Revealing the state space of turbulent pipe flow by symmetry reduction

Symmetry reduction by the method of slices is applied to pipe flow in order to quotient the stream-wise translation and azimuthal rotation symmetries of turbulent flow states. Within the symmetry-reduced state space, all travelling wave solutions reduce to equilibria, and all relative periodic orbits reduce to periodic orbits. Projections of these solutions and their unstable manifolds from their $\infty$-dimensional symmetry-reduced state space onto suitably chosen 2- or 3-dimensional subspaces reveal their interrelations and the role they play in organising turbulence in wall-bounded shear flows. Visualisations of the flow within the slice and its linearisation at equilibria enable us to trace out the unstable manifolds, determine close recurrences, identify connections between different travelling wave solutions, and find, for the first time for pipe flows, relative periodic orbits that are embedded within the chaotic attractor, which capture turbulent dynamics at transitional Reynolds numbers.Comment: 24 pages, 12 figure

Agronomic efficiency of selected phosphorus fertilisers derived from secondary raw materials for European agriculture. A meta-analysis

International audiencePhosphorus (P) is a macronutrient essential for all living organisms. Food production has become highly dependent on mineral P-fertilisers derived from phosphate rock, a non-renewable and finite resource. Based on supply risk and economic importance for the European Union, phosphate rock and elemental P have been identified as critical raw materials. Moreover, P dissipation can lead to adverse impacts on the aquatic environment. The production and use of P-fertilisers derived from secondary raw materials could possibly contribute to a more sustainable agriculture in line with a circular economy. Biogenic and industrial resources and waste streams can be converted into value added materials, such as precipitated phosphate salts, thermal oxidation materials and derivates, and pyrolysis and gasification materials. A condition is, however, that the P must be recovered in a plant-available form and that the recovered P-fertiliser supports plant growth and nutrient uptake in European agroecosystems. Here, we review the agronomic efficiency of selected P-fertilisers derived from secondary raw materials by comparing plant responses relative to those after mined and synthetic P-fertiliser application in settings relevant for European agriculture, using meta-analyses. The major points are the following: (1) precipitated phosphate salts show similar agronomic efficiency to mined and synthetic P-fertilisers, with results that are consistent and generalisable across soil and crop types relevant for European agriculture; (2) thermal oxidation materials and derivates can deliver an effective alternative for mined and synthetic P-fertilisers, but the relative agronomic efficiency is dependent on the feedstock applied, possible post-combustion manufacturing processes, and the length of the plant growing season; (3) the agronomic efficiency of pyrolysis and gasification materials remains indeterminate due to a lack of available data for European settings. It is concluded that the agronomic efficiency of selected P-fertilisers derived from secondary raw materials supports their use in conventional and organic European agricultural sectors

Integrated research on sand suppletion as a coastal defence system: application to the Flemish East Coast

An integrated technical research explores a complete synergy of physical scale modelling, numerical simulations and field records in order to validate the potential use of sand suppletion as a coastal defence for the Flemish East coast. Detailed analysis of the rich field data forms an optimum reflective mirror to put the respective design and calculation tools in both a comparative and evaluating framework. Combining all available instruments in an interactive modelling approach leads to an optimum design and a more economic application of beach nourishment techniques in this area

Controlling light-with-light without nonlinearity

According to Huygens' superposition principle, light beams traveling in a linear medium will pass though one another without mutual disturbance. Indeed, it is widely held that controlling light signals with light requires intense laser fields to facilitate beam interactions in nonlinear media, where the superposition principle can be broken. We demonstrate here that two coherent beams of light of arbitrarily low intensity can interact on a metamaterial layer of nanoscale thickness in such a way that one beam modulates the intensity of the other. We show that the interference of beams can eliminate the plasmonic Joule losses of light energy in the metamaterial or, in contrast, can lead to almost total absorbtion of light. Applications of this phenomenon may lie in ultrafast all-optical pulse-recovery devices, coherence filters and THz-bandwidth light-by-light modulators

Discretely guided electromagnetic effective medium

A material comprised of an array of subwavelength coaxial waveguides decomposes incident electromagnetic waves into spatially discrete wave components, propagates these components without frequency cut-off, and reassembles them on the far side of the material. The propagation of these wave components is fully controlled by the physical properties of the waveguides and their geometrical distribution in the array. This allows for an exceptional degree of control over the electromagnetic response of this effective medium, with numerous potential applications. With the development of nanoscale subwavelength coaxial waveguides, these applications (including metamaterial functionality) can be enabled in the visible frequency range