Optimal kinematic control of an autonomous underwater vehicle

This note investigates the motion control of an autonomous underwater vehicle (AUV). The AUV is modeled as a nonholonomic system as any lateral motion of a conventional, slender AUV is quickly damped out. The problem is formulated as an optimal kinematic control problem on the Euclidean Group of Motions SE(3), where the cost function to be minimized is equal to the integral of a quadratic function of the velocity components. An application of the Maximum Principle to this optimal control problem yields the appropriate Hamiltonian and the corresponding vector fields give the necessary conditions for optimality. For a special case of the cost function, the necessary conditions for optimality can be characterized more easily and we proceed to investigate its solutions. Finally, it is shown that a particular set of optimal motions trace helical paths. Throughout this note we highlight a particular case where the quadratic cost function is weighted in such a way that it equates to the Lagrangian (kinetic energy) of the AUV. For this case, the regular extremal curves are constrained to equate to the AUV's components of momentum and the resulting vector fields are the d'Alembert-Lagrange equations in Hamiltonian form.

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.

Optimal discrimination and classification of THz spectra in the wavelet domain

In rapid scan Fourier transform spectrometry, we show that the noise in the wavelet coefficients resulting from the filter bank decomposition of the complex insertion loss function is linearly related to the noise power in the sample interferogram by a noise amplification factor. By maximizing an objective function composed of the power of the wavelet coefficients divided by the noise amplification factor, optimal feature extraction in the wavelet domain is performed. The performance of a classifier based on the output of a filter bank is shown to be considerably better than that of an Euclidean distance classifier in the original spectral domain. An optimization procedure results in a further improvement of the wavelet classifier. The procedure is suitable for enhancing the contrast or classifying spectra acquired by either continuous wave or THz transient spectrometers as well as for increasing the dynamic range of THz imaging systems. (C) 2003 Optical Society of America.

Semantic-associative visual content labelling and retrieval: A multimodal approach

A novel framework referred to as collaterally confirmed labelling (CCL) is proposed, aiming at localising the visual semantics to regions of interest in images with textual keywords. Both the primary image and collateral textual modalities are exploited in a mutually co-referencing and complementary fashion. The collateral content and context-based knowledge is used to bias the mapping from the low-level region-based visual primitives to the high-level visual concepts defined in a visual vocabulary. We introduce the notion of collateral context, which is represented as a co-occurrence matrix of the visual keywords. A collaborative mapping scheme is devised using statistical methods like Gaussian distribution or Euclidean distance together with collateral content and context-driven inference mechanism. We introduce a novel high-level visual content descriptor that is devised for performing semantic-based image classification and retrieval. The proposed image feature vector model is fundamentally underpinned by the CCL framework. Two different high-level image feature vector models are developed based on the CCL labelling of results for the purposes of image data clustering and retrieval, respectively. A subset of the Corel image collection has been used for evaluating our proposed method. The experimental results to-date already indicate that the proposed semantic-based visual content descriptors outperform both traditional visual and textual image feature models. (C) 2007 Elsevier B.V. All rights reserved.

Meson properties in an extended nonlocal NJL model

We consider a non-local version of the NJL model, based on a separable quark-quark interaction. The interaction is extended to include terms that bind vector and axial-vector mesons. The non-locality means that no further regulator is required. Moreover the model is able to confine the quarks by generating a quark propagator without poles at real energies. Working in the ladder approximation, we calculate amplitudes in Euclidean space and discuss features of their continuation to Minkowski energies. Conserved currents are constructed and we demonstrate their consistency with various Ward identities. Various meson masses are calculated, along with their strong and electromagnetic decay amplitudes. We also calculate the electromagnetic form factor of the pion, as well as form factors associated with the processes γγ* → π0 and ω → π0γ*. The results are found to lead to a satisfactory phenomenology and lend some dynamical support to the idea of vector-meson dominance.

