Homogenization of weakly coupled systems of Hamilton--Jacobi equations with fast switching rates

We consider homogenization for weakly coupled systems of Hamilton--Jacobi equations with fast switching rates. The fast switching rate terms force the solutions converge to the same limit, which is a solution of the effective equation. We discover the appearance of the initial layers, which appear naturally when we consider the systems with different initial data and analyze them rigorously. In particular, we obtain matched asymptotic solutions of the systems and rate of convergence. We also investigate properties of the effective Hamiltonian of weakly coupled systems and show some examples which do not appear in the context of single equations.Comment: final version, to appear in Arch. Ration. Mech. Ana

Learning from multimedia and hypermedia

Computer-based multimedia and hypermedia resources (e.g., the world wide web) have become one of the primary sources of academic information for a majority of pupils and students. In line with this expansion in the field of education, the scientific study of learning from multimedia and hypermedia has become a very active field of research. In this chapter we provide a short overview with regard to research on learning with multimedia and hypermedia. In two review sections, we describe the educational benefits of multiple representations and of learner control, as these are the two defining characteristics of hypermedia. In a third review section we describe recent scientific trends in the field of multimedia/hypermedia learning. In all three review sections we will point to relevant European work on multimedia/hypermedia carried out within the last 5 years, and often carried out within the Kaleidoscope Network of Excellence. According to the interdisciplinary nature of the field this work might come not only from psychology, but also from technology or pedagogy. Comparing the different research activities on multimedia and hypermedia that have dominated the international scientific discourse in the last decade reveals some important differences. Most important, a gap seems to exist between researchers mainly interested in a “serious” educational use of multimedia/ hypermedia and researchers mainly interested in “serious” experimental research on learning with multimedia/hypermedia. Recent discussions about the pros and cons of “design-based research” or “use-inspired basic research” can be seen as a direct consequence of an increasing awareness of the tensions within these two different cultures of research on education

Configurations and Path Planning of Convex Planar Polygonal Loops

Polygonal loops are interesting both as classical geometric objects and in modeling practical engineering systems, e.g., grasping systems with fingers having planar revolute joints. Convex loop configurations and path planning between them are important since many naturally occurring manipulation poses for human and robotic hands are convex or close to convex, and current collision-free path planning methods for polygonal loops use convex configurations in intermediate steps. We prove that, in a set of triangle-based parameters, the space CConvex of convex configurations of a planar polygonal loop with fixed edge lengths and orientation, and one link pinned to the plane, is star-shaped with respect to an easily computed triangular configuration; with a further condition on edge lengths, CConvex is actually a convex polyhedron. Thus reconfiguration between identically oriented convex configurations of a planar polygonal loop can be achieved by one or two straight-line motions within CConvex. We conjecture that, in our parameter space, the straight-line motion joining any two such configurations passes through only non-self-intersecting configurations, although it may leave CConvex. These results are substantially simpler and more efficient than prior work, and demonstrate the importance of suitable system parametrization

Deriving pre-eutrophic conditions from an ensemble model approach for the North-West European seas

The pre-eutrophic state of marine waters is generally not well known, complicating target setting for management measures to combat eutrophication. We present results from an OSPAR ICG-EMO model assessment to simulate the pre-eutrophic state of North-East Atlantic marine waters. Using an ecosystem model ensemble combined with an observation-based weighting method we derive sophisticated estimates for key eutrophication indicators. Eight modelling centres applied the same riverine nutrient loads, atmospheric nutrient deposition rates and boundary conditions to their specific model set-up to ensure comparability. The pre-eutrophic state was defined as a historic scenario of estimated nutrient inputs (riverine, atmospheric) at around the year 1900, before the invention and widespread use of industrial fertilizers. The period 2009-2014 was used by all participants to simulate both the current state of eutrophication and the pre-eutrophic scenario, to ensure that differences are solely due to the changes in nutrient inputs between the scenarios. Mean values were reported for winter dissolved inorganic nutrients and total nutrients (nitrogen, phosphorus) and the nitrogen to phosphorus ratio, and for growing season chlorophyll, chlorophyll 90th percentile, near-bed oxygen minimum and net phytoplankton production on the level of the OSPAR assessment areas. Results showed distinctly lower nutrient concentrations and nitrogen to phosphorus ratio’s in coastal areas under pre-eutrophic conditions compared to current conditions (except in the Meuse Plume and Seine Plume areas). Chlorophyll concentrations were estimated to be as much as ~40% lower in some areas, as were dissolved inorganic phosphorus levels. Dissolved inorganic nitrogen levels were found to be up to 60% lower in certain assessment areas. The weighted average approach reduced model disparities, and delivered pre-eutrophic concentrations in each assessment area. Our results open the possibility to establish reference values for indicators of eutrophication across marine regions. The use of the new assessment areas ensures local ecosystem functioning is better represented while political boundaries are largely ignored. As such, the reference values are less associated to member states boundaries than to ecosystem boundaries