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The transient behavior of confined HMX in response to an external heat flux has been simulated using a detailed kinetic model. The model is spatially one-dimensional, fully transient, and consists of equations for modeling the solid (condensed) phase HMX, the gas phase, and the surrounding container for fast cook-off conditions. The condensed-phase decomposition reactions are described by semi-global, distributed kinetics. The gas phase description includes a detailed chemistry model for the combustion of HMX. A nonlinear, numerical solution of the partial differential equations results in predictions of temperature, pressure, velocity, and species fractions as a function of position and time. Predicted time-to-ignition yields good agreement with experimentally measured fast cook-off times. Temperature at ignition is found to be a function of heating rate. The ignition process for fast cook-off is consistent with laser ignition of bare HMX samples. Simulation results depend on accurate boundary conditions applied to the steel container. Pressurization rates are calculated and insight is given into the fast cook-off behavior of HMX. The main decomposition pathway is the conversion of HMX into CH 2 O and N 2 O.

The laser-induced ignition response of HMX has been investigated using a detailed numerical model. The model is one-dimensional, fully transient, and solves the conservation equations for both the condensed and gas phases. The condensed phase representation includes radiation absorption, solid-phase transitions, melting, evaporation, and distributed semi-global decomposition kinetics. The gas phase utilizes a detailed kinetic mechanism to predict species formation and destruction. Ignition occurs in the gas phase and the flame propagates back toward the surface of the HMX in what is known as the ‘snap-back’ effect. The model then transitions to steady-state combustion. Calculations were performed in which the solid HMX is irradiated with heat fluxes ranging from 50 to 1600 W/cm2. Results are compared to empirical data for the laser-induced ignition of HMX. Good agreement with these data and other steady-state data (burning rate, surface temperature, melt thickness) provide the necessary validation of the developed model.

Combustion simulations at the micro and meso-scales are coupled to give a more theoretically based and accurate description of AP (ammonium perchlorate)/HTPB (hydroxyl-terminated polybutadiene) composite propellant combustion. One and two-dimensional micro-scale combustion models of AP and AP/HTPB, which include detailed kinetics and species transport, are utilized to define semi-global kinetics for a meso-scale propellant combustion model capable of representing the complex morphology of an actual propellant. The AP/HTPB flame structure predicted with the micro-scale models is separated into four flames. Each flame is represented with a single reaction, thus a new four-step kinetic mechanism is implemented into the meso-scale model. Physical and kinetic parameters are determined with the micro-scale models. The meso-scale model is calibrated and validated with the micro-scale models to ensure the correct flame structure, as a function of pressure and AP particle sizes, is recreated with the four-step mechanism. The primary focus of this work is to outline the methodology used to couple the two numerical scales. Results of the meso-scale model are compared with the previous empirically-parameterized meso-scale model results and experimental data. Predictions are within 10% of experimental values for a range of AP/HTPB propellants.

We propose a method for optimal portfolio selection using a Bayesian decision theoretic framework that addresses two major shortcomings of the traditional Markowitz approach: the ability to handle higher moments and parameter uncertainty. We employ the skew normal distribution which has many attractive features for modeling multivariate returns. Our results suggest that it is important to incorporate higher order moments in portfolio selection. Further, our comparison to other methods where parameter uncertainty is either ignored or accommodated in an ad hoc way, shows that our approach leads to higher expected utility than competing methods, such as the resampling methods that are common in the practice of finance.

The complexities of the flame structure above a composite propellant containing 86% ammonium perchlorate (AP) and 14% hydroxy-terminated-polybutadiene (HTPB) have been elucidated using a two-dimensional, detailed gas-phase kinetic mechanism diffusion flame model. The model utilizes a vorticity formulation of the transport equations, which essentially eliminates the pressure field calculation and speeds convergence. Mass and energy coupling between the condensed and gas phases are achieved through iteration with one-dimensional, premixed combustion models to dynamically update the inlet boundary conditions. The model uses a detailed gas-phase kinetic mechanism consisting of 37 species and 127 reactions. Numerical studies have been performed to examine the influence of particle size on the flame structure above the AP/HTPB propellant. Three different combustion zones, based on AP particle size, were predicted: the AP monopropellant limit, the diffusion flame region, and the premixed limit. The modeled flame structure changed dramatically with particle size and was found to be qualitatively similar to the Beckstead–Derr–Price Model. Mechanistic insights are presented to explain AP’s unique ability to modify a propellant burning rate based on particle size alone. The premixed limit at which decreasing the size of the AP particles no longer influences the burning rate was also predicted. Results show promise in predicting formulistic effects using fundamental calculations.

