2003

S. Shellman, K. Sikorski.
**“A Recursive Algorithm for the Infinity-Norm Fixed Point Problem,”** In *Journal of Complexity*, Vol. 19, No. 6, pp. 799--834. 2003.

DOI: 10.1016/j.jco.2003.06.001

S.D. Shellman, K. Sikorski.
**“Algorithm 825: A deep-cut bisection envelope algorithm for fixed points,”** In *ACM Transactions on Mathematical Software (TOMS)*, Vol. 29, No. 3, pp. 309--325. September, 2003.

DOI: 10.1145/838250.838255

We present the BEDFix (Bisection Envelope Deep-cut Fixed point) algorithm for the problem of approximating a fixed point of a function of two variables. The function must be Lipschitz continuous with constant 1 with respect to the infinity norm; such functions are commonly found in economics and game theory. The computed approximation satisfies a residual criterion given a specified error tolerance. The BEDFix algorithm improves the BEFix algorithm presented in Shellman and Sikorski [2002] by utilizing "deep cuts," that is, eliminating additional segments of the feasible domain which cannot contain a fixed point. The upper bound on the number of required function evaluations is the same for BEDFix and BEFix, but our numerical tests indicate that BEDFix significantly improves the average-case performance. In addition, we show how BEDFix may be used to solve the absolute criterion fixed point problem with significantly better performance than the simple iteration method, when the Lipschitz constant is less than but close to 1. BEDFix is highly efficient when used to compute residual solutions for bivariate functions, having a bound on function evaluations that is twice the logarithm of the reciprocal of the tolerance. In the tests described in this article, the number of evaluations performed by the method averaged 31 percent of this worst-case bound. BEDFix works for nonsmooth continuous functions, unlike methods that require gradient information; also, it handles functions with minimum Lipschitz constants equal to 1, whereas the complexity of simple iteration approaches infinity as the minimum Lipschitz constant approaches 1. When BEDFix is used to compute absolute criterion solutions, the worst-case complexity depends on the logarithm of the reciprocal of 1-q, where q is the Lipschitz constant, as well as on the logarithm of the reciprocal of the tolerance.

G.D. Smith, D. Bedrov, O. Borodin.
**“Structural Relaxation and Dynamic Heterogeneity in a Polymer Melt at Attractive Surfaces,”** In *Physical Review Lett.*, Vol. 90, No. 22, pp. 226103.1--226103.4. 2003.

DOI: 10.1103/PhysRevLett.90.226103

Molecular dynamics simulations of polymer melts at flat and structured surfaces reveal that, for the former, slow dynamics and increased dynamic heterogeneity for an adsorbed polymer is due to densification of the polymer in a surface layer, while, for the latter, the energy topography of the surface plays the dominant role in determining dynamics of interfacial polymer. The dramatic increase in structural relaxation time for polymer melts at the attractive structured surface is largely the result of dynamic heterogeneity induced by the surface and does not resemble dynamics of a bulk melt approaching * T_{g}*.

G.D. Smith, D. Bedrov, O. Byutner, O. Borodin, C. Ayyagari, T.D. Sewell.
**“A Quantum-Chemistry-Based Potential for a Poly(ester urethane),”** In *Journal of Physical Chemistry, A*, Vol. 107, No. 38, pp. 7552--7560. August, 2003.

DOI: 10.1021/jp0225018

We have carried out extensive high-level quantum chemistry studies of the geometry, charge distribution, conformational energies, and hydrogen-bonding energies of model compounds for a family of Estane thermoplastic urethanes (TPUs). Upon the basis of these studies, we have parametrized a classical potential for use in atomistic simulations of Estane TPUs that can also be applied directly or with minor extensions to a wide variety of polyesters and polyurethanes.

J.S. Smith, D. Bedrov, G.D. Smith.
**“A molecular dynamics simulation study of nanoparticle interactions in a model polymer-nanoparticle composite,”** In *Composites Science and Technology*, Vol. 63, No. 11, pp. 1599--1605. August, 2003.

