Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

Psychophysiological responses to appraisal dimensions in a computer game

A computer game was used to study psychophysiological reactions to emotion-relevant events. Two dimensions proposed by Scherer (1984a, 1984b) in his appraisal theory, the intrinsic pleasantness and goal conduciveness of game events, were studied in a factorial design. The relative level at which a player performed at the moment of an event was also taken into account. A total of 33 participants played the game while cardiac activity, skin conductance, skin temperature, and muscle activity as well as emotion self-reports were assessed. The self-reports indicate that game events altered levels of pride, joy, anger, and surprise. Goal conduciveness had little effect on muscle activity but was associated with significant autonomic effects, including changes to interbeat interval, pulse transit time, skin conductance, and finger temperature. The manipulation of intrinsic pleasantness had little impact on physiological responses. The results show the utility of attempting to manipulate emotion-constituent appraisals and measure their peripheral physiological signatures.

An efficient numerical scheme for the two-dimensional shallow water equations using arithmetic averaging

A finite difference scheme based on flux difference splitting is presented for the solution of the two-dimensional shallow water equations of ideal fluid flow. A linearised problem, analogous to that of Riemann for gas dynamics is defined, and a scheme, based on numerical characteristic decomposition is presented for obtaining approximate solutions to the linearised problem, and incorporates the technique of operator splitting. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver, where the computational expense can be prohibitive. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids nonphysical, spurious oscillations. An extension to the two-dimensional equations with source terms is included. The scheme is applied to the one-dimensional problems of a breaking dam and reflection of a bore, and in each case the approximate solution is compared to the exact solution of ideal fluid flow. The scheme is also applied to a problem of stationary bore generation in a channel of variable cross-section. Finally, the scheme is applied to two other dam-break problems, this time in two dimensions with one having cylindrical symmetry. Each approximate solution compares well with those given by other authors.

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains.

Consistent Dirichlet Boundary Conditions for Numerical Solution of Moving Boundary Problems

We consider the imposition of Dirichlet boundary conditions in the finite element modelling of moving boundary problems in one and two dimensions for which the total mass is prescribed. A modification of the standard linear finite element test space allows the boundary conditions to be imposed strongly whilst simultaneously conserving a discrete mass. The validity of the technique is assessed for a specific moving mesh finite element method, although the approach is more general. Numerical comparisons are carried out for mass-conserving solutions of the porous medium equation with Dirichlet boundary conditions and for a moving boundary problem with a source term and time-varying mass.

Approximations to the scattering of water waves by steep topography

A new method is developed for approximating the scattering of linear surface gravity waves on water of varying quiescent depth in two dimensions. A conformal mapping of the fluid domain onto a uniform rectangular strip transforms steep and discontinuous bed profiles into relatively slowly varying, smooth functions in the transformed free-surface condition. By analogy with the mild-slope approach used extensively in unmapped domains, an approximate solution of the transformed problem is sought in the form of a modulated propagating wave which is determined by solving a second-order ordinary differential equation. This can be achieved numerically, but an analytic solution in the form of a rapidly convergent infinite series is also derived and provides simple explicit formulae for the scattered wave amplitudes. Small-amplitude and slow variations in the bedform that are excluded from the mapping procedure are incorporated in the approximation by a straightforward extension of the theory. The error incurred in using the method is established by means of a rigorous numerical investigation and it is found that remarkably accurate estimates of the scattered wave amplitudes are given for a wide range of bedforms and frequencies.

Aperiodicity, structure, and dynamics in Ni(CN)(2)

By combining the results of both x-ray diffraction and neutron total-scattering experiments, we show that Ni(CN)(2) exhibits long-range structural order only in two dimensions, with no true periodicity perpendicular to its gridlike layers. Reverse Monte Carlo analysis gives an experimental distinction between M-C and M-N bond lengths in a homometallic cyanide framework and identifies the vibrational modes responsible for anomalous positive and negative thermal expansion in the title compound.

