Improving the Rate of Convergence of High-Order Finite Elements on Polyhedra I: A Priori Estimates

ABSTRACT

Let 𝒯 _k be a sequence of triangulations of a polyhedron Ω ? ? ⁿ and let S _k be the associated finite element space of continuous, piecewise polynomials of degree m. Let u _k  ∈ S _k be the finite element approximation of the solution u of a second-order, strongly elliptic system Pu = f with zero Dirichlet boundary conditions. We show that a weak approximation property of the sequence S _k ensures optimal rates of convergence for the sequence u _k . The method relies on certain a priori estimates in weighted Sobolev spaces for the system Pu = 0 that we establish. The weight is the distance to the set of singular boundary points. We obtain similar results for the Poisson problem with mixed Dirichlet–Neumann boundary conditions on a polygon.     

Inviscid Limit for Damped and Driven Incompressible Navier-Stokes Equations in $$\mathbb R^2$$

We consider the zero viscosity limit of long time averages of solutions of damped and driven Navier-Stokes equations in . We prove that the rate of dissipation of enstrophy vanishes. Stationary statistical solutions of the damped and driven Navier-Stokes equations converge to renormalized stationary statistical solutions of the damped and driven Euler equations. These solutions obey the enstrophy balance.     

Measurement of direct photon production in p+p collisions at sqrt[s] = 200 GeV

Cross sections for midrapidity production of direct photons in p+p collisions at the Relativistic Heavy Ion Collider (RHIC) are reported for transverse momenta of 3 < pT < 16 GeV/c. Next-to-leading order perturbative QCD (pQCD) describes the data well for pT >5 GeV/c, where the uncertainties of the measurement and theory are comparable. We also report on the effect of requiring the photons to be isolated from parton jet energy. The observed fraction of isolated photons is well described by pQCD for pT >7 GeV/c.     

Regioselective synthesis of 5-alkylsalicylates, 5-alkyl-2-hydroxy-acetophenones, and 5-alkyl-2-hydroxy-benzophenones by [3 + 3] cyclization of 1,3-bis(silyl enol ethers) with 2-alkyl-1,1,3,3-tetraethoxypropanes

A variety of 5-alkylsalicylates, 5-alkyl-2-hydroxy-acetophenones, and 5-alkyl-2-hydroxy-benzophenones was regioselectively prepared by TiCl4 mediated formal [3 + 3] cyclization of 1,3-bis(silyl enol ethers) with 2-alkyl-1,1,3,3-tetraethoxypropanes.     

The first trialkylphosphane telluride complexes of Ag(I): molecular, ionic and supramolecular structural alternatives

The structures of the first phosphane telluride complexes of silver(I), obtained from i-Pr3PTe (1) with AgNMs2 [Ms = SO2CH3] and with AgSbF6, reveal the superior coordinating ability of 1, particularly as a bridging ligand, compared with related i-Pr3PS and i-Pr3PSe ligands.     

An investigation of the feasibility of applying Raman microscopy for exploring stained glass

Raman microscopy (RM) is widely used in archaeometrical studies of pigments, geomaterials and biomaterials in the Cultural Heritage, but one domain has received relatively less attention: the colouring of stained glass. This feasibility study investigates the advantages and disadvantages of employing RM alone in this field by means of a study of modern commercial glasses, modern commercial pigments, and a few archaeological stained glasses, but especially by an experimental project whereby the authors created stained glass. The different kinds of possible unreacted or reacted material are rigorously established. The distinction between Na, K, Ca glasses was explored, as well as the red colouring of an industrial glass which was proved to be due to the presence of (Zn, Cd)S(x)Se(1-x). Yellow, green, blue and maroon pigments were studied before and after an initial firing and then after heating on glass. The quality of the Raman spectra varied enormously and was sometimes disappointing. Nevertheless RM successfully identified various coloured products such as bindheimite, crocoite, cobalt aluminate, haematite; relict reactants such as corundum, eskolaite and oxides of Co or Pb; and provided indications of other phases such as maghemite or Co-olivine. One conclusion is that the amount of chemical reaction between the pigments and the glass is small compared to the amount in between the pigments. Comments are made on the potential for dating archaeological glass from the known age of synthesis of the pigments, and of the dangers of this approach. Overall it has been shown that RM can be useful for studying stained glass, especially for remote in situ analytical operations with mobile RM, but one must expect some problems either with fluorescence or weak spectra.     