DOI: 10.1016/S0266-3538(03)00061-7

Molecular dynamics (MD) simulations were performed on a model polymer–nanoparticle composite (PNPC) consisting of spherical nanoparticles in a bead-spring polymer melt. The polymer-mediated effective interaction (potential of mean force) between nanoparticles was determined as a function of polymer molecular weight and strength of the polymer–nanoparticle interaction. For all polymer–nanoparticle interactions and polymer molecular weights investigated the range of the matrix-induced interaction was greater than the direct nanoparticle–nanoparticle interaction employed in the simulations. When the polymer–nanoparticle interactions were relatively weak the polymer matrix promoted nanoparticle aggregation, an effect that increased with polymer molecular weight. Increasingly attractive nanoparticle–polymer interactions led to strong adsorption of the polymer chains on the surface of the nanoparticles and promoted dispersion of the nanoparticles. For PNPCs with strongly adsorbed chains the matrix-induced interaction between nanoparticles reflected the structure (layering) imposed on the melt by the nanoparticle surface and was independent of polymer molecular weight. The nanoparticle second virial coefficient obtained from the potential of mean force was utilized as an indicator of dispersion or aggregation of the particles in the PNPC, and was found to be in qualitative agreement with the aggregation properties obtained from simulations of selected PNPCs with multiple nanoparticles.

J.P. Spinti, D.W. Pershing.
**“The Fate of Char-N at Pulverized Coal Conditions,”** In *Combustion and Flame*, Vol. 135, No. 3, pp. 299--313. November, 2003.

DOI: 10.1016/S0010-2180(03)00168-8

The fate of char-N (nitrogen removed from the coal matrix during char oxidation) has been widely studied at fluidized bed conditions. This work extends the study of char-N to pulverized coal conditions. Coal chars from five parent coals were prepared and burned in a laboratory-scale pulverized coal combustor in experiments designed to identify the parameters controlling the fate of char-N. The chars were burned with natural gas (to simulate volatiles combustion) in both air and in a nitrogen-free oxidant composed of Ar, CO_{2}, and O_{2}. In some experiments, the char flames were doped with various levels of NO or NH_{3} to simulate formation of NO_{x} from volatile-N (nitrogen removed during coal devolatilization). The conversion of char-N to NO_{x} in chars burned in the nitrogen-free oxidant was 50–60% for lignites and 40–50% for bituminous coals. In char flames doped with NO_{x}, the apparent conversion of char-N to NO_{x} (computed using the NO_{x} measurements made before and after the addition of char to the system) decreased significantly as the level of NO_{x} doping increased. With 900 ppm NO_{x} present before the addition of char, apparent conversion of char-N to NO_{x} was close to 0% for most chars. While there is no clear correlation between nitrogen content of the char and char-N to NO_{x} conversion at any level of NO_{x} in the flame, the degree of char burnout within a given family of chars does play a role. Increasing the concentration of O_{2} in the system in both air and nitrogen-free oxidant experiments increased the conversion of char-N to NO_{x}. The effects of temperature on NO_{x} emissions were different at low (0 ppm) and high (900 ppm) levels of NO_{x} present in the flame before char addition.

A. Violi, G.A. Voth, A.F. Sarofim.
**“A Time-scale Problem for the Formation of Soot Precursors in Premixed Flames,”** In *American Chemical Society, Division of Fuel Chemistry*, Vol. 48, No. 2, pp. 545--547. 2003.

2002

B. Banerjee, D.O. Adams.
**“Micromechanics-Based Prediction of Thermoelastic Properties of High Energy Materials,”** In *Constitutive Modeling of Geomaterials*, In *Constitutive Modeling of Geomaterials*, Edited by H.I. Ling et al., CRC Press, New York, pp. 158--164. 2002.

High energy materials such as polymer bonded explosives are commonly used as propellants. These particulate composites contain explosive crystals suspended in a rubbery binder. However, the explosive nature of these materials limits the determination of their mechanical properties by experimental means. Therefore micromechanics-based methods for the determination of the effective thermoelastic properties of polymer bonded explosives are investigated in this research. Polymer bonded explosives are twocomponent particulate composites with high volume fractions of particles (volume fraction > 90%) and high modulus contrast (ratio of Young’s modulus of particles to binder of 5,000-10,000). Experimentally determined elastic moduli of one such material, PBX 9501, are used to validate the micromechanics methods examined in this research. The literature on micromechanics is reviewed; rigorous bounds on effective elastic properties and analytical methods for determining effective properties are investigated in the context of PBX 9501. Since detailed numerical simulations of PBXs are computationally expensive, simple numerical homogenization techniques have been sought. Two such techniques explored in this research are the Generalized Method of Cells and the Recursive Cell Method. Effective properties calculated using these methods have been compared with finite element analyses and experimental data.

