Projective and Coarse Projective Integration for Problems with Continuous Symmetries

Temporal integration of equations possessing continuous symmetries (e.g. systems with translational invariance associated with traveling solutions and scale invariance associated with self-similar solutions) in a ``co-evolving'' frame (i.e. a frame which is co-traveling, co-collapsing or co-exploding with the evolving solution) leads to improved accuracy because of the smaller time derivative in the new spatial frame. The slower time behavior permits the use of {\it projective} and {\it coarse projective} integration with longer projective steps in the computation of the time evolution of partial differential equations and multiscale systems, respectively. These methods are also demonstrated to be effective for systems which only approximately or asymptotically possess continuous symmetries. The ideas of projective integration in a co-evolving frame are illustrated on the one-dimensional, translationally invariant Nagumo partial differential equation (PDE). A corresponding kinetic Monte Carlo model, motivated from the Nagumo kinetics, is used to illustrate the coarse-grained method. A simple, one-dimensional diffusion problem is used to illustrate the scale invariant case. The efficiency of projective integration in the co-evolving frame for both the macroscopic diffusion PDE and for a random-walker particle based model is again demonstrated

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

Access to Land and Poverty Reduction in Rural Zambia: Connecting the Policy Issues

Key Policy Message: - Despite having relatively low population densities, inadequate access to land is one of the major causes of rural poverty in Zambia. - The apparent paradox of inadequate access to land for many rural households in a country of low population density is partially reconciled when taking into account that economically viable arable land requires at least some degree of access to basic services, water, road infrastructure, and markets. The basic public investments to make settlement economically viable have yet been made in many areas of Zambia. - Depending of future land allocation policy, access to good quality land with a market potential may become increasingly beyond the reach of many small-scale farm households, making it more difficult to achieve a smallholder-led, pro-poor agricultural development trajectory.zambia, food security, land, policy, Agricultural and Food Policy, Community/Rural/Urban Development, Consumer/Household Economics, Food Security and Poverty, Land Economics/Use, q18, q15,

Group inquiry to aid organisational learning in enterprises

This paper describes a method for surfacing and exploring ‘situated knowledge’ in medium-sized organisations, with employee groups utilising a ‘low impact’ form of group support system (GSS), based on wireless handsets. Some results of piloting this method are summarised and one intervention is presented in detail. The method encouraged organisational members to give voice to the emotions and politics of leadership and learning in organisations, and helped to articulate how situated knowledge was ignored, as well as utilised. The method is practical, and may be used by organisations for themselves to aid the development of group as well as individual reflection, to stimulate the consideration of change

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

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

Herschel observations of gamma-ray burst host galaxies: implications for the topology of the dusty interstellar medium

Long-duration gamma-ray bursts (GRBs) are indisputably related to star formation, and their vast luminosity in gamma rays pin-points regions of star formation independent of galaxy mass. As such, GRBs provide a unique tool for studying star forming galaxies out to high-z independent of luminosity. Most of our understanding of the properties of GRB hosts (GRBHs) comes from optical and near-infrared (NIR) follow-up observations, and we therefore have relatively little knowledge of the fraction of dust-enshrouded star formation that resides within GRBHs. Currently ~20% of GRBs show evidence of significant amounts of dust along the line of sight to the afterglow through the host galaxy, and these GRBs tend to reside within redder and more massive galaxies than GRBs with optically bright afterglows. In this paper we present Herschel observations of five GRBHs with evidence of being dust-rich, targeted to understand the dust attenuation properties within GRBs better. Despite the sensitivity of our Herschel observations, only one galaxy in our sample was detected (GRBH 070306), for which we measure a total star formation rate (SFR) of ~100Mstar/yr, and which had a relatively high stellar mass (log[Mstar]=10.34+0.09/-0.04). Nevertheless, when considering a larger sample of GRBHs observed with Herschel, it is clear that stellar mass is not the only factor contributing to a Herschel detection, and significant dust extinction along the GRB sightline (A_{V,GRB}>1.5~mag) appears to be a considerably better tracer of GRBHs with high dust mass. This suggests that the extinguishing dust along the GRB line of sight lies predominantly within the host galaxy ISM, and thus those GRBs with A_{V,GRB}>1~mag but with no host galaxy Herschel detections are likely to have been predominantly extinguished by dust within an intervening dense cloud.Comment: 14 pages, 7 figures. Accepted for publication in A&

On the form of growing strings

Patterns and forms adopted by Nature, such as the shape of living cells, the geometry of shells and the branched structure of plants, are often the result of simple dynamical paradigms. Here we show that a growing self-interacting string attached to a tracking origin, modeled to resemble nascent polypeptides in vivo, develops helical structures which are more pronounced at the growing end. We also show that the dynamic growth ensemble shares several features of an equilibrium ensemble in which the growing end of the polymer is under an effective stretching force. A statistical analysis of native states of proteins shows that the signature of this non-equilibrium phenomenon has been fixed by evolution at the C-terminus, the growing end of a nascent protein. These findings suggest that a generic non-equilibrium growth process might have provided an additional evolutionary advantage for nascent proteins by favoring the preferential selection of helical structures.Comment: 4 pages, 3 figures. Accepted for publication in Phys. Rev. Let