Computation of non-smooth local centre manifolds

^** Email: msjolly{at}indiana.edu^*** Email: rrosa{at}ufrj.br An iterative Lyapunov–Perron algorithm for the computationof inertial manifolds is adapted for centre manifolds and appliedto two test problems. The first application is to compute aknown non-smooth manifold (once, but not twice differentiable),where a Taylor expansion is not possible. The second is to asmooth manifold arising in a porous medium problem, where rigorouserror estimates are compared to both the correction at eachiteration and the addition of each coefficient in a Taylor expansion.While in each case the manifold is 1D, the algorithm is well-suitedfor higher dimensional manifolds. In fact, the computationalcomplexity of the algorithm is independent of the dimension,as it computes individual points on the manifold independentlyby discretising the solution through them. Summations in thealgorithm are reformulated to be recursive. This accelerationapplies to the special case of inertial manifolds as well.     

Valence electron binding energies of some silicon compounds from x-ray photoelectron spectroscopy

X-ray photoelectron spectra in the valence electron region were obtained for gaseous SiH₄, SiH₃CH₃, Si(CH₃)₄, SiH₃Cl, and SiF₄. The experimental ionization potentials and relative peak intensities are consistent with extended Hückel theory MO calculations. The data can be rationalized without assuming substantial participation of silicon d orbitals in the bonding of these compounds.     

The preparation and structure of (divinylcyclohexene)nickel—phosphine complexes

Butadiene reacts with (hexatriene)nickel—phosphine complexes to give (divinylcyclohexene)nickel derivatives; the structure of the product from the reaction involving octatriene has been determined crystallographically.     

Estimates on enstrophy, palinstrophy, and invariant measures for 2-D turbulence

We construct semi-integral curves which bound the projection of the global attractor of the 2-D Navier-Stokes equations in the plane spanned by enstrophy and palinstrophy. Of particular interest are certain regions of the plane where palinstrophy dominates enstrophy. Previous work shows that if solutions on the global attractor spend a significant amount of time in such a region, then there is a cascade of enstrophy to smaller length scales, one of the main features of 2-D turbulence theory. The semi-integral curves divide the plane into regions having limited ranges for the direction of the flow. This allows us to estimate the average time it would take for an intermittent solution to burst into a region of large palinstrophy. We also derive a sharp, universal upper bound on the average palinstrophy and show that it is achieved only for forces that admit statistical steady states where the nonlinear term is zero.     

The present state of modeling entrainment defects in the shape casting process

The entrainment of oxide films into the bulk material has been shown to have a detrimental effect on casting integrity. A number of mechanisms have been shown to initiate the entrainment of oxide films, including: returning waves, plunging jets, bubble trails and fountains. Therefore, the assessment of the casting system for these features by the foundry engineer is critical in improving casting quality.     

Measured integrated band intensities and simulated line-by-line spectra for 12C2HD between 25 and 2.5 μm,and new global vibration–rotation parameters for the bending vibrations

The global analysis of published high-resolution vibration–rotation spectra of ¹²C₂HD in the bending spectral range is presented, resulting in an extension of the known vibration–rotation assignments, including a new band 2v₄+v₅←2v₄ (^IΠ←Δ). Experimental integrated band intensities are reported in the range from 25 to 2.5 μm, and both v₄ and v₅ bending fundamentals are simulated line by line. An extensive line list is produced in the bending energy range, to supply previously missing information in databases.