Physical and numerical sources of computational inefficiency in integration of chemical kinetic rate equations: Etiology, treatment and prognosis

The design of a very fast, automatic black-box code for homogeneous, gas-phase chemical kinetics problems requires an understanding of the physical and numerical sources of computational inefficiency. Some major sources reviewed in this report are stiffness of the governing ordinary differential equations (ODE's) and its detection, choice of appropriate method (i.e., integration algorithm plus step-size control strategy), nonphysical initial conditions, and too frequent evaluation of thermochemical and kinetic properties. Specific techniques are recommended (and some advised against) for improving or overcoming the identified problem areas. It is argued that, because reactive species increase exponentially with time during induction, and all species exhibit asymptotic, exponential decay with time during equilibration, exponential-fitted integration algorithms are inherently more accurate for kinetics modeling than classical, polynomial-interpolant methods for the same computational work. But current codes using the exponential-fitted method lack the sophisticated stepsize-control logic of existing black-box ODE solver codes, such as EPISODE and LSODE. The ultimate chemical kinetics code does not exist yet, but the general characteristics of such a code are becoming apparent

CREKID: A computer code for transient, gas-phase combustion of kinetics

A new algorithm was developed for fast, automatic integration of chemical kinetic rate equations describing homogeneous, gas-phase combustion at constant pressure. Particular attention is paid to the distinguishing physical and computational characteristics of the induction, heat-release and equilibration regimes. The two-part predictor-corrector algorithm, based on an exponentially-fitted trapezoidal rule, includes filtering of ill-posed initial conditions, automatic selection of Newton-Jacobi or Newton iteration for convergence to achieve maximum computational efficiency while observing a prescribed error tolerance. The new algorithm was found to compare favorably with LSODE on two representative test problems drawn from combustion kinetics

Constructionism and the space of reasons

Constructionism, best known as the framework for action underpinning Seymour Papert’s work with Logo, has stressed the importance of engaging students in creating their own products. Noss and Hoyles have argued that such activity enables students to participate increasingly in a web of connections to further their activity. Ainley and Pratt have elaborated that learning is best facilitated when the student is engaged in a purposeful activity that leads to appreciation of the power of mathematical ideas. Constructionism gives prominence to how the learner’s logical reasoning and emotion-driven reasons for engagement are inseparable. We argue that the dependence of constructionism upon the orienting framework of constructivism fails to provide sufficient theoretical underpinning for these ideas. We therefore propose an alternative orienting framework, in which learning takes place through initiation into the space of reasons, such that a person’s thoughts, actions and feelings are increasingly open to critique and justification. We argue that knowing as responsiveness to reasons encompasses not only the powerful ideas of mathematics and disciplinary knowledge of modes of enquiry but also the extralogical, such as in feelings of the aesthetic, control, excitement, elegance and efficiency. We discuss the implication that mathematics educators deeply consider the learner’s reasons for purposeful activity and design settings in which these reasons can be made public and open to critique

Balancing Local Order and Long-Ranged Interactions in the Molecular Theory of Liquid Water

A molecular theory of liquid water is identified and studied on the basis of computer simulation of the TIP3P model of liquid water. This theory would be exact for models of liquid water in which the intermolecular interactions vanish outside a finite spatial range, and therefore provides a precise analysis tool for investigating the effects of longer-ranged intermolecular interactions. We show how local order can be introduced through quasi-chemical theory. Long-ranged interactions are characterized generally by a conditional distribution of binding energies, and this formulation is interpreted as a regularization of the primitive statistical thermodynamic problem. These binding-energy distributions for liquid water are observed to be unimodal. The gaussian approximation proposed is remarkably successful in predicting the Gibbs free energy and the molar entropy of liquid water, as judged by comparison with numerically exact results. The remaining discrepancies are subtle quantitative problems that do have significant consequences for the thermodynamic properties that distinguish water from many other liquids. The basic subtlety of liquid water is found then in the competition of several effects which must be quantitatively balanced for realistic results.Comment: 8 pages, 6 figure

A coalescence/dispersion model for turbulent flame stability

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77010/1/AIAA-1982-1158-855.pd

Pairing of 1-hexyl-3-methylimidazolium and tetrafluoroborate ions in n-pentanol

Molecular dynamics simulations are obtained and analyzed to study pairing of 1-hexyl-3-methylimidazolium and tetrafluoroborate ions in n-pentanol, in particular by evaluating the potential-of-mean-force between counter ions. The present molecular model and simulation accurately predicts the dissociation constant Kd in comparison to experiment, and thus the behavior and magnitudes for the ion-pair pmf at molecular distances, even though the dielectric constant of the simulated solvent differs from the experimental value by about 30%. A naive dielectric model does not capture molecule structural effects such as multiple conformations and binding geometries of the Hmim+ and BF4- ion-pairs. Mobilities identify multiple time-scale effects in the autocorrelation of the random forces on the ions, and specifically a slow, exponential time-decay of those long-ranged forces associated here with dielectric friction effects.Comment: 5 pages, 7 figures. V2: Figs. 4 & 7 redrawn for better visual clarity with log-scales. No change in results. In press J. Chem. Phys. 201

Tsunamis, Viscosity and the HBT Puzzle

The equation of state and bulk and shear viscosities are shown to be able to affect the transverse dynamics of a central heavy ion collision. The net entropy, along with the femtoscopic radii are shown to be affected at the 10-20% level by both shear and bulk viscosity. The degree to which these effects help build a tsunami-like pulse is also discussed.Comment: Contribution to SQM 2007 in Levoca, Slovaki

Advanced analog television study final report, 4 nov. - 19 dec. 1963

Information bandwidth reduction for analog television signals - Description of multiple interlace syste