A crack-closure method was developed for use in material point method (MPM) calculations. The method can be used for calculation of the dynamic energy release rate in a variety of dynamic fracture mechanics problems. Most previous MPM analyses have used regular grids and a “lumped” mass matrix. For the most accurate energy release rate calculations, the regular grid had to be replaced by an adaptive grid that automatically refined the mesh around the crack tip and the lumped mass matrix had to be replaced by a full mass matrix. Using an adaptive mesh was more important to accuracy than was switching to a full mass matrix. Some sample calculations are given for energy release rate in a double cantilever beam specimen carried out by several different MPM methods.

In an earlier study of inexact Newton methods, we pointed out that certain counterintuitive behavior may occur when applying residual backtracking to the Navier-Stokes equations with heat and mass transport. Specifically, it was observed that a Newton-GMRES method globalized by backtracking (linesearch, damping) may be less robust when high accuracy is required of each linear solve in the Newton sequence than when less accuracy is required. In this brief discussion, we offer a possible explanation for this phenomenon, together with an illustrative numerical experiment involving the Navier-Stokes equations.

The emphasis in this paper is on presenting a new methodology, together with some illustrative applications, for the study of polycyclic aromatic hydrocarbon polymerization leading to soot, widely recognized as a very important and challenging combustion problem. The new code, named fully integrated Kinetic Monte Carlo/Molecular Dynamics (KMC/MD), places the two simulation procedures on an equal footing and involves alternating between KMC and MD steps during the simulation. The KMC/MD simulations are used in conjunction with high-level quantum chemical calculations. With traditional kinetic rates and dealing with the growth of particles, it is often necessary to perform a lurnping procedure in which much atomic-scale information is lost. Our KMC/MD approach is designed to preserve atomic-scale structure: a single particle evolves in time with real three-dimensional structure (bonds, bond angles, dihedralangles). In this paper, the methodology is illustrated by a sample simulation of high molecular mass compound growth in an environment (T, H, H₂, naphthalene, and acenaphthylene concentrations) of a low-pressure laminar premixed benzene/oxygen/argon flame with an equivalence ratio of 1.8. The use of this approach enables the investigation of the physical (e.g., porosity, density, sphericity) as well as chemical (e.g. H/C, aromatic moieties, number of cross-links) properties.

Pathways for the growth of high-molecular-mass compounds are presented, showing how reactions between aromatic moieties can explain recent experimental findings. A fundamental molecular analysis of polycyclic aromatic hydrocarbon growth processes in combustion systems involving five-membered ring compounds is presented using quantum mechanical density functional methods. Higher aromatics are produced through a two-step radical-molecule addition reaction and the iteration of this mechanism followed by rearrangement of the carbon framework ultimately leads to high-molecular-mass compounds. The distinguishing features of the proposed model lie in the chemical specificity of the routes considered. Naphthalene and acenaphthylene are used as examples of the aromatic and cyclopentafused aromatic classes of compounds postulated to be of importance in molecular weight growth. These reaction pathways are analyzed with a view toward explaining recent experimental findings on H/C ratio, NMR, and LMMS of soot precursors.

Jet A and JP-8 are kerosene fuels used in aviation and consist of complex mixtures of higher order hydrocarbons, including alkanes, cycloalkanes, and aromatic molecules. The objectives of the current work are to develop a surrogate mixture to represent JP-8 fuels and to discuss a general detailed chemical kinetic model for jet fuels, which is suitable for future reduction. Asurrogate blend of six pure hydrocarbons is found to adequately simulate the distillation and compositional characteristics of a practical JP-8. A hierarchically constructed kinetic model already available for the oxidation of alkanes and simple aromatic molecules (benzene, toluene, ethylbenzene, xylene, etc.) is extended to include methylcyclohexane and tetralin as new reference fuel components. The kinetic model is validated through comparisons with experimental data for the pure components and it is also used to verify and predict the structures of laminar premixed flames of different pure components as well as conventional kerosene fuels.

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.

This paper presents a hierarchical cluster analysis of the principal values of the 13C chemical shift tensors encountered in polycyclic aromatic hydrocarbons (PAHs). Because of the limited set of experimental data presently available, the analysis was performed using chemical shifts tensors calculated using the DFT (B3PW91) GIAO method with a D95 basis set on optimized molecular geometries obtained using the CVFF force field and the DISCOVER routine in MSI's InsightII package. The good correlation observed between the calculated and the available experimental values supports the use of calculated values in the analysis. The hierarchical cluster analysis was performed for two data sets of increasing size and the classification was found independent of the size of the sample, leading to the conclusion that the results presented here are valid for the types of PAHs reported. The classification of the tensors using hierarchical cluster analysis produces classes of chemical shift principal values that can be associated with intuitive chemical types of carbons present in PAHs.

Improvements to the Sankey-Niklewaki method [O. F. Sankey and D. J. Niklewski, Phys. Rev. B 40, 3979 (1989)] for computing total energies and forces, within an ab initio tight-binding formalism, are presented here. In particular, the improved method (called FIREBALL) uses the separable pseudopotential (Hamann or Troullier) and goes beyond the minimal sp² basis set of the Sankey-Niklewski method, allowing for double numerical basis sets with the addition of polarization orbitals and d orbitals to the basis set. A major improvement includes the use of more complex exchange-correlation functionals, such as Becke exchange with the Lee-Yang-Parr correlation. Results for Cu and GaN band structures using d orbitals within the improved method are reported; the results for GaN are greatly improved compared to the minimal basis results. Finally, to demonstrate the flexibility of the method, results for the H₂O dimer system and the energetics of a gas-phase octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine molecule are reported.

Self-consistent Polymer Reference Interaction Site Model (PRISM) calculations and molecular dynamics (MD) simulations were performed on athermal solutions of linear polymers. Unlike most previous treatments of polymer solutions, we explicitly included the solvent molecules. The polymers were modeled as tangent site chains and the solvent molecules were taken to be spherical sites having the same intermolecular potential as the polymer sites. The PRISM theory was solved self-consistently for both the single chain structure and intermolecular correlations as a function of chain length and concentration. The rms end-to-end distance from PRISM theory was found to be in agreement with corresponding MD simulations, and exhibited molecular weight dependence in accordance with scaling predictions in the dilute and concentrated solution limits. The presence of explicit solvent molecules had a significant effect on the packing of the polymer by inducing additional structure in the intermolecular radial distribution function between polymer sites. Using the direct correlation functions from the athermal solution and the random phase approximation, we were able to estimate the spinodal curves for solutions when polymer and solvent attractions were turned on. We found significant deviations from Flory-Huggins theory that are likely due to compressibility and nonrandom mixing effects.

Globalized inexact Newton methods are well suited for solving large-scale systems of nonlinear equations. When combined with a Krylov iterative method, an explicit Jacobian is never needed, and the resulting matrix-free Newton--Krylov method greatly simplifies application of the method to complex problems. Despite asymptotically superlinear rates of convergence, the overall efficiency of a Newton--Krylov solver is determined by the preconditioner. High-quality preconditioners can be constructed from methods that incorporate problem-specific information, and for the incompressible Navier--Stokes equations, classical pressure-correction methods such as SIMPLE and SIMPLER fulfill this requirement. A preconditioner is constructed by using these pressure-correction methods as smoothers in a linear multigrid procedure. The effectiveness of the resulting Newton--Krylov-multigrid method is demonstrated on benchmark incompressible flow problems.