The Liang/Beckstead aluminum-particle combustion model has been successfully joined with a detailed chemical-kinetic mechanism. The model has been used to investigate the effect of oxidizer concentration, pressure, and particle diameter on the combustion of CO2/Ar and O2/Ar with micrometer-sized aluminum particles. The simulation results when varying the oxidizer compare well with experimental data. With CO2 as the oxidizer, the trend of each simulated diameter follows that of the experimental data, especially the simulated 7 μm particles compared to experimental data for a mass average diameter of 11 μm. For oxygen, the simulated burn times with a particle size of 11 μm has excellent agreement compared to experimental data with a mass average diameter of 11 μm. The simulation results for both CO2/Ar and O2/Ar show a transition from kinetically-controlled combustion to diffusion-controlled combustion as the pressure increases. The burn time of the particles decreases as the pressure increases, until the diffusion-controlled combustion regime is reached and then the pressure has no effect on burn time. The opposite is true for the CO2 experimental data, in that the observed burn time increases with increasing pressure. The simulations indicate that the observed experimental trend could be the result of using a distribution of particle diameters. As the pressure decreases, larger particles may not ignite and the apparent burn time does not increase. The effect of particle diameter was also investigated. The effects of particle size, oxidizer, and oxidizer concentration on the calculated surface temperatures are also shown. This is the first model to show the beginning of the transition from diffusion-limited to kinetic-limited combustion control for aluminum particles.

By introducing auxiliary variables, the traditional Markov chain Monte Carlo method can be improved in certain cases by implementing a “slice sampler.” In the current literature, this sampling technique is used to sample from multivariate distributions with both single and multiple auxiliary variables. When the latter is employed, it generally updates one component at a time. In this article, we propose two variations of a new multivariate normal slice sampling method that uses multiple auxiliary variables to perform multivariate updating. These methods are flexible enough to allow for truncation to a rectangular region and/or exclusion of any n-dimensional hyper-quadrant. We present results of our methods and existing state-of-the-art slice samplers by comparing efficiency and accuracy. We find that we can generate approximately iid samples at a rate that is more efficient than other methods that update all dimensions at once. Supplemental materials are available online.

In this article we consider posterior simulation in models with constrained parameter or sampling spaces. Constraints on the support of sampling and prior distributions give rise to a normalization constant in the complete conditional posterior distribution for the (hyper-) parameters of the respective distribution, complicating posterior simulation. To mitigate the problem of evaluating normalization constants, we propose a computational approach based on model augmentation. We include an additional level in the probability model to separate the (hyper-) parameter from the constrained probability model, and we refer to this additional level in the probability model as a shadow prior. This approach can significantly reduce the overall computational burden if the original (hyper-) prior includes a complicated structure, but a simple form is chosen for the shadow prior, for example, if the original prior includes a mixture model or multivariate distribution, and the shadow prior defines a set of shadow para...

We propose prior probability models for variance-covariance matrices in order to address two important issues. First, the models allow a researcher to represent substantive prior information about the strength of correlations among a set of variables. Secondly, even in the absence of such information, the increased flexibility of the models mitigates dependence on strict parametric assumptions in standard prior models. For example, the model allows a posteriori different levels of uncertainty about correlations among different subsets of variables. We achieve this by including a clustering mechanism in the prior probability model. Clustering is with respect to variables and pairs of variables. Our approach leads to shrinkage towards a mixture structure implied by the clustering. We discuss appropriate posterior simulation schemes to implement posterior inference in the proposed models, including the evaluation of normalising constants that are functions of parameters of interest. The normalising constants result from the restriction that the correlation matrix be positive definite. We discuss examples based on simulated data, a stock return dataset and a population genetics dataset.

Equations that describe acoustic oscillations in a Rijke burner have been developed. Eigenvalues giving frequencies and growth rates of acoustic modes can be calculated from these equations. In their most general form, these acoustic equations include the effects of nonuniform gas temperature and entrained, burning particles. In general, analytical solution of the equations is not possible. A computer program has been developed that uses numerical methods to calculate eigenvalues from the general equations. For some limiting cases, analytical solution of the equations is possible. Analytical solutions are presented for three such cases. Eigenvalues predicted by the numerical model compare well to the analytical solutions. The Bailey and McIntosh flame-acoustic interaction models were tested with the computer program. Predicted frequencies and growth rates agreed well with experimental data when heat loss was taken into account. The program matched one experimental frequency and growth rate exactly when a time lag was added to the Bailey model. The McIntosh model did nearly as well without any adjustments. A particle combustion-acoustic interaction model for burning aluminum particles has been developed. This model was also tested in the Rijke burner model. The predictions show qualitative but not quantitative agreement with experimental measurements of particle combustion effects. A mechanism is suggested that may explain the discrepancy.

This paper reports the effect of ZrO{sub 2} addition on the phase transformation of Bi{sub 2}O{sub 3} studied with powder x-ray diffraction and differential thermal analysis. Samples containing higher than a few mole percent ZrO{sub 2} were obtained as the metastable {beta} phase (tetragonal) at room temperature when they were cooled at 20{degrees}C/min from 800{degrees}C where the {delta} phase (fcc) is stable. When the same samples were cooled at the same rate from 1000{degrees}C, which is above the solidus, they formed the stable {alpha} phase (monoclinic) at room temperature. Evidence for the relatively higher solubility of ZrO{sub 2} in the {delta} phase is discussed to explain this observation.

The paper presents the development of a fault detection and diagnosis (FDD) system with applications to the Space Shuttle main engine. The FDD utilizes a model-based method with real-time identification and hypothesis testing for actuation, sensor, and performance degradation faults.