A non-conforming finite element method with anisotropic mesh grading for the Stokes problem in domains with edges

The solution of the Stokes problem in three-dimensional domainswith edges has anisotropic singular behaviour which is treatednumerically by using anisotropic finite element meshes. Thevelocity is approximated by Crouzeix–Raviart (nonconformingP₁ ) elements and the pressure by piecewise constants. Thismethod is stable for general meshes (without minimal or maximalangle condition). Denoting by N_e the number of elements in themesh, the interpolation and consistency errors are of the optimalorder h N_e^–1/3 which is proved for tensor product meshes.As a by-product, we analyse also nonconforming prismatic elementswith P₁ [oplus ] span {x₃²} as the local space for the velocitywhere x₃ is the direction of the edge.     

Fagnano Orbits of Polygonal Dual Billiards

Given a convex n-gon P, a Fagnano periodic orbit of the respective dual billiard map is an n-gon Q whose sides are bisected by the vertices of P. For which polygons P does the ratio Area Q/Area P have the minimal value? The answer is shown to be: for affine-regular polygons.     

New trends in polylactide (PLA)-based materials: “Green” PLA-Calcium sulfate (nano)composites tailored with flame retardant properties

Starting from gypsum, a by-product of lactic acid fabrication process, novel “green” composites have been produced by melt-blending polylactide (PLA) and this filler after a previous specific dehydration to obtain anhydrite II (AII). Such a material is potentially interesting in biodegradable/rigid packaging and in technical applications requiring rigidity, heat resistance and dimensional stability. In order to obtain PLA-AII composites characterized by specific end-use flame retardant properties, the addition of selected organo-modified layered silicates (OMLS) was considered. Co-addition of AII and OMLS leads to PLA (nano)composites characterized by good (nano)filler dispersion, thermal stability and adequate mechanical resistance. The flame retardant properties as shown by cone calorimetry showed significant increase in the ignition time compared to neat PLA and a substantial decrease, i.e., ca. 40%, of the maximum rate of heat release, whereas the UL94 HB test was successfully passed revealing non-dripping effect and extensive char formation. The study represents a new approach in formulating novel PLA grades with improved characteristic features.     

Electrogenerated chemiluminescence of poly[(2,2′-bipyridyl)(4-(2-pyrrol-1-ylethyl)-4′-methyl-2,2′-bipyridyl)2]ruthenium (II) film

Elelctrogenerated chemiluminescence (ECL) of electropolymerized films based on [(2,2′-bipyridyl)(4-(2-pyrrol-1-ylethyl)-4′-methyl-2,2′-bipyridyl)₂]ruthenium (II) was firstly investigated in both organic and aqueous solution. The ECL behaviors have been explained by two typical mechanisms, namely, redox-cycling type and oxidative-reduction type. For the former, no co-reactant was required and for the latter, tripropylamine (TPA) and (NH₄)₂C₂O₄ were selected as co-reactants in the organic and aqueous system, respectively.     

A short and efficient synthesis of the NMDA glycine site antagonist: (3R,4R)-3-amino-1-hydroxy-4-methyl pyrrolidin-2-one (L-687,414)

A short and efficient synthesis of the NMDA glycine site antagonist: (3R,4R)-3-amino-1-hydroxy-4-methyl pyrrolidin-2-one (L-687,414) is described.     

Totally skew embeddings of manifolds

We study a version of Whitney’s embedding problem in projective geometry: What is the smallest dimension of an affine space that can contain an n-dimensional submanifold without any pairs of parallel or intersecting tangent lines at distinct points? This problem is related to the generalized vector field problem, existence of non-singular bilinear maps, and the immersion problem for real projective spaces. We use these connections and other methods to obtain several specific and general bounds for the desired dimension.     

Time domain study of the Drude–Born–Fedorov model for a class of heterogeneous chiral materials

We deal with the well‐posedness of the transient Maxwell equations in a particular class of heterogeneous isotropic chiral material modeled by the Drude–Born–Fedorov constitutive relations with different boundary conditions. A new formulation of the underlying evolution problems allows us to establish existence and uniqueness results. The selfadjointness of the curl operator multiplied by a piecewise smooth function in an appropriated Hilbert space is also proved. Copyright © 2012 John Wiley & Sons, Ltd.