D. Bedrov, G.D. Smith, K.F. Freed, J. Dudowicz.
**“A Comparison of Self-Assembly in Lattice and Off-Lattice Model Amphiphile Solutions,”** In *Journal of Chemical Physics*, Vol. 116, No. 12, pp. 4765--4768. 2002.

DOI: 10.1063/1.1461355

Lattice Monte Carlo and off-lattice molecular dynamics simulations of * h_{1}t_{4}* and

D. Bedrov, G.D. Smith, T.D. Sewell.
**“Molecular Dynamics Simulations of HMX Crystal Polymorphs Using A Flexible Molecule Force Field,”** In *Journal of Computer-Aided Materials Design*, Vol. 8, No. 2-3, pp. 77--85. 2002.

DOI: 10.1023/A:1020046817543

Molecular dynamics simulations using a recently developed quantum chemistry-based atomistic force field [J. Phys. Chem. B, 103 (1999) 3570 ] were performed in order to obtain unit cell parameters, coefficients of thermal expansion, and heats of sublimation for the three pure crystal polymorphs of octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX). The predictions for β-, α-, and δ-HMX showed good agreement with the available experimental data. For the case of β-HMX, anisotropic sound speeds were calculated from the molecular dynamics simulation-predicted elastic coefficients and compared with recent Impulsive Stimulated Light Scattering (ISLS) sound speed measurements. The level of agreement is encouraging.

O. Byutner, G.D. Smith.
**“Viscoelastic Properties of Polybutadiene in the Glassy Regime from Molecular Dynamic Simulations,”** In *Macromolecules*, Vol. 35, No. 9, pp. 3769--3771. 2002.

DOI: 10.1021/ma0105690

J.D. de St. Germain, A. Morris, S.G. Parker, A.D. Malony, S. Shende.
**“Integrating Performance Analysis in the Uintah Software Development Cycle,”** In *Proceedings of The 4th International Symposium on High Performance Computing*, pp. 190--206. May 15-17, 2002.

C.R. Johnson, S.G. Parker, D. Weinstein, S. Heffernan.
**“Component-Based Problem Solving Environments for Large-Scale Scientific Computing,”** In *J. Conc. & Comp.: Prac. & Exper.*, Vol. 14, pp. 1337--1349. 2002.

G.T. Long, B.A. Brems, C.A. Wight.
**“Thermal Activation of the High Explosive NTO: Sublimation, Decomposition, and Autocatalysis,”** In *Journal of Physical Chemistry, B*, Vol. 106, No. 15, pp. 4022--4026. March, 2002.

DOI: 10.1021/jp012894v

Thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) show that the heating of 5-nitro-2,4-dihydro-3H-1,2,4-triazol-3-one (NTO) leads to competitive sublimation and condensed-phase exothermic decomposition. Model-free isoconversional analysis has determined activation energies (*E*_{α}) for these processes as a function of the extent of conversion, α. Sublimation occurs most readily in an open pan; although more than simple sublimation was observed, a global activation energy of *E _{α}* = 130−140 kJ mol

G.T. Long, C.A. Wight.
**“Thermal Decomposition of a Melt-Castable High Explosive: Isoconversional Analysis of TNAZ,”** In *Journal of Physical Chemistry, B*, Vol. 106, No. 10, pp. 2791--2795. February, 2002.

DOI: 10.1021/jp012859o

The thermal decomposition kinetics of the high explosive 1,3,3-trinitroazetidine (TNAZ) have been measured by nonisothermal differential scanning calorimetry (DSC). Samples of TNAZ in open pans and pierced pans undergo mainly melting (Δ*H*_{fus} = 27 ± 3 kJ mol^{-1}) and vaporization (Δ*H*_{vap} = 74 ± 10 kJ mol^{-1}) during heating. However, when confined in sealed high-pressure crucibles, exothermic thermal decomposition is observed. The activation energy for thermal decomposition has been determined as a function of the extent of reaction by isoconversional analysis. The initial value of 184 kJ mol^{-1} at the start of the reaction decreases to 38 kJ mol^{-1} near the end of the reaction. The rates clearly exhibit acceleratory behavior that is ascribed to autocatalysis. The measured heat release of thermal decomposition (*Q* = 640 ± 150 kJ mol^{-1}) is independent of the heating rate and the sample mass. These results are consistent with proposed mechanisms of TNAZ decomposition in which the initial step is preferential loss of the nitramine NO_{2} group over loss of a *gem*-dinitroalkyl NO_{2} group.

