Influenza, a general review of recent developments

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Analysis of the accuracy and convergence of equation-free projection to a slow manifold

In [C.W. Gear, T.J. Kaper, I.G. Kevrekidis, and A. Zagaris, Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes, SIAM J. Appl. Dyn. Syst. 4 (2005) 711-732], we developed a class of iterative algorithms within the context of equation-free methods to approximate low-dimensional, attracting, slow manifolds in systems of differential equations with multiple time scales. For user-specified values of a finite number of the observables, the m-th member of the class of algorithms (m = 0, 1, ...) finds iteratively an approximation of the appropriate zero of the (m+1)-st time derivative of the remaining variables and uses this root to approximate the location of the point on the slow manifold corresponding to these values of the observables. This article is the first of two articles in which the accuracy and convergence of the iterative algorithms are analyzed. Here, we work directly with explicit fast--slow systems, in which there is an explicit small parameter, epsilon, measuring the separation of time scales. We show that, for each m = 0, 1, ..., the fixed point of the iterative algorithm approximates the slow manifold up to and including terms of O(epsilon^m). Moreover, for each m, we identify explicitly the conditions under which the m-th iterative algorithm converges to this fixed point. Finally, we show that when the iteration is unstable (or converges slowly) it may be stabilized (or its convergence may be accelerated) by application of the Recursive Projection Method. Alternatively, the Newton-Krylov Generalized Minimal Residual Method may be used. In the subsequent article, we will consider the accuracy and convergence of the iterative algorithms for a broader class of systems-in which there need not be an explicit small parameter-to which the algorithms also apply

The design of decentralised controllers for large scale systems

Bibliography:leaves 203-205.Decentralised control schemes are becoming more common in industry as the advantages of decentralised control become more apparent. These advantages include fewer tuning parameters than centralised controllers, the simplification and cost reduction of hardware requirements and greater reliability. In addition the application of decentralised controller design to large scale systems allows established CAD methods to be implemented easily and efficiently. When the control engineer designs a distributed controller the system is divided up into a number of subsystems and a controller designed for each subsystem. The controllers are designed independently for each subsystem ignoring any interaction that may occur between the different subsystems. In terms of the input-output representation of the system this means that the matrix representing the controller will be in a block diagonal form. In general the interactions between the different subsystems will not be negligible. In some cases the interactions will be such that stabilising the individual subsystems will not be sufficient to stabilise the system as a whole. Stability theorems are required to enable the designer to check if the decentralised controller that he has designed will in fact stabilise the system as a whole. Such stability theorems have been devised although at present they are too conservative. However even with such theorems available the designer must still select the subsystems to be controlled in such a way as to satisfy the conditions laid down for stability. The stability theories usually are based on a particular matrix structure. If the matrix representing the system possesses a structure detailed by the stability theorem in question then, subject to various conditions, the system as a whole will be stable under decentralised control. In this thesis a number of different matrix structures are considered that give information as to the stability of the closed loop system. Methods are developed that allow the designer to rearrange the matrix in such a way as to obtain a particular structure, if this is possible

Early evolution of electron cyclotron driven current during suppression of tearing modes in a circular tokamak

When electron cyclotron (EC) driven current is first applied to the inside of a magnetic island, the current spreads throughout the island and after a short period achieves a steady level. Using a two equation fluid model for the EC current that allows us to examine this early evolution in detail, we analyze high-resolution simulations of a 2/1 classical tearing mode in a low-beta large aspect-ratio circular tokamak. These simulations use a nonlinear 3D reduced-MHD fluid model and the JOREK code. During the initial period where the EC driven current grows and spreads throughout the magnetic island, it is not a function of the magnetic flux. However, once it has reached a steady-state, it should be a flux function. We demonstrate numerically that if sufficiently resolved toroidally, the steady-state EC driven current becomes approximately a flux function. We discuss the physics of this early period of EC evolution and its impact on the size of the magnetic island.Comment: 12 pages, 7 figure

High spatial resolution observations of CUDSS14A: a SCUBA-selected ultraluminous galaxy at high redshift

The definitive version is available at www.blackwell-synergy.com '. Copyright Blackwell Publishing DOI : 10.1046/j.1365-8711.2000.03822.xWe present a high-resolutionmillimetre interferometric image of the brightest SCUBA- selected galaxy from the Canada-UK deep SCUBA survey (CUDSS). We make a very clear detection at 1.3 mm, but fail to resolve any structure in the source.Peer reviewe