A new cyano-bridged one-dimensional (GdFeIII)-Fe-III coordination polymer with o-phenanthroline as the blocking ligand: synthesis, structure, and magnetic properties

Synthesis, structural characterization, and magnetic properties of a new cyano-bridged one-dimensional iron (III)-gadolinium (III) compound, trans-[Gd(o-phen)(2)(H2O)(2)(mu-CN)(2)Fe(CN)(4)], - 2no-phen (o-phen = 1,10-phenanthroline), have been described. The compound crystallizes in the triclinic P (1) over bar space group with the following unit cell parameters: a = 10.538(14) angstrom, b = 12.004(14) angstrom, c = 20.61(2) angstrom, alpha = 92.41(1)degrees, beta = 92.76(1)degrees, gamma = 11 2.72(1)degrees, and Z = 2. In this complex, each gadolinium (III) is coordinated to two nitrile nitrogens of the CN groups coming from two different ferricyanides, the mutually trans cyanides of each of which links another different Gd-III to create -NC-Fe(CN)(4)-CN-Gd-NC- type 1-D chain structure. The one-dimensional chains are self-assembled in two-dimensions via weak C-H center dot center dot center dot N hydrogen bonds. Both the variable-temperature (2-300 K, 0.01 T and 0.8 T) and variable-field (0-50 000 Gauss, 2 K) magnetic measurements reveal the existence of very weak interaction in this molecule. The temperature dependence of the susceptibilities has been analyzed using a model for a chain of alternating classic (7/2) and quantum (1/2) spins. (c) 2005 Elsevier B.V. All rights reserved.

Literacy as a complex activity: deconstructing the simple view of reading

The Rose Review into the teaching of early reading recommended that the conceptual framework incorporated into the National Literacy Strategy Framework for Teaching – the Searchlights model of reading and its development – should be replaced by the Simple View of Reading. In this paper, we demonstrate how these two frameworks relate to each other, and show that nothing has been lost in this transformation from Searchlights to Simple View: on the contrary, much has been gained. That nothing has been lost is demonstrated by consideration of the underlying complexity inherent in each of the two dimensions delineated in the Simple View. That much has been gained is demonstrated by the increased understanding of each dimension that follows from careful scientific investigation of each. The better we understand what is involved in each dimension, the better placed we are to unravel and understand the essential, complex and continual interactions between each dimension which underlie skilled reading. This has clear implications for further improving the early teaching of reading.

Mouse movements of motion-impaired users: a submovement analysis

Understanding human movement is key to improving input devices and interaction techniques. This paper presents a study of mouse movements of motion-impaired users, with an aim to gaining a better understanding of impaired movement. The cursor trajectories of six motion-impaired users and three able-bodied users are studied according to their submovement structure. Several aspects of the movement are studied, including the frequency and duration of pauses between submovements, verification times, the number of submovements, the peak speed of submovements and the accuracy of submovements in two-dimensions. Results include findings that some motion-impaired users pause more often and for longer than able-bodied users, require up to five times more submovements to complete the same task, and exhibit a correlation between error and peak submovement speed that does not exist for able-bodied users.

Individual differences in brain structure underpin empathizing–systemizing cognitive styles in male adults

Individual differences in cognitive style can be characterized along two dimensions: ‘systemizing’ (S, the drive to analyze or build ‘rule-based’ systems) and ‘empathizing’ (E, the drive to identify another's mental state and respond to this with an appropriate emotion). Discrepancies between these two dimensions in one direction (S > E) or the other (E > S) are associated with sex differences in cognition: on average more males show an S > E cognitive style, while on average more females show an E > S profile. The neurobiological basis of these different profiles remains unknown. Since individuals may be typical or atypical for their sex, it is important to move away from the study of sex differences and towards the study of differences in cognitive style. Using structural magnetic resonance imaging we examined how neuroanatomy varies as a function of the discrepancy between E and S in 88 adult males from the general population. Selecting just males allows us to study discrepant E-S profiles in a pure way, unconfounded by other factors related to sex and gender. An increasing S > E profile was associated with increased gray matter volume in cingulate and dorsal medial prefrontal areas which have been implicated in processes related to cognitive control, monitoring, error detection, and probabilistic inference. An increasing E > S profile was associated with larger hypothalamic and ventral basal ganglia regions which have been implicated in neuroendocrine control, motivation and reward. These results suggest an underlying neuroanatomical basis linked to the discrepancy between these two important dimensions of individual differences in cognitive style.

An in-depth view of the facets, antecedents and effects of leaders’ change competency: lessons from a case study

Leaders across companies initiate and implement change and thus are crucial for successful organizations. This study takes a competency perspective on leaders and investigates the competencies leaders show to facilitate effective change. The article explores the content of the construct of leaders’ change competency and examines its antecedents and effects. We conducted a case study in a German tourism company undergoing a major change process. The study identified (a) distinct content facets regarding the construct of leaders’ change competency along its two dimensions of leaders’ readiness for change and leaders’ change ability; (b) the construct’s antecedents, specifically contextual factors, leaders’ competency potentials, and attitudes toward change; and (c) beneficial effects of leaders’ change competency. The study ends with implications for research and leadership practice as well as suggestions for future studies on leaders’ change competency.

