Induction parameter model

The general problem has been to extend the usefulness of the induction parameter model proposed by Oran et al. (1). This induction parameter model (IPM) is proposed as a means to enable one to estimate, relatively easily, the energy necessary to achieve ignition when using a thermal heating source Much of the calibration of this model, for example the effect of deposition volume (quench volume), can be done with one-dimensional models, and shock tube experiments. There are phenomena, however, which must be studied in two or three dimensions. Examples are turbulence and buoyancy. This paper discusses the effect of buoyancy and possible extensions to the IPM. 

E.S. Oran, J.P. Boris, T.R. Young, M. Flanigan, M. Picone and T. Burks, "Simulation of Gas Phase Detonation Introduction of an Induction Parameter Model," NRL Memorandum Report 4255 (1980). 

L.J. Clifford, A.M. Mime, T. Tur nyi and D. Boulton, An Induction Parameter Model for Shock-Induced Hydrogen Combustion Simulations, Comb, and Flame (1996) in press. 

Figure 11.1 Chemistry effects on the time histories of the impulse from simulations of a 60-centimeter-long PDE operating on a stoichiometric hydrogen-air mixture 1 — two-step induction parameter model and 2 — detailed chemistry.

Clifford, L.J., Milne, A.M., Turanyi, T., Boulton, D. An induction parameter model for shock-induced hydrogen combustion simulations. Combust. Flame 113, 106-118 (1998)... 

Marriott and Topsom have recently developed theoretical scales of substituent field and resonance parameters. The former correspond to the traditional inductive parameters but these authors are firm believers in the field model of the so-called inductive effect and use the symbol The theoretical substituent field effect scale is based on ab initio molecular orbital calculations of energies or electron populations of simple molecular systems. The results of the calculations are well correlated with Op values for a small number of substituents whose Op values on the various experimental scales (gas-phase, non-polar solvents, polar solvents) are concordant, and the regression equations are the basis for theoretical Op values of about 50 substituents. These include SOMe and S02Me at 0.37 and 0.60 respectively, which agree well with inherent best values in the literature of 0.36 and 0.58. However, it should be noted that a, for SOMe is given as 0.50 by Ehrenson and coworkers . 

Long, G., J. McKinney, and L. Pedersen. 1987. Polychlorinated Dibenzofuran (PCDF) Binding to the Ah Receptor(s) and Associated Enzyme Induction. Theoretical Model based on Molecular Parameters. Quant. Struct.-Act. Relat. 6, 1. 

The model requires one further definition in order to predict ignition. A curve of chemical induction time as a function of temperature must be included in order to define the induction parameter,... 

A crucial point of the four-parameter model is that T2 is assumed to be independent of cross-link density which is valid only in a first approximation [FU13]. Moreover, the experimental relaxation signal can be modelled at short and intermediate time scales with good agreement without the inclusion of dangling chains in the model the free induction decay of one such cross-link chain can be written as a product of an inhomogeneous and... 

There are five adjustable parameters per molecule X, the dispersion parameter q, the induction parameter x, the polarity parameter a, the hydrogen-bond acidity parameter and p, the hydrogen-bond basicity parameter. The induction parameter q often is set to a value of 1.0, yielding a four-parameter model. The terms fj and are asymmetry factors calculated from the other parameters. A database of parameter values for 150 compounds, determined by regression of phase equilibrium data, is given by Lazzaroni et al. [Ind. Eng. Chem. Res., 44(11), pp. 4075-4083 (2005)]. An application of MOSCED in the study of liquid-liquid extraction is described by Escudero, Cabezas, and Coca [Chem. Eng. Comm., 173, pp. 135—146 (1999)]. Also see Frank et al., Ind. Eng. Chem. Res., 46, pp. 4621-4625 (2007). 

Wheland and Pauling (1959) tried to explain the inductive effect in terms of ar-electron theory by varying the ax and ySxY parameters for nearest-neighbour atoms, then for next-nearest-neighbour atoms and so on. But, as many authors have also pointed out, it is always easy to introduce yet more parameters into a simple model, obtain agreement with an experimental finding and then claim that the model represents some kind of absolute truth. 

In order to use PBTK modeling in the assessment of mixtures, Cassee et al. (1998) suggest that one of the components is first modeled and regarded as the prime toxicant being modified by the other components. Based on in vitro data on the other components, effects of, e.g., inhibition or induction of specific biotransformation isoenzymes can be incorporated in the model. Effects of competition between chemicals in a mixture for the same biotransformation enzymes may also be incorporated by translating the effects into effects on the Michaelis-Menten parameters that are then incorporated into the model. 

Bayesian statistics are applicable to analyzing uncertainty in all phases of a risk assessment. Bayesian or probabilistic induction provides a quantitative way to estimate the plausibility of a proposed causality model (Howson and Urbach 1989), including the causal (conceptual) models central to chemical risk assessment (Newman and Evans 2002). Bayesian inductive methods quantify the plausibility of a conceptual model based on existing data and can accommodate a process of data augmentation (or pooling) until sufficient belief (or disbelief) has been accumulated about the proposed cause-effect model. Once a plausible conceptual model is defined, Bayesian methods can quantify uncertainties in parameter estimation or model predictions (predictive inferences). Relevant methods can be found in numerous textbooks, e.g., Carlin and Louis (2000) and Gelman et al. (1997). 

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