Model results

The theoretical model and numerical method outlined in the above sections were implemented to study steady-state combustion of nitramine monopropellants [33.34], laser-induced ignition of RDX [39,40], and steady-state combustion of nitramine/GAP pseudo-propellants [37-39]. The analyses were carried out over a broad range of operating conditions. Various important burning and ignition characteristics were investigated systematically, with emphasis placed on the detailed flame structure and the effect of the subsurface two-phase layer on propellant deflagration. 

During the parameter estimation, it was noted that the model is relatively insensitive to changes in k, and therefore it should not be taken as a reliable prediction of the Diels-Alder reaction rate constant. Effectively, the rate R is very large compared with the rates of initiation and chain transfer, and therefore the DH ratio calculation could be simplified without significantly changing the model results  

There are two other implications (1) the relative magnitude of the rates validates Hui and Hameilec s simplifying assumption that lead to a third-order rate equation for thermal initiation (2) the uncertainty in the prediction of k precludes any argument for or against the possibility that acid catalyzes the Diels-Alder reaction as well as the aromatization of DH. 

Several possible explanations for the poor A/w predictions can be considered. Since Mw is the problem, a review of the moments equations contained in the base model is in order to see if they are compatible with the way in which f is implemented. All of the moment concentration rate equations are based on either the rate of propagation or ratios of termination and chain transfer to the propagation rate. These ratios are very straightforward to correct using the Mayo dimer factor, / . The zeroth- and first-order moment rates appear correct, as they are the concentration of terminated chains and the concentration of monomer that has been polymerized, respectively. Mn data are not available to validate the ratio of first to zeroth moment. Calculation of Mw requires the second-order moment, but re-deriving it as a check is beyond the scope of this work. 

Another source of model error could be the Cm equation shown earlier. A linear correction factor is applied to compensate for the gel effect on propagation rate. Since the datapoints available are at relatively low conversion where the 

Assuming that the equations are reasonably accurate, the chain transfer mechanism could be called into question next. The model as written requires chain transfer to monomer or dimer, but not both. Since the two cases fall on either side of the experimental results, a modification to allow both to occur simultaneously might lead to a better fit. 

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In order to describe inherited stress state of weldment the finite element modelling results are used. A series of finite element calculations were conducted to model step-by-step residual stresses as well as its redistribution due to heat treatment and operation [3]. The solutions for the reference weldment geometries are collected in the data base. If necessary (some variants of repair) the modelling is executed for this specific case. 

If the scalar order parameter of the Ising model is replaced by a two-component vector n = 2), the XY model results. All important example that satisfies this model is the 3-transition in helium, from superfiuid helium-II... 

Mixing the 2J + 1 Ai levels, for the K active model, results in the following sums and densities of states ... 

I liis simulation provides the quantitative measures required for evaluation of the extent of deviation from a perfect viscometric flow. Specifically, the finite element model results can be used to calculate the torque corresponding to a given set of experimentally determined material parameters as... 

To ensure that computational chemistry develops in an orderly way, researchers must provide certain information so that others can reproduce and analyze their results. Gund et al. proposed guidelines for reporting molecular modeling results. You should consider these guidelines for your publications. 

Detailed Modeling Results. The results of a series of detailed calculations for an ideal isothermal plug-flow Langmuir system are summarized in Figure 15. The soHd lines show the form of the theoretical breakthrough curves for adsorption and desorption, calculated from the following set of model equations and expressed in terms of the dimensionless variables T, and P ... 

Models can be used to study human exposure to air pollutants and to identify cost-effective control strategies. In many instances, the primary limitation on the accuracy of model results is not the model formulation, but the accuracy of the available input data (93). Another limitation is the inabiUty of models to account for the alterations in the spatial distribution of emissions that occurs when controls are appHed. The more detailed models are currendy able to describe the dynamics of unreactive pollutants in urban areas. 

Mathematically speaking, a process simulation model consists of a set of variables (stream flows, stream conditions and compositions, conditions of process equipment, etc) that can be equalities and inequalities. Simulation of steady-state processes assume that the values of all the variables are independent of time a mathematical model results in a set of algebraic equations. If, on the other hand, many of the variables were to be time dependent (m the case of simulation of batch processes, shutdowns and startups of plants, dynamic response to disturbances in a plant, etc), then the mathematical model would consist of a set of differential equations or a mixed set of differential and algebraic equations. 

Applying this training model results in what can be seen as three levels of training topics. 

Similarly, contaminant concentrations in rivers or streams can be roughly assessed based on rate of contaminant introduction and dilution volumes. Estuary or impoundment concentration regimes are highly dependent on the transport mechanisms enumerated. Contaminants may be localized and remain concentrated or may disperse rapidly and become diluted to insignificant levels. The conservative approach is to conduct a more in-depth assessment and use model results or survey data as a basis for determining contaminant concentration levels. 

Abstract—Experimental and theoretical studies of the vibrational modes of carbon nanotubes are reviewed. The closing of a 2D graphene sheet into a tubule is found to lead to several new infrared (IR)- and Raman-active modes. The number of these modes is found to depend on the tubule symmetry and not on the diameter. Their diameter-dependent frequencies are calculated using a zone-folding model. Results of Raman scattering studies on arc-derived carbons containing nested or single-wall nanotubes are discussed. They are compared to theory and to that observed for other sp carbons also present in the sample. 

After intakes have been estimated, they arc organized by population, as appropriate. Then, tlie sources of uncertainty (e.g., variability in analytical data, modeling results, parameter assumptions) and their effect on tlie exposure estimates are evaluated and sunuiumzed. Tliis information on uncertainty is important to site decision-makers who must evaluate tlie results of the e.xposure... 

Figure 9-17. Photoinduced absorption in s-LPPP al 0.26 eV versus temperature (filled squares). Full lines represent the model results (lower curve for two activation energies, higher curve for one). The doited lines represent the decay rates for the 0.12eV (a) and 0.37 eV (b) activated processes the dash-dolled horizontal line represents the temperature-independent part E.

Table 11.1. Summary of modelling results. Dimensionless numbers dictating the magnitude of electrochemical promotion and metal support interactions23...

Consider the closely related ion [FeCHiO/e] ". The only difference is in the formal oxidation state of the metal ion. If an ionic model is assumed (9.6), the charge on the metal center is +2. A purely covalent model results in the placing of a formal quadruple negative charge upon the iron center (9.7). To satisfy the electroneutrality principle, and establish a near-zero charge on the metal, each oxygen atom is... 

Conclusions - Dissolved Oxygen. Continued attainment of DO standards in the Willamette Basin in the face of a current regional growth rate of 1% yr will require continued augmentation of flow as well as pollution control, particularly with respect to ammonia. Based on model results discussed, there appears to be little justification for the installation of advanced wastewater treatment systems in the basin for the purpose of maintaining acceptable DO levels. 

Location RK Model results Projection % sat. RK DEQ Results Verification Measured % sat... 

Table 15-6 Model results for metal speciation in natural waters ...

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