Categorisation of synoptic environments associated with mesoscale convective systems over the UK

Mesoscale convective systems (MCSs) are relatively rare events in the UK but, when they do occur, can be associated with weather that is considered extreme with respect to climatology (as indicated by the number of such events that have been analysed as case studies). These case studies usually associate UK MCSs with a synoptic environment known as the Spanish plume. Here a previously published 17 year climatology of UK MCS events is extended to the present day (from 1998 to 2008) and these events classified according to the synoptic environment in which they form. Three distinct synoptic environments have been identified, here termed the classical Spanish plume, modified Spanish plume, and European easterly plume. Detailed case studies of the two latter, newly defined, environments are presented. Composites produced for each environment further reveal the differences between them. The classical Spanish plume is associated with an eastward propagating baroclinic cyclone that evolves according to idealised life cycle 1. Conditional instability is released from a warm moist plume of air advected northeastwards from Iberia that is capped by warmer, but very dry air, from the Spanish plateau. The modified Spanish plume is associated with a slowly moving mature frontal system associated with a forward tilting trough (and possibly cut-off low) at 500 hPa that evolves according to idealised life cycle 2. As in the classical Spanish plume, conditional instability is released from a warm plume of air advected northwards from Iberia. The less frequent European easterly plume is associated with an omega block centred over Scandinavia at upper levels. Conditional instability is released from a warm plume of air advected westwards across northern continental Europe. Unlike the Spanish plume environments, the European easterly plume is not a warm sector phenomena associated with a baroclinic cyclone. However, in all environments the organisation of convection is associated with the interaction of an upper-level disturbance with a low-level region of warm advection.

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).

Application of neural network to hybrid systems with binary inputs

Boolean input systems are in common used in the electric industry. Power supplies include such systems and the power converter represents these. For instance, in power electronics, the control variable are the switching ON and OFF of components as thyristors or transistors. The purpose of this paper is to use neural network (NN) to control continuous systems with Boolean inputs. This method is based on classification of system variations associated with input configurations. The classical supervised backpropagation algorithm is used to train the networks. The training of the artificial neural network and the control of Boolean input systems are presented. The design procedure of control systems is implemented on a nonlinear system. We apply those results to control an electrical system composed of an induction machine and its power converter.

Connectivity measures for internet topologies on the level of autonomous systems

Classical measures of network connectivity are the number of disjoint paths between a pair of nodes and the size of a minimum cut. For standard graphs, these measures can be computed efficiently using network flow techniques. However, in the Internet on the level of autonomous systems (ASs), referred to as AS-level Internet, routing policies impose restrictions on the paths that traffic can take in the network. These restrictions can be captured by the valley-free path model, which assumes a special directed graph model in which edge types represent relationships between ASs. We consider the adaptation of the classical connectivity measures to the valley-free path model, where it is -hard to compute them. Our first main contribution consists of presenting algorithms for the computation of disjoint paths, and minimum cuts, in the valley-free path model. These algorithms are useful for ASs that want to evaluate different options for selecting upstream providers to improve the robustness of their connection to the Internet. Our second main contribution is an experimental evaluation of our algorithms on four types of directed graph models of the AS-level Internet produced by different inference algorithms. Most importantly, the evaluation shows that our algorithms are able to compute optimal solutions to instances of realistic size of the connectivity problems in the valley-free path model in reasonable time. Furthermore, our experimental results provide information about the characteristics of the directed graph models of the AS-level Internet produced by different inference algorithms. It turns out that (i) we can quantify the difference between the undirected AS-level topology and the directed graph models with respect to fundamental connectivity measures, and (ii) the different inference algorithms yield topologies that are similar with respect to connectivity and are different with respect to the types of paths that exist between pairs of ASs.

Towards a general theory of extremes for observables of chaotic dynamical systems

In this paper we provide a connection between the geometrical properties of the attractor of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the classical generalised Pareto distribution and derive explicit expressions for the scaling and the shape parameter. In particular, we derive that the shape parameter does not depend on the cho- sen observables, but only on the partial dimensions of the invariant measure on the stable, unstable, and neutral manifolds. The shape parameter is negative and is close to zero when high-dimensional systems are considered. This result agrees with what was derived recently using the generalized extreme value approach. Combining the results obtained using such physical observables and the properties of the extremes of distance observables, it is possible to derive estimates of the partial dimensions of the attractor along the stable and the unstable directions of the flow. Moreover, by writing the shape parameter in terms of moments of the extremes of the considered observable and by using linear response theory, we relate the sensitivity to perturbations of the shape parameter to the sensitivity of the moments, of the partial dimensions, and of the Kaplan–Yorke dimension of the attractor. Preliminary numer- ical investigations provide encouraging results on the applicability of the theory presented here. The results presented here do not apply for all combinations of Axiom A systems and observables, but the breakdown seems to be related to very special geometrical configurations.