Meson properties in an extended nonlocal NJL model

A nonlocal version of the NJL model is investigated. It is based on a separable quark-quark interaction, as suggested by the instanton liquid picture of the QCD vacuum. The interaction is extended to include terms that bind vector and axial-vector mesons. The nonlocality means that no further regulator is required. Moreover the model is able to confine the quarks by generating a quark propagator without poles at real energies. Features of the continuation of amplitudes from Euclidean space to Minkowski energies are discussed. These features lead to restrictions on the model parameters as well as on the range of applicability of the model. Conserved currents are constructed, and their consistency with various Ward identities is demonstrated. In particular, the Gell-Mann-Oakes-Renner relation is derived both in the ladder approximation and at meson loop level. The importance of maintaining chiral symmetry in the calculations is stressed throughout. Calculations with the model are performed to all orders in momentum. Meson masses are determined, along with their strong and electromagnetic decay amplitudes. Also calculated are the electromagnetic form factor of the pion and form factors associated with the processes gamma gamma* --> pi0 and omega --> pi0 gamma*. The results are found to lead to a satisfactory phenomenology and demonstrate a possible dynamical origin for vector-meson dominance. In addition, the results produced at meson loop level validate the use of 1/Nc as an expansion parameter and indicate that a light and broad scalar state is inherent in models of the NJL type.

The climatology of the middle atmosphere in a vertically extended version of the Met Office's climate model. Part I: mean state

The climatology of a stratosphere-resolving version of the Met Office’s climate model is studied and validated against ECMWF reanalysis data. Ensemble integrations are carried out at two different horizontal resolutions. Along with a realistic climatology and annual cycle in zonal mean zonal wind and temperature, several physical effects are noted in the model. The time of final warming of the winter polar vortex is found to descend monotonically in the Southern Hemisphere, as would be expected for purely radiative forcing. In the Northern Hemisphere, however, the time of final warming is driven largely by dynamical effects in the lower stratosphere and radiative effects in the upper stratosphere, leading to the earliest transition to westward winds being seen in the midstratosphere. A realistic annual cycle in stratospheric water vapor concentrations—the tropical “tape recorder”—is captured. Tropical variability in the zonal mean zonal wind is found to be in better agreement with the reanalysis for the model run at higher horizontal resolution because the simulated quasi-biennial oscillation has a more realistic amplitude. Unexpectedly, variability in the extratropics becomes less realistic under increased resolution because of reduced resolved wave drag and increased orographic gravity wave drag. Overall, the differences in climatology between the simulations at high and moderate horizontal resolution are found to be small.

Classification of instability modes in a model of aluminium reduction cells with a uniform magnetic field

A unified view on the interfacial instability in a model of aluminium reduction cells in the presence of a uniform, vertical, background magnetic field is presented. The classification of instability modes is based on the asymptotic theory for high values of parameter β, which characterises the ratio of the Lorentz force based on the disturbance current, and gravity. It is shown that the spectrum of the travelling waves consists of two parts independent of the horizontal cross-section of the cell: highly unstable wall modes and stable or weakly unstable centre, or Sele’s modes. The wall modes with the disturbance of the interface being localised at the sidewalls of the cell dominate the dynamics of instability. Sele’s modes are characterised by a distributed disturbance over the whole horizontal extent of the cell. As β increases these modes are stabilized by the field.

Impact of stratospheric variability on tropospheric climate change

An improved stratospheric representation has been included in simulations with the Hadley Centre HadGEM1 coupled ocean atmosphere model with natural and anthropogenic forcings for the period 1979–2003. An improved stratospheric ozone dataset is employed that includes natural variations in ozone as well as the usual anthropogenic trends. In addition, in a second set of simulations the quasi biennial oscillation (QBO) of stratospheric equatorial zonal wind is also imposed using a relaxation towards ERA-40 zonal wind values. The resulting impact on tropospheric variability and trends is described. We show that the modelled cooling rate at the tropopause is enhanced by the improved ozone dataset and this improvement is even more marked when the QBO is also included. The same applies to warming trends in the upper tropical troposphere which are slightly reduced. Our stratospheric improvements produce a significant increase of internal variability but no change in the positive trend of annual mean global mean near-surface temperature. Warming rates are increased significantly over a large portion of the Arctic Ocean. The improved stratospheric representation, especially the QBO relaxation, causes a substantial reduction in near-surface temperature and precipitation response to the El Chichón eruption, especially in the tropical region. The winter increase in the phase of the northern annular mode observed in the aftermath of the two major recent volcanic eruptions is partly captured, especially after the El Chichón eruption. The positive trend in the southern annular mode (SAM) is increased and becomes statistically significant which demonstrates that the observed increase in the SAM is largely subject to internal variability in the stratosphere. The possible inclusion in simulations for future assessments of full ozone chemistry and a gravity wave scheme to internally generate a QBO is discussed.

