An adaptive variable order quadrature strategy

In this article we propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this way we aim to account for local smoothness properties of the function to be integrated as effectively as possible, and thereby achieve highly accurate results in a very efficient manner. Indeed, this idea originates from so-called hp-version finite element methods which are known to deliver high-order convergence rates, even for nonsmooth functions

Evaluation of ADAS with a supported-driver model for desired allocation of tasks between human and technology performance

Partly automated driving is relevant for solving mobility problems, but also causes concerns with respect to the driver‟s reliability in task performance. The supported driver model presented in this paper is therefore intended to answer the question, what type of support and in which circumstances, will enhance the driver‟s ability to control the vehicle. It became apparent that prerequisites for performing tasks differ per driving task‟s type and require different support. The possible support for each driving task‟s type, has been combined with support-types to reduce the error causations from each different performance level (i.e. knowledge-based, rule-based and skill-based performance). The allocation of support in relation to performance level and driving task‟s type resulted in a supported driver model and this model relates the requested circumstances to appropriate support types. Among three tested ADAS systems, semi-automated parking showed best allocation of support; converting the demanding parallel parking task into a rather routine-like operation

Moving lattice kinks and pulses: an inverse method

We develop a general mapping from given kink or pulse shaped travelling-wave solutions including their velocity to the equations of motion on one-dimensional lattices which support these solutions. We apply this mapping - by definition an inverse method - to acoustic solitons in chains with nonlinear intersite interactions, to nonlinear Klein-Gordon chains, to reaction-diffusion equations and to discrete nonlinear Schr\"odinger systems. Potential functions can be found in at least a unique way provided the pulse shape is reflection symmetric and pulse and kink shapes are at least $C^2$ functions. For kinks we discuss the relation of our results to the problem of a Peierls-Nabarro potential and continuous symmetries. We then generalize our method to higher dimensional lattices for reaction-diffusion systems. We find that increasing also the number of components easily allows for moving solutions.Comment: 15 pages, 5 figure

Against all odds? Forming the planet of the HD196885 binary

HD196885Ab is the most "extreme" planet-in-a-binary discovered to date, whose orbit places it at the limit for orbital stability. The presence of a planet in such a highly perturbed region poses a clear challenge to planet-formation scenarios. We investigate this issue by focusing on the planet-formation stage that is arguably the most sensitive to binary perturbations: the mutual accretion of kilometre-sized planetesimals. To this effect we numerically estimate the impact velocities $dv$ amongst a population of circumprimary planetesimals. We find that most of the circumprimary disc is strongly hostile to planetesimal accretion, especially the region around 2.6AU (the planet's location) where binary perturbations induce planetesimal-shattering $dv$ of more than 1km/s. Possible solutions to the paradox of having a planet in such accretion-hostile regions are 1) that initial planetesimals were very big, at least 250km, 2) that the binary had an initial orbit at least twice the present one, and was later compacted due to early stellar encounters, 3) that planetesimals did not grow by mutual impacts but by sweeping of dust (the "snowball" growth mode identified by Xie et al., 2010b), or 4) that HD196885Ab was formed not by core-accretion but by the concurent disc instability mechanism. All of these 4 scenarios remain however highly conjectural.Comment: accepted for publication by Celestial Mechanics and Dynamical Astronomy (Special issue on EXOPLANETS

A corpus-assisted study of the discourse marker well as an indicator of judges' institutional roles in court cases with litigants in person

In this paper, I concentrate on court cases with litigants in person (lay people who act on their own behalf in legal proceedings without a counsel or solicitor) and discuss the challenges of building a corpus of courtroom discourse where it is crucial to distinguish between speakers due to their distinct institutional roles. The corpus incorporates seven sub-corpora of verbatim transcripts from different court cases with litigants in person and comprises over eleven-million tokens. The focus of this paper is on the interplay between the legal and lay discourse types and how judges project their institutional roles through well-initiated turns directed at litigants in person and counsels. As a versatile discourse marker, well provides a good opportunity to explore how judges have to adapt their roles to ensure lay litigants in person receive the necessary support and that their lack of competence does not impede on the fairness of the proceedings. Given the breadth and importance of the topic of litigation in person, I discuss how the tools and approaches of corpus linguistics can be helpful in this multi-disciplinary area where multiple functions and uses of individual linguistic features need to be explored in depth

A mathematical framework for critical transitions: normal forms, variance and applications

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio

Photospheric and Subphotospheric Dynamics of Emerging Magnetic Flux

Magnetic fields emerging from the Sun's interior carry information about physical processes of magnetic field generation and transport in the convection zone. Soon after appearance on the solar surface the magnetic flux gets concentrated in sunspot regions and causes numerous active phenomena on the Sun. This paper discusses some properties of the emerging magnetic flux observed on the solar surface and in the interior. A statistical analysis of variations of the tilt angle of bipolar magnetic regions during the emergence shows that the systematic tilt with respect to the equator (the Joy's law) is most likely established below the surface. However, no evidence of the dependence of the tilt angle on the amount of emerging magnetic flux, predicted by the rising magnetic flux rope theories, is found. Analysis of surface plasma flows in a large emerging active region reveals strong localized upflows and downflows at the initial phase of emergence but finds no evidence for large-scale flows indicating future appearance a large-scale magnetic structure. Local helioseismology provides important tools for mapping perturbations of the wave speed and mass flows below the surface. Initial results from SOHO/MDI and GONG reveal strong diverging flows during the flux emergence, and also localized converging flows around stable sunspots. The wave speed images obtained during the process of formation of a large active region, NOAA 10488, indicate that the magnetic flux gets concentrated in strong field structures just below the surface. Further studies of magnetic flux emergence require systematic helioseismic observations from the ground and space, and realistic MHD simulations of the subsurface dynamics.Comment: 21 pages, 15 figures, to appear in Space Science Review

Delivering a multi-functional and resilient urban forest

Tree planting is widely advocated and applied in urban areas, with large-scale projects underway in cities globally. Numerous potential benefits are used to justify these planting campaigns. However, reports of poor tree survival raise questions about the ability of such projects to deliver on their promises over the long-term. Each potential benefit requires different supporting conditions—relating not only to the type and placement of the tree, but also to the broader urban system within which it is embedded. This set of supporting conditions may not always be mutually compatible and may not persist for the lifetime of the tree. Here, we demonstrate a systems-based approach that makes these dependencies, synergies, and tensions more explicit, allowing them to be used to test the decadal-scale resilience of urban street trees. Our analysis highlights social, environmental, and economic assumptions that are implicit within planting projects; notably that high levels of maintenance and public support for urban street trees will persist throughout their natural lifespan, and that the surrounding built form will remain largely unchanged. Whilst the vulnerability of each benefit may be highly context specific, we identify approaches that address some typical weaknesses, making a functional, resilient, urban forest more attainable