S. Shellman, K. Sikorski.
**“A Two Dimensional Bisection-Envelope Algorithm for Fixed Points,”** In *Journal of Complexity*, Vol. 18, No. 2, pp. 641--659. June, 2002.

DOI: 10.1006/jcom.2001.0625

In this paper we present a new algorithm for the two-dimensional fixed point problem *f*(*x*)=*x* on the domain [0, 1]×[0, 1], where *f* is a Lipschitz continuous function with respect to the infinity norm, with constant 1. The computed approximation *x* satisfies ‖*f*(*x*)−*x*‖_{∞}⩽*ε* for a specified tolerance *ε*0.5. The upper bound on the number of required function evaluations is given by 2⌈log_{2}(1/*ε*)⌉+1. Similar bounds were derived for the case of the 2-norm by Z. Huang *et al.* (1999, *J. Complexity***15**, 200–213), our bound is the first for the infinity norm case.

G.D. Smith, O. Borodin, W. Paul.
**“A Molecular Dynamics Simulation Study of Dielectric Relaxation in a 1,4-Polybutadiene Melt,”** In *Journal of Chemical Physics*, Vol. 117, No. 22, pp. 10350--10359. 2002.

DOI: 10.1063/1.1518684

We have carried out atomistic molecular dynamics simulations of a melt of 1,4-poly(butadiene) from temperatures well above the experimentally observed merging of the primary α process and secondary β process down to temperatures approaching the experimentally observed bifurcation temperature. The relaxation strength and maximum loss frequency and its temperature dependence for the combined α-β dielectric relaxation process from simulations were in good agreement with experiment. The maximum loss frequency, melt viscosity, chain normal-mode relaxation times and torsional autocorrelation times were found to exhibit nearly identical non-Arrhenius temperature dependencies well represented by a Vogel–Fulcher fit with parameters in good agreement with experimental values obtained from dielectric and viscosity measurements. The dielectric susceptibility showed increasing intensity at high frequency for the lower temperatures investigated, indicative of a breakdown in time-temperature superposition due to an emerging β process. Comparison of time scales for the chain normal-mode dynamics and dielectric relaxation revealed that the latter is associated with motions on the segmental length scale. The correspondence of time scales and temperature dependence for the dielectric relaxation and the torsional autocorrelation function further confirmed the localized nature of the dielectric relaxation and indicated that the combined α-β dielectric process is fundamentally tied to microscopic conformational dynamics of individual dihedrals. However, the mean conformational transition rates were found to exhibit Arrhenius temperature dependence, leading to a divergence of time scales between the torsional, dielectric, chain and mechanical relaxation processes and the rates of conformational transitions with decreasing temperature. This divergence was associated with the increasingly heterogeneous character of conformational dynamics in the melt with decreasing temperature. Hence, the time scale of the principal (α) relaxation in the melt is fundamentally correlated with the time scale for homogenization of conformational dynamics, and not to the time scale of the conformational transitions themselves.

H. Tan, J.A. Nairn.
**“Hierarchical, Adaptive, Material Point Method in Dynamic Energy Release Rate Calculations,”** In *Computer Methods in Applied Mechanics and Engineering*, Vol. 191, No. 19-20, pp. 2123--2137. March, 2002.

DOI: 10.1016/S0045-7825(01)00377-2

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.

R.S. Tuminaro, H.F. Walker, J.N. Shadid.
**“On Backtracking Failure in Newton-GMRES Methods,”** In *Journal of Computational Physics*, Vol. 180, No. 2, pp. 549--558. August, 2002.

DOI: 10.1006/jcph.2002.7102

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.

A. Violi, A. Kubota, W.J. Pitz, C.K. Westbrook, A.F. Sarofim.
**“Fully-integrated Molecular Dynamics - Kinetic Monte Carlo Code: a New Tool for the Study of Soot Precursor Growth in Combustion Conditions,”** In *American Chemical Society, Division of Fuel Chemistry*, Vol. 47, No. 2, pp. 771--772. 2002.