On some properties of traveling water waves with vorticity

We prove that for a large class of vorticity functions the crests of any corresponding traveling gravity water wave of finite depth are necessarily points of maximal horizontal velocity. We also show that for waves with nonpositive vorticity the pressure everywhere in the fluid is larger than the atmospheric pressure. A related a priori estimate for waves with nonnegative vorticity is also given.

Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth

We study weak solutions for a class of free-boundary problems which includes as a special case the classical problem of travelling gravity waves on water of finite depth. We show that such problems are equivalent to problems in fixed domains and study the regularity of their solutions. We also prove that in very general situations the free boundary is necessarily the graph of a function.

On the existence of extreme waves and the Stokes conjecture with vorticity

This is a study of singular solutions of the problem of traveling gravity water waves on flows with vorticity. We show that, for a certain class of vorticity functions, a sequence of regular waves converges to an extreme wave with stagnation points at its crests. We also show that, for any vorticity function, the profile of an extreme wave must have either a corner of 120° or a horizontal tangent at any stagnation point about which it is supposed symmetric. Moreover, the profile necessarily has a corner of 120° if the vorticity is nonnegative near the free surface.

Steady periodic water waves with constant vorticity: regularity and local bifurcation

This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is transformed into a quasilinear pseudodifferential equation for a periodic function of one variable. The new formulation leads to a regularity result and, by use of bifurcation theory, to the existence of waves of small amplitude even in the presence of stagnation points in the flow.

Lightning-induced intensification of the ionospheric sporadic E layer

A connection between thunderstorms and the ionosphere has been hypothesized since the mid-1920s(1). Several mechanisms have been proposed to explain this connection(2-7), and evidence from modelling(8) as well as various types of measurements(9-14) demonstrate that lightning can interact with the lower ionosphere. It has been proposed, on the basis of a few observed events(15), that the ionospheric 'sporadic E' layer - transient, localized patches of relatively high electron density in the mid-ionosphere E layer, which significantly affect radio-wave propagation - can be modulated by thunderstorms, but a more formal statistical analysis is still needed. Here we identify a statistically significant intensification and descent in altitude of the mid-latitude sporadic E layer directly above thunderstorms. Because no ionospheric response to low-pressure systems without lightning is detected, we conclude that this localized intensification of the sporadic E layer can be attributed to lightning. We suggest that the co-location of lightning and ionospheric enhancement can be explained by either vertically propagating gravity waves that transfer energy from the site of lightning into the ionosphere, or vertical electrical discharge, or by a combination of these two mechanisms.

Dual-orthogonal radial basis function networks for nonlinear time series prediction

A new structure of Radial Basis Function (RBF) neural network called the Dual-orthogonal RBF Network (DRBF) is introduced for nonlinear time series prediction. The hidden nodes of a conventional RBF network compare the Euclidean distance between the network input vector and the centres, and the node responses are radially symmetrical. But in time series prediction where the system input vectors are lagged system outputs, which are usually highly correlated, the Euclidean distance measure may not be appropriate. The DRBF network modifies the distance metric by introducing a classification function which is based on the estimation data set. Training the DRBF networks consists of two stages. Learning the classification related basis functions and the important input nodes, followed by selecting the regressors and learning the weights of the hidden nodes. In both cases, a forward Orthogonal Least Squares (OLS) selection procedure is applied, initially to select the important input nodes and then to select the important centres. Simulation results of single-step and multi-step ahead predictions over a test data set are included to demonstrate the effectiveness of the new approach.