An improved finite element space for discontinuous pressures

We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L(2)(Omega)-norm is of order h(1/2)). We propose a modification of the P(1)-conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system. The unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element, so that the implementation of the proposed space into existing codes is straightforward. With this modification, numerical tests show that the interpolation order improves to O(h(3/2)). The new pressure space is implemented for the stable P(1)(+)/P(1) mini-element discretization, and for the stabilized equal-order P(1)/P(1) discretization. Assessment is carried out for Poiseuille flow with a forcing surface and for a static bubble. In all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard P(1) space. In addition, two Navier-Stokes simulations with moving interfaces (Rayleigh-Taylor instability and merging bubbles) are reported to show that the proposed space is robust enough to carry out realistic simulations. (c) 2009 Elsevier B.V. All rights reserved.

A note on finite determinacy for corank 2 map germs from surfaces to 3-space

We study properties of finitely determined corank 2 quasihomogeneous map germs f: (C(2), 0) -> (C(3), 0). Examples and counter examples of such map germs are presented.

Periodic window arising in the parameter space of an impact oscillator

In the bi-dimensional parameter space of an impact-pair system, shrimp-shaped periodic windows are embedded in chaotic regions. We show that a weak periodic forcing generates new periodic windows near the unperturbed one with its shape and periodicity. Thus, the new periodic windows are parameter range extensions for which the controlled periodic oscillations substitute the chaotic oscillations. We identify periodic and chaotic attractors by their largest Lyapunov exponents. (C) 2010 Elsevier B.V. All rights reserved.

A simplified description of the evolution of organic aerosol composition in the atmosphere

Organic aerosol (OA) in the atmosphere consists of a multitude of organic species which are either directly emitted or the products of a variety of chemical reactions. This complexity challenges our ability to explicitly characterize the chemical composition of these particles. We find that the bulk composition of OA from a variety of environments (laboratory and field) occupies a narrow range in the space of a Van Krevelen diagram (H: C versus O:C), characterized by a slope of similar to-1. The data show that atmospheric aging, involving processes such as volatilization, oxidation, mixing of air masses or condensation of further products, is consistent with movement along this line, producing a more oxidized aerosol. This finding has implications for our understanding of the evolution of atmospheric OA and representation of these processes in models. Citation: Heald, C. L., J. H. Kroll, J. L. Jimenez, K. S. Docherty, P. F. DeCarlo, A. C. Aiken, Q. Chen, S. T. Martin, D. K. Farmer, and P. Artaxo (2010), A simplified description of the evolution of organic aerosol composition in the atmosphere, Geophys. Res. Lett., 37, L08803, doi: 10.1029/2010GL042737.

Crystal engineering using functionalized adamantane

We performed a first-principles investigation on the structural, electronic and optical properties of crystals made of chemically functionalized adamantane molecules. Several molecular building blocks, formed by boron and nitrogen substitutional functionalizations, were considered to build zinc blende and wurtzite crystals, and the resulting structures presented large bulk moduli and cohesive energies, wide and direct bandgaps, and low dielectric constants (low-kappa materials). Those properties provide stability for such structures up to room temperature, superior to those of typical molecular crystals. This indicates a possible road map for crystal engineering using functionalized diamondoids, with potential applications ranging from space filling between conducting wires in nanodevices to nano-electromechanical systems.