Permutonestohedra

There are several real spherical models associated with a root arrangement, depending on the choice of a building set. The connected components of these models are manifolds with corners which can be glued together to obtain the corresponding real De Concini–Procesi models. In this paper, starting from any root system with finite Coxeter group W and any W -invariant building set, we describe an explicit realization of the real spherical model as a union of polytopes (nestohedra) that lie inside the chambers of the arrangement. The main point of this realization is that the convex hull of these nestohedra is a larger polytope, a permutonestohedron, equipped with an action of W or also, depending on the building set, of Aut ( ). The permutonestohedra are natural generalizations of Kapranov’s permutoassociahedra

Comparison of Macro-Scale Porosity Implementations for CFD Modelling of Wave Interaction with Thin Porous Structures

This is the final version. Available on open access from MDPI via the DOI in this recordData Availability Statement: The research data supporting this publication are provided within this paper. The code used for data collection is the existing open source code OpenFOAM® (The OpenFOAM Foundation v5) and the open source libraries OlaFlow/IHFoam [48] and waves2Foam [39,49].Computational fluid dynamics (CFD) modelling of wave interaction with thin perforated structures is of interest in a range of engineering applications. When large-scale effects such as forces and the overall flow behaviour are of interest, a microstructural resolution of the perforated geometry can be excessive or prohibitive in terms of computational cost. More efficiently, a thin porous structure can be represented by its macro-scale effects by means of a quadratic momentum source or pressure-drop respectively. In the context of regular wave interaction with thin porous structures and within an incompressible, two-phase Navier–Stokes and volume-of-fluid framework (based on interFoam of OpenFOAM®), this work investigates porosity representation as a porous surface with a pressure-jump condition and as volumetric isotropic and anisotropic porous media. Potential differences between these three types of macro-scale porosity implementations are assessed in terms of qualitative flow visualizations, velocity profiles along the water column, the wave elevation near the structures and the horizontal force on the structures. The comparison shows that all three types of implementation are capable of reproducing large-scale effects of the wave-structure interaction and that the differences between all obtained results are relatively small. It was found that the isotropic porous media implementation is numerically the most stable and requires the shortest computation times. The pressure-jump implementation requires the smallest time steps for stability and thus the longest computation times. This is likely due to the spurious local velocities at the air-water interface as a result of the volume-of-fluid interface capturing method combined with interFoam’s segregated pressure-velocity coupling algorithm. This paper provides useful insights and recommendations for effective macro-scale modelling of thin porous structures.University of ExeterEngineering and Physical Sciences Research Council (EPSRC)Newton Fun

Using a porous-media approach for CFD modelling of wave interaction with thin perforated structures

This is the final version. Available on open access from Springer via the DOI in this recordAvailability of data and material: The research data supporting this publication are provided within this paper.This work presents the use of a porous-media approach for computational fluid dynamics (CFD) modelling of wave interaction with thin perforated sheets and cylinders. The perforated structures are not resolved explicitly but represented by a volumetric porous zone where a volume-averaged pressure gradient in the form of a drag term is applied to the Navier–Stokes momentum equation. The horizontal force on the structures and the free-surface elevation at wave gauges around the cylinder model have been analysed for a range of porosities and regular wave conditions. The CFD results are verified against results from a linear potential-flow model and validated against experimental results. The applied pressure gradient formulation produces good agreement for all porosity values, wave frequencies and wave steepnesses investigated. It is demonstrated that an isotropic macroscopic porosity representation used for large volumetric granular material can also be used for thin perforated structures. This approach offers greater flexibility in the range of wave conditions that can be modelled compared to approaches based on linear potential-flow theory and requires a smaller computational effort compared to CFD approaches which resolve the flow through the openings. The approach can therefore be an efficient alternative for engineering problems where large-scale effects such as global forces and the overall flow-behaviour are of the main interest.University of ExeterEngineering and Physical Sciences Research Council (EPSRC)National Natural Science Foundation of ChinaNewton Fun

Resonant behavior of a single plasmonic helix

Chiral plasmonic nanostructures will be of increasing importance for future applications in the field of nano optics and metamaterials. Their sensitivity to incident circularly polarized light in combination with the ability of extreme electromagnetic field localization renders them ideal candidates for chiral sensing and for all-optical information processing. Here, the resonant modes of single plasmonic helices are investigated. We find that a single plasmonic helix can be efficiently excited with circularly polarized light of both equal and opposite handedness relative to that of the helix. An analytic model provides resonance conditions matching the results of full-field modeling. The underlying geometric considerations explain the mechanism of excitation and deliver quantitative design rules for plasmonic helices being resonant in a desired wavelength range. Based on the developed analytical design tool, single silver helices were fabricated and optically characterized. They show the expected strong chiroptical response to both handednesses in the targeted visible range. With a value of 0.45 the experimentally realized dissymmetry factor is the largest obtained for single plasmonic helices in the visible range up to now.Comment: main: typo in the author's name corrected, SI: update

