. The corresponding frame bundles are equal to the Euclidean group of motions SE(3), the rotation group SO(4), and the Lorentz group SO (1, 3). The maximum principle of optimal control shifts the emphasis for these systems to the associated Hamiltonian formalism. For an integrable case, the extremal curves are explicitly expressed in terms of elliptic functions. In this paper, a study at the singularities of the extremal curves are given, which correspond to critical points of these elliptic functions. The extremal curves are characterized as the intersections of invariant surfaces and are illustrated graphically at the singular points. It. is then shown that the projections, of the extremals onto the base space, called elastica, at these singular points, are curves of constant curvature and torsion, which in turn implies that the oriented vehicles trace helices.

Chemistry and biology of maculalactone A from the marine cyanobacterium Kyrtuthrix maculans

Maculalactone A is the most abundant secondary metabolite in Kyrtuthrix maculans, a marine cyanobacterium found in the mid-high shore of moderately exposed to sheltered rocky shores in Hong Kong and South East Asia. This species appears to survive as pure colonies forming distinct black zones on the rock. Maculalactone A may provide K. maculans with a chemical defense against several marine organisms, including the common grazer, Chlorostoma argyrostoma and settlement by larvae of the barnacles, Tetraclita japonica, Balanus amphitrite and Ibla cumingii. The natural concentration of maculalactone A varied with season and also with tidal height on the shore and although a strong positive linear correlation was observed between maculalactone A concentration and herbivore grazing pressure, manipulative experiments demonstrated that grazing pressure was not directly responsible for inducing the biosynthesis of this metabolite. The potential of maculalactone A as a natural marine anti-fouling agent (i.e. as an alternative to environmentally-damaging copper- and tin-based anti-fouling paints) was investigated after achieving a gram-scale synthesis of this compound. Preliminary field trials with anti-fouling paints which contained synthetic maculalactone A as the active principle have confirmed that this compound seems to have a specific activity against molluscan settlers.

Physical interpretation of the correlation between multi-angle spectral data and canopy height

Recent empirical studies have shown that multi-angle spectral data can be useful for predicting canopy height, but the physical reason for this correlation was not understood. We follow the concept of canopy spectral invariants, specifically escape probability, to gain insight into the observed correlation. Airborne Multi-Angle Imaging Spectrometer (AirMISR) and airborne Laser Vegetation Imaging Sensor (LVIS) data acquired during a NASA Terrestrial Ecology Program aircraft campaign underlie our analysis. Two multivariate linear regression models were developed to estimate LVIS height measures from 28 AirMISR multi-angle spectral reflectances and from the spectrally invariant escape probability at 7 AirMISR view angles. Both models achieved nearly the same accuracy, suggesting that canopy spectral invariant theory can explain the observed correlation. We hypothesize that the escape probability is sensitive to the aspect ratio (crown diameter to crown height). The multi-angle spectral data alone therefore may not provide enough information to retrieve canopy height globally.

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.

Efficient on the fly calculation of time correlation functions in computer simulations

Time correlation functions yield profound information about the dynamics of a physical system and hence are frequently calculated in computer simulations. For systems whose dynamics span a wide range of time, currently used methods require significant computer time and memory. In this paper, we discuss the multiple-tau correlator method for the efficient calculation of accurate time correlation functions on the fly during computer simulations. The multiple-tau correlator is efficacious in terms of computational requirements and can be tuned to the desired level of accuracy. Further, we derive estimates for the error arising from the use of the multiple-tau correlator and extend it for use in the calculation of mean-square particle displacements and dynamic structure factors. The method described here, in hardware implementation, is routinely used in light scattering experiments but has not yet found widespread use in computer simulations.

On the regulation of spatial externalities: coexistence between GM and conventional crops in the EU and the 'newcomer principle'

Pollen-mediated gene flow is one of the main concerns associated with the introduction of genetically modified (GM) crops. Should a premium for non-GM varieties emerge on the market, ‘contamination’ by GM pollen would generate a revenue loss for growers of non-GM varieties. This paper analyses the problem of pollen-mediated gene flow as a particular type of production externality. The model, although simple, provides useful insights into coexistence policies. Following on from this and taking GM herbicide-tolerant oilseed rape (Brassica napus) as a model crop, a Monte Carlo simulation is used to generate data and then estimate the effect of several important policy variables (including width of buffer zones and spatial aggregation) on the magnitude of the externality associated with pollen-mediated gene flow.

Synchronisation error resistant CDMA detection

A bit-level linear CDMA detector is presented which is based on the minimum variance distortionless response (MVDR) principle. Owing to the interference suppression capability made possible by basing the detector on the MVDR principle and the fact that no inversion of the user correlation matrix is involved, the influence of synchronisation errors is greatly suppressed.

A linear CDMA detector based on minimum variance distortionless response (MVDR)

A bit-level processing (BLP) based linear CDMA detector is derived following the principle of minimum variance distortionless response (MVDR). The combining taps for the MVDR detector are determined from (1) the covariance matrix of the matched filter output, and (2) the corresponding row (or column) of the user correlation matrix. Due to the interference suppression capability of MVDR and the fact that no inversion of the user correlation matrix is involved, the influence of the synchronisation errors is greatly reduced. The detector performance is demonstrated via computer simulations (both synchronisation errors and intercell interference are considered).

Correlation between regioselectivity and site charge in propene polymerisation catalysed by metallocene

The reactions of propene with [Zr(cyclopentadienyl)(2)Me](+) have been investigated using density functional theory in order to study the correlation between regioselectivity and site charge in propene polymerisation. The reaction paths of the 1,2 and 2,1 additions of the methyl group to propene have been established. The geometries and energies of the reactants, transition states and products have been obtained using both PBEPBE/LANL2DZ and B3LYP/LANL2DZ methodologies. The results with both density functionals show that the activation energy for 1,2-insertion is lower than that for 2,1-insertion (Fig. 5) and this is consistent with the experiment results. Also for both density functionals, the difference of the thermal dynamic driving forces between the 2,1 product named 2-21 and the 1,2 product named 2-12 is significantly lower than the difference between the energy barriers. It is noted that in the reactants, the Mulliken partial charge on the central carbon atom C2 is positive and it can be concluded that 1,2-insertion is favoured because it can proceed via a cationic reaction.

A study of the antioxidant capacity of oak wood used in wine ageing and the correlation with polyphenol composition

The antioxidant capacity of oak wood used in the ageing of wine was studied by four different methods: measurement of scavenging capacity against a given radical (ABTS, DPPH), oxygen radical absorbance capacity (ORAC) and the ferric reducing antioxidant power (FRAP). Although, the four methods tested gave comparable results for the antioxidant capacity measured in oak wood extracts, the ORAC method gave results with some differences from the other methods. Non-toasted oak wood samples displayed more antioxidant power than toasted ones due to differences in the polyphenol compositon. A correlation analysis revealed that ellagitannins were the compounds mainly responsible for the antioxidant capacity of oak wood. Some phenolic acids, mainly gallic acid, also showed a significant correlation with antioxidant capacity.