SCI Publications

We present a semi-Lagrangian method for integrating the three-dimensional incompressible Navier–Stokes equations. We develop stable schemes of secondorder accuracy in time and spectral accuracy in space. Specifically, we employ a spectral element (Jacobi) expansion in one direction and Fourier collocation in the other two directions. We demonstrate exponential convergence for this method, and investigate the non-monotonic behavior of the temporal error for an exact three-dimensional solution. We also present direct numerical simulations of a turbulent channel-flow, and demonstrate the stability of this approach even for marginal resolution unlike its Eulerian counterpart.

The principal values of the ¹³C chemical-shift tensor (CST) for biphenyl have been determined with the FIREMAT experiment. The internal dihedral angle between the benzene rings in biphenyl is estimated to fall between 10 and 20° on the basis of quantum mechanical calculations of the CST principal values. A composite model of motion in the system, with contributions both from internal jumping between enantiomeric structures and from overall molecular librations, yields the smallest variance between predicted and measured values for an internal twist angle of 15° between the rings and a mean libration angle of ±12° from the most favored molecular orientation. The composite model is clearly preferred to a motionless model (with >98% probability) and is also preferred over either of the isolated contributing dynamics, i.e., only libration or only internal jumping.

Parallel tempering molecular dynamics simulations have been performed for 1,4-polybutadiene polymer melts in the 323 K–473 K temperature domain at atmospheric pressure. The parallel tempering approach provides a vast improvement in the equilibration and sampling of conformational phase space for the atomistic melt chains in comparison with conventional molecular dynamics simulations even for molecular weights and temperatures considered to be routinely accessible via the latter technique.

In a previous article, we described how the frequency-dependent complex shear modulus and the time-dependent shear stress relaxation modulus for a highly entangled polybutadiene (PBD) melt can be obtained from molecular dynamics (MD) simulations of an unentangled PBD melt.1 In that work, we obtained from simulations of an unentangled melt all properties required for the prediction of the dynamic shear modulus with three reptation theories for the dynamics of entangled melts of linear, monodisperse polymers.2–5 More recently, we showed how the high-frequency (glassy) behavior of PBD can be obtained directly from MD simulations.6 The calculated complex and stress relaxation shear moduli for a PBD melt with a molecular weight of 1.3 · 10⁵ Da at 298 K were found to be in excellent agreement with experimental data.1, 6 In this work, we investigate the ability of MD simulations of the unentangled melt, in conjunction with reptation theory, to reproduce the molecular weight and temperature dependence of the viscoelastic properties of PBD. Here we concentrate on the low-frequency/long-time dynamics that determine the zero shear-rate viscosity, a property that has been extensively studied for PBD as a function of molecular weight and temperature.

Aromatics growth beyond 2-, 3-ring PAH is analyzed through a radical-molecule reaction mechanism which, in combination with a previously developed PAH model, is able to predict the size distribution of aromatic structures formed in rich premixed flames of ethylene at atmospheric pressure with C/O ratios across the soot threshold limit. Modeling results are in good agreement with experimental data and are used to interpret the ultraviolet absorption and the light scattering measured in flames before soot inception. The model shows that the total number concentration of high molecular mass aromatics and the different moments of the size distribution are functions of both the PAH and H-atom concentrations, two quantities which have different trends as functions of the residence time and the C/O ratio. Regimes of nearly stoichiometric or slightly rich premixed combustion are dominated by reactions between aromatics which lead to the formation of particles with sizes of the order of 3 to 4 nm. At higher C/O ratios the formation of nanoparticles is less efficient. Particles with sizes of the order of 2 nm are predicted in flames at the threshold of soot formation, whereas particles with sizes around 1 to 1.5 nm are predicted in fully sooting conditions.