Around the tangent cone theorem

A cornerstone of the theory of cohomology jump loci is the Tangent Cone theorem, which relates the behavior around the origin of the characteristic and resonance varieties of a space. We revisit this theorem, in both the algebraic setting provided by cdga models, and in the topological setting provided by fundamental groups and cohomology rings. The general theory is illustrated with several classes of examples from geometry and topology: smooth quasi-projective varieties, complex hyperplane arrangements and their Milnor fibers, configuration spaces, and elliptic arrangements.Comment: 39 pages; to appear in the proceedings of the Configurations Spaces Conference (Cortona 2014), Springer INdAM serie

Aging restricts the ability of mesenchymal stem cells to promote the generation of oligodendrocytes during remyelination.

Multiple sclerosis (MS) is a demyelinating disease of the central nervous system (CNS) that leads to severe neurological deficits. Due to their immunomodulatory and neuroprotective activities and their ability to promote the generation of oligodendrocytes, mesenchymal stem cells (MSCs) are currently being developed for autologous cell therapy in MS. As aging reduces the regenerative capacity of all tissues, it is of relevance to investigate whether MSCs retain their pro-oligodendrogenic activity with increasing age. We demonstrate that MSCs derived from aged rats have a reduced capacity to induce oligodendrocyte differentiation of adult CNS stem/progenitor cells. Aging also abolished the ability of MSCs to enhance the generation of myelin-like sheaths in demyelinated cerebellar slice cultures. Finally, in a rat model for CNS demyelination, aging suppressed the capability of systemically transplanted MSCs to boost oligodendrocyte progenitor cell (OPC) differentiation during remyelination. Thus, aging restricts the ability of MSCs to support the generation of oligodendrocytes and consequently inhibits their capacity to enhance the generation of myelin-like sheaths. These findings may impact on the design of therapies using autologous MSCs in older MS patients.The authors would like to thank the following funding agencies for their support: Paracelsus Medical University PMU-FFF Long-Term Fellowship L-12/01/001-RIV (to and Stand-Alone Grant E-12/15/077-RIT (both to F.J.R.); Chilean Comisión Nacional de Investigación Científica y Tecnológica (CONICYT) FONDECYT Program Regular Grant Nº 1161787 (to F.J.R.), Regular Grant Nº 1141015 (to L.F.B.); Chilean CONICYT PCI Program Grant Nº REDES170233 (to F.J.R.), Grant Nº REDES180139 and Grant Nº REDI170037; Chilean CONICYT FONDEFIDeA Program Grant Nº ID17AM0043 (to M.E.S. and F.J.R.); European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreements N HEALTH-F2-2011-278850 (INMiND) and HEALTH-F2-2011-279288 (IDEA). The work in the Küry laboratory was supported by the German Research Foundation (DFG; KU1934/2_1, KU1934/5-1) and the Christiane and Claudia Hempel Foundation for clinical and iBrain. The work in the Franklin laboratory was supported by grants from the UK Multiple Sclerosis Society and the Adelson Medical Research Foundation, and a core support grant from the Wellcome Trust and MRC to the Wellcome-MRC Cambridge Stem Cell Institute. In addition, the present work was supported by the state of Salzburg (to L.A.). We thank Armin Schneider, Sygnis Pharma AG Heidelberg, Germany, for the MBP promoter construct. We disclose any conflict of interest

A Review on the Modelling of Wave-Structure Interactions Based on OpenFOAM

The modelling of wave-structure interaction (WSI) has significant applications in understanding natural processes as well as securing the safety and efficiency of marine engineering. Based on the technique of Computational Fluid Dynamics (CFD) and the open-source simulation framework - OpenFOAM, this paper provides a state-of-the-art review of WSI modelling methods. The review categorises WSI scenarios and suggests their suitable computational approaches, concerning a rigid, deformable or porous structure in regular, irregular, non-breaking or breaking waves. Extensions of WSI modelling for wave-structure-seabed interactions and various wave energy converters are also introduced. As a result, the present review aims to help understand the CFD modelling of WSI and guide the use of OpenFOAM for target WSI problems

A Grassmann algebra for matroids

We introduce an idempotent analogue of the exterior algebra for which the theory of tropical linear spaces (and valuated matroids) can be seen in close analogy with the classical Grassmann algebra formalism for linear spaces. The top wedge power of a tropical linear space is its Plucker vector, which we view as a tensor, and a tropical linear space is recovered from its Plucker vector as the kernel of the corresponding wedge multiplication map. We prove that an arbitrary d-tensor satisfies the tropical Plucker relations (valuated exchange axiom) if and only if the d-th wedge power of the kernel of wedge-multiplication is free of rank one. This provides a new cryptomorphism for valuated matroids, including ordinary matroids as a special case