Multitime dynamic programming for multiple integral actions

This paper introduces a new type of dynamic programming PDE for optimal control problems with performance criteria involving multiple integrals. The main novel feature of the multitime dynamic programming PDE, relative to the standard Hamilton-Jacobi-Bellman PDE, is that it is connected to the multitime maximum principle and is of divergence type. Introducing a generating vector field for the maximum value function, we present an interesting and useful connection between the multitime maximum principle and the multitime dynamic programming, characterizing the optimal control by means of a multitime Hamilton-Jacobi-Bellman (divergence) PDE that may be viewed as a feedback law. Section 1 recalls the multitime maximum principle. Section 2 shows how a multitime control dynamics determines the multitime Hamilton-Jacobi-Bellman PDE via a generating vector field of the value function. Section 3 gives an example of two-time dynamics with nine velocities proving that our theory works well. Section 4 shows that the Hamilton PDEs are characteristic PDEs of multitime Hamilton-Jacobi PDE and that the costates in the multitime maximum principle are in fact gradients of the components of the generating vector field.     

Spatial distribution of 7Be in soils of Lower Austria after heavy rains

The ⁷Be approach in estimating the erosion rates is based on the assumption that the deposition of ⁷Be fallout associated with the erosive event is spatially uniform. The objective of the present work was to verify this assumption by assessing the influence of heavy rainfalls on the ⁷Be spatial distribution in Seibersdorf soils, Austria. Incremental and bulk soil depth profiles were collected from a flat site, undisturbed for the last 9 months prior sampling and with no evidence of erosion or deposition after the occurrence of heavy rains (>30 mm day^?1). The mean value of the ⁷Be areal activities (Bq m^?2) measured at 10 different points from the selected area was 312 Bq m^?2. This value corresponded to a total rainfall of 295 mm within the last 5 months prior sampling, considering that the highest mass activity of ⁷Be at soil surface will decay below the minimum detectable activity after 5 months’ time. The resulted coefficient of variation had a value of 19 % showing acceptable spatial variability of ⁷Be fallout connected with individual storm events on a local scale.     

Studies on new hybrid materials prepared by both Diels–Alder and Michael addition reactions

New polyurethane chemically crosslinked networks containing silica were synthesized by both Diels–Alder polymerization and Michael addition reaction. Structural characterization of the products was evidenced by proton nuclear magnetic resonance and attenuated total reflectance in conjunction with Fourier transform infrared spectroscopy techniques. Differential scanning calorimetry was used to demonstrate the thermally remendable character of the materials obtained through Diels–Alder polymerization. The influence of increasing silica content on the glass transition temperatures was studied. It was observed that the glass transition temperatures increased with increasing silica content. Absolute heat capacities and crosslinking densities were determined for the thermoreversible materials. A comparison between materials obtained through Diels–Alder process and Michael addition method was studied. A kinetic study was conducted via an isoconversional method. Morphological studies were conducted by atomic force microscopy technique.     

Synthesis,characterization of SiO2 supported-industrial phosphoric acid catalyst for hydrolysis of NaBH4 solution

Abstract

Tunisian industrial phosphoric acid H₃PO₄ was supported on silica gel SiO₂ (SIPA) to catalyze the hydrolysis reaction of aqueous alkaline sodium borohydride (NaBH₄). The SiO₂ was produced from purified quartz sand using alkali fusion-acidification chemical process. The BET surface area results indicate that the prepared silica gel could reach a specific surface area up to 585 m²/g. The addition of PO₃H₂ functional groups resulted in an increase of surface acidity of SiO₂ catalyst as shown by FT-IR and DTA-DTG spectra. The total acidity of SIPA catalyst was determined by titration to be 2.8?mmol H⁺/g. SEM/EDS maps reveal the distribution of heavy metals on the silica surface. The effect of supported PO₃H₂ functional groups and heavy metals on the NaBH₄ hydrolysis reaction was studied for different ratios of SIPA catalyst to NaBH₄. The sample 12SIPA/NaBH₄ leads to a very high hydrogen generation rate (up to 90%). The activation energy of hydrogen generation by NaBH₄ hydrolysis was 25.7?kJ mol^?1.