Generalized sensitivity criterion

The sensitivity analysis of chemical reactors can be completed by applying the generalized sensitivity criterion to the case of a single n-th order irreversible exothermic reaction, occurring in a nonadiabatic CSTR, whose steady-state behavior can be represented in the following compact dimensionless form [cf. Kaushus et al. (1978)] ... 

According to the analysis reported above in the context of thermal explosion theory, we can use the generalized sensitivity criterion to identify the explosion limits of the hydrogen - oxygen mixture. By this we imply that the runaway of such a system actually coincides with its explosion (i.e. a very rapid reaction). 

We have shown that the generalized sensitivity criterion illustrated above can be used to identify the location of the critical transition between sensitive and nonsensitive behavior in the parameter space for a variety of chemical reacting systems. In particular, when dealing with explosive... 

Sensitivity by itself is not sufficient to completely evaluate an LCEC system for analytical purposes. The minimum detectable quantity (detection limit) is of more practical importance. The detection limit takes into consideration the amount of baseline noise as well as the response to the analyte. The detection limit is then defined as the quantity of analyte which gives a signal-to-noise ratio of three (a S/N of 3 is the generally accepted criterion although other values have been used). For a complete description of an LCEC application, both the sensitivity and detection limit, along with the S/N criteria used, should be provided. 

If the complex is paramagnetic, then the chemical shift can occur over a much wider range (see Table XVIII). These large chemical shifts arise from either contact shifts due to delocalization of unpaired electron density from the metal to the ligand or from pseudo contact shifts due to the magnetic field produced by the unpaired electron density. The interpretation of such shifts is generally difficult, but a sensitive criterion for TT-delocalization using methyl substituents has been proposed on the basis of theoretical considerations (66), namely Eq. (5)... 

Triphenylborane is a colorless, vacuum-sublimable, crystalline compound, which is very air- and moisture-sensitive but is thermally stable to ca. 380°. Because of a large molar melting-point depression, the melting point is a sensitive criterion of purity. In general crystals with a m.p. of 147-148° are obtained, but pure products melt at 151°.5... 

A second general criterion for pressure sensitivity is that the glass transition temperature of the adhesive be below the use temperature, which is usually room temperature. Broadly speaking, the To will be about 30-70°C below room temperature, depending on the base polymer and any added modifiers. 

The simplest definition of sensitivity is the signal-to-noise ratio. One criterion for judging the sensitivity of an NMR spectrometer or an NMR experiment is to measure the height of a peak under standard conditions and to compare it with the noise level in the same spectrum. Resolution is the extent to which the line shape deviates from an ideal Lorentzian line. Resolution is generally determined by measuring the width of a signal at half-height, in hertz. 

A more recent class of criteria to identify runaway conditions is based on the evidence that, close to runaway boundaries, the system behavior becomes highly sensitive to even small changes of the model parameters. Within this class, the generalized criterion of Morbidelli and Varma [14] makes use of the absolute value of the normalized objective sensitivity s of the temperature maximum 7 max to the generic model parameter 0, defined as... 

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