Magma flow through elastic-walled dikes

A convection–diffusion model for the averaged flow of a viscous, incompressible magma through an elastic medium is considered. The magma flows through a dike from a magma reservoir to the Earth’s surface; only changes in dike width and velocity over large vertical length scales relative to the characteristic dike width are considered. The model emerges when nonlinear inertia terms in the momentum equation are neglected in a viscous, low-speed approximation of a magma flow model coupled to the elastic response of the rock.\ud Stationary- and traveling-wave solutions are presented in which a Dirichlet condition is used at the magma chamber; and either a (i) free-boundary condition, (ii) Dirichlet condition, or (iii) choked-flow condition is used at the moving free or fixed-top boundary. A choked-flow boundary condition, generally used in the coupled elastic wave and magma flow model, is also used in the convection–diffusion model. The validity of this choked-flow condition is illustrated by comparing stationary flow solutions of the convection–diffusion and coupled elastic wave and magma flow model for parameter values estimated for the Tolbachik volcano region in Kamchatka, Russia. These free- and fixed-boundary solutions are subsequently explored in a conservative, local discontinuous Galerkin finite-element discretization. This method is advantageous for the accurate implementation of the choked flow and free-boundary conditions. It uses a mixed Eulerian–Lagrangian finite element with special infinite curvature basis function near the free boundary and ensures positivity of the mean aperture subject to a time-step restriction. We illustrate the model further by simulating magma flow through host rock of variable density, and magma flow that is quasi-periodic due to the growth and collapse of a lava dome

Block designs for experiments with non-normal response

Many experiments measure a response that cannot be adequately described by a linear model withnormally distributed errors and are often run in blocks of homogeneous experimental units. Wedevelop the first methods of obtaining efficient block designs for experiments with an exponentialfamily response described by a marginal model fitted via Generalized Estimating Equations. Thismethodology is appropriate when the blocking factor is a nuisance variable as, for example, occursin industrial experiments. A D-optimality criterion is developed for finding designs robust to thevalues of the marginal model parameters and applied using three strategies: unrestricted algorithmicsearch, use of minimum-support designs, and blocking of an optimal design for the correspondingGeneralized Linear Model. Designs obtained from each strategy are critically compared and shownto be much more efficient than designs that ignore the blocking structure. The designs are comparedfor a range of values of the intra-block working correlation and for exchangeable, autoregressive andnearest neighbor structures. An analysis strategy is developed for a binomial response that allows es-timation from experiments with sparse data, and its efectiveness demonstrated. The design strategiesare motivated and demonstrated through the planning of an experiment from the aeronautics industr

Beyond swarm intelligence: The Ultraswarm

This paper explores the idea that it may be possible to combine two ideas – UAV flocking, and wireless cluster computing – in a single system, the UltraSwarm. The possible advantages of such a system are considered, and solutions to some of the technical problems are identified. Initial work on constructing such a system based around miniature electric helicopters is described

Are Nonclinical Obsessive-Compulsive Symptoms Associated with Bias Toward Habits?

In a sample of student volunteers (N=93), we found that obsessive-compulsive symptoms (although not hoarding) were associated with overreliance on stimulus-response habits at the expense of goal-directed control during instrumental responding. Only checking symptoms were associated with bias toward habits after negative affect was controlled for. Further research is warranted to examine if overreliance on habits represents an aberrant learning process that confers risk for obsessive-compulsive psychopathology

On the boundaries of solvability and unsolvability in tag systems. Theoretical and Experimental Results

Several older and more recent results on the boundaries of solvability and unsolvability in tag systems are surveyed. Emphasis will be put on the significance of computer experiments in research on very small tag systems

Poincar\'e and sl(2) algebras of order 3

In this paper we initiate a general classification for Lie algebras of order 3 and we give all Lie algebras of order 3 based on $\mathfrak{sl}(2,\mathbb C)$ and $\mathfrak{iso}(1,3)$ the Poincar\'e algebra in four-dimensions. We then set the basis of the theory of the deformations (in the Gerstenhaber sense) and contractions for Lie algebras of order 3.Comment: Title and presentation change

Progression and assessment in foreign languages at Key Stage 2

The teaching of primary languages has been increasing steadily, in response to the future entitlement for all Key Stage 2 (KS2) pupils aged 7-11 to learn a foreign language by 2010. However, there remain concerns about progression both within KS2 and through to secondary school and about how learners' progress is assessed. This paper presents findings on the issues of progression and assessment taken from case studies which formed part of a project funded by the then Department for Education and Skills (DfES), now the Department for Children, Schools and Families (DCSF). This project set out to evaluate 19 local authority (LA) Pathfinders in England that were piloting the introduction of foreign language learning at KS2 between 2003 and 2005. Findings revealed that there was inconsistency between schools, even within each LA Pathfinder, in the use of schemes of work and that assessment was generally underdeveloped in the majority of the Pathfinders. In order to set these findings in context, this paper examines the issues of progression and assessment in foreign language learning in England. Finally, it investigates the challenges English primary schools face in terms of progression and assessment in the light of the new entitlement and discusses implications for the future. Managing progression, both within KS2 and through to secondary school at KS3 (ages 11-14), is one of the key factors in determining the overall success of starting languages in primary school

Explosive reconnection in magnetars

X-ray activity of Anomalous X-ray Pulsars and Soft Gamma-Ray Repeaters may result from the heating of their magnetic corona by direct currents dissipated by magnetic reconnection. We investigate the possibility that X-ray flares and bursts observed from AXPs and SGRs result from magnetospheric reconnection events initiated by development of tearing mode in magnetically-dominated relativistic plasma. We formulate equations of resistive force-free electrodynamics, discuss its relation to ideal electrodynamics, and give examples of both ideal and resistive equilibria. Resistive force-free current layers are unstable toward the development of small-scale current sheets where resistive effects become important. Thin current sheets are found to be unstable due to the development of resistive force-free tearing mode. The growth rate of tearing mode is intermediate between the short \Alfven time scale $\tau_A$ and a long resistive time scale $\tau_R$: $\Gamma \sim 1/(\tau_R \tau_A)^{1/2}$, similar to the case of non-relativistic non-force-free plasma. We propose that growth of tearing mode is related to the typical rise time of flares, $\sim 10$ msec. Finally, we discuss how reconnection may explain other magnetar phenomena and ways to test the model.Comment: 27 pages, 3 figures, submitted to MNRA

The effect of flares on total solar irradiance

Flares are powerful energy releases occurring in stellar atmospheres. Solar flares, the most intense energy bursts in the solar system, are however hardly noticeable in the total solar luminosity. Consequently, the total amount of energy they radiate 1) remains largely unknown and 2) has been overlooked as a potential contributor to variations in the Total Solar Irradiance (TSI), i.e. the total solar flux received at Earth. Here, we report on the detection of the flare signal in the TSI even for moderate flares. We find that the total energy radiated by flares exceeds the soft X-ray emission by two orders of magnitude, with an important contribution in the visible domain. These results have implications for the physics of flares and the variability of our star.Comment: accepted in Nature Physic