Waste cooking oil as an energy resource: review of Chinese policies

Converting waste cooking oil into biofuel represents a three-win solution, dealing simultaneously with food security, pollution, and energy security. In this paper, we encode the policy documents of waste cooking oil refining biofuel in China based on content analysis, and explore the related policies from the two dimensions as basic policy tools and enterprises supply chain. Research indicates the weak institution coordination of policy issuing entities. Also, the findings show that tools of regulatory control and goal planning are overused. Policies of government procurement, outsourcing and biofuel consumption are relatively scarce. Generally, government focuses more on formulating policies from the strategic, administrative and regulatory aspects, while less on market-oriented initiatives as funding input and financial support.

Task design and second language performance: the effect of narrative type on learner output

This article reports on a detailed empirical study of the way narrative task design influences the oral performance of second-language (L2) learners. Building on previous research findings, two dimensions of narrative design were chosen for investigation: narrative complexity and inherent narrative structure. Narrative complexity refers to the presence of simultaneous storylines; in this case, we compared single-story narratives with dual-story narratives. Inherent narrative structure refers to the order of events in a narrative; we compared narratives where this was fixed to others where the events could be reordered without loss of coherence. Additionally, we explored the influence of learning context on performance by gathering data from two comparable groups of participants: 60 learners in a foreign language context in Teheran and 40 in an L2 context in London. All participants recounted two of four narratives from cartoon pictures prompts, giving a between-subjects design for narrative complexity and a within-subjects design for inherent narrative structure. The results show clearly that for both groups, L2 performance was affected by the design of the task: Syntactic complexity was supported by narrative storyline complexity and grammatical accuracy was supported by an inherently fixed narrative structure. We reason that the task of recounting simultaneous events leads learners into attempting more hypotactic language, such as subordinate clauses that follow, for example, while, although, at the same time as, etc. We reason also that a tight narrative structure allows learners to achieve greater accuracy in the L2 (within minutes of performing less accurately on a loosely structured narrative) because the tight ordering of events releases attentional resources that would otherwise be spent on finding connections between the pictures. The learning context was shown to have no effect on either accuracy or fluency but an unexpectedly clear effect on syntactic complexity and lexical diversity. The learners in London seem to have benefited from being in the target language environment by developing not more accurate grammar but a more diverse resource of English words and syntactic choices. In a companion article (Foster & Tavakoli, 2009) we compared their performance with native-speaker baseline data and see that, in terms of nativelike selection of vocabulary and phrasing, the learners in London are closing in on native-speaker norms. The study provides empirical evidence that L2 performance is affected by task design in predictable ways. It also shows that living within the target language environment, and presumably using the L2 in a host of everyday tasks outside the classroom, confers a distinct lexical advantage, not a grammatical one.

Wave-activity conservation laws for the three-dimensional anelastic and Boussinesq equations with a horizontally homogeneous background flow

Wave-activity conservation laws are key to understanding wave propagation in inhomogeneous environments. Their most general formulation follows from the Hamiltonian structure of geophysical fluid dynamics. For large-scale atmospheric dynamics, the Eliassen–Palm wave activity is a well-known example and is central to theoretical analysis. On the mesoscale, while such conservation laws have been worked out in two dimensions, their application to a horizontally homogeneous background flow in three dimensions fails because of a degeneracy created by the absence of a background potential vorticity gradient. Earlier three-dimensional results based on linear WKB theory considered only Doppler-shifted gravity waves, not waves in a stratified shear flow. Consideration of a background flow depending only on altitude is motivated by the parameterization of subgrid-scales in climate models where there is an imposed separation of horizontal length and time scales, but vertical coupling within each column. Here we show how this degeneracy can be overcome and wave-activity conservation laws derived for three-dimensional disturbances to a horizontally homogeneous background flow. Explicit expressions for pseudoenergy and pseudomomentum in the anelastic and Boussinesq models are derived, and it is shown how the previously derived relations for the two-dimensional problem can be treated as a limiting case of the three-dimensional problem. The results also generalize earlier three-dimensional results in that there is no slowly varying WKB-type requirement on the background flow, and the results are extendable to finite amplitude. The relationship A E =cA P between pseudoenergy A E and pseudomomentum A P, where c is the horizontal phase speed in the direction of symmetry associated with A P, has important applications to gravity-wave parameterization and provides a generalized statement of the first Eliassen–Palm theorem.