Inaccuracies

The maximum temperature cross which can be tolerated is normally set by rules of thumb, e.g., FrSQ,75 °. It is important to ensure that Ft > 0.75, since any violation of the simplifying assumptions used in the approach tends to have a particularly significant effect in areas of the Ft chart where slopes are particularly steep. Any uncertainties or inaccuracies in design data also have a more significant effect when slopes are steep. Consequently, to be confident in a design, those parts of the Ft chart where slopes are steep should be avoided, irrespective of Ft 0.75. 

Each of the input parameters has an uncertainty associated with it. This uncertainty arises from the inaccuracy in the measured data, plus the uncertainty as to what the values are for the parts of the field for which there are no measurements. Take for example a field with five appraisal wells, with the following values of average porosity for a particular sand ... 

Elimination of the inaccuracy due to misalignment of cross sectional images ... 

For this reason, there has been much work on empirical potentials suitable for use on a wide range of systems. These take a sensible functional form with parameters fitted to reproduce available data. Many different potentials, known as molecular mechanics (MM) potentials, have been developed for ground-state organic and biochemical systems [58-60], They have the advantages of simplicity, and are transferable between systems, but do suffer firom inaccuracies and rigidity—no reactions are possible. Schemes have been developed to correct for these deficiencies. The empirical valence bond (EVB) method of Warshel [61,62], and the molecular mechanics-valence bond (MMVB) of Bemardi et al. [63,64] try to extend MM to include excited-state effects and reactions. The MMVB Hamiltonian is parameterized against CASSCF calculations, and is thus particularly suited to photochemistry. 

While simulations reach into larger time spans, the inaccuracies of force fields become more apparent on the one hand properties based on free energies, which were never used for parametrization, are computed more accurately and discrepancies show up on the other hand longer simulations, particularly of proteins, show more subtle discrepancies that only appear after nanoseconds. Thus force fields are under constant revision as far as their parameters are concerned, and this process will continue. Unfortunately the form of the potentials is hardly considered and the refinement leads to an increasing number of distinct atom types with a proliferating number of parameters and a severe detoriation of transferability. The increased use of quantum mechanics to derive potentials will not really improve this situation ab initio quantum mechanics is not reliable enough on the level of kT, and on-the-fly use of quantum methods to derive forces, as in the Car-Parrinello method, is not likely to be applicable to very large systems in the foreseeable future. 

The original motivation [7] for using was to compensate for the inaccuracies arising from evaluating at point values of... 

Tlierc are two major sources of error associated with the calculation of free energies fi computer simulations. Errors may arise from inaccuracies in the Hamiltonian, be it potential model chosen or its implementation (the treatment of long-range forces, e j lie second source of error arises from an insufficient sampling of phase space. 

The well-known inaccuracy of numerical differentiation precludes the direct calculation of pressure by the insertion of the computed velocity field into Equation (3.6). This problem is, however, very effectively resolved using the following variational recovery method Consider the discretized form of Equation (3.6) given as... 

In general, we know bond lengths to within an uncertainty of 0.00.5 A — 0.5 pm. Bond angles are reliably known only to one or twx) degrees, and there arc many instances of more serious angle enxirs. Tn addition to experimental uncertainties and inaccuracies due to the model (lack of coincidence between model and molecule), some models present special problems unique to their geometry. For example, some force fields calculate the ammonia molecule. Nlln to be planar when there is abundant ex p er i m en ta I evidence th at N H is a 11 i g o n a I pyramid. 

Even within a particular approximation, total energy values relative to the method s zero of energy are often very inaccurate. It is quite common to find that this inaccuracy is almost always the result of systematic error. As such, the most accurate values are often relative energies obtained by subtracting total energies from separate calculations. This is why the difference in energy between conformers and bond dissociation energies can be computed extremely accurately. 

Further problems arise if measurements of the rate of nitration have been made at temperatures other than 25 °C under these circumstances two procedures are feasible. The first is discussed in 8.2.2 below. In the second the rate profile for the compound imder investigation is corrected to 25 °C by use of the Arrhenius parameters, and then further corrected for protonation to give the calculated value of logio/i fb. at 25 °C, and thus the calculated rate profile for the free base at 25 °C. The obvious disadvantage is the inaccuracy which arises from the Arrhenius extrapolation, and the fact that, as mentioned above, it is not always known which acidity functions are appropriate. 

For small molecules, the accuracy of solutions to the Schrodinger equation competes with the accuracy of experimental results. However, these accurate ab initio calculations require enormous computation and are only suitable for the molecular systems with small or medium size. Ab initio calculations for very large molecules are beyond the realm of current computers, so HyperChem also supports semi-empirical quantum mechanics methods. Semi-empirical approximate solutions are appropriate and allow extensive chemical exploration. The inaccuracy of the approximations made in semi-empirical methods is offset to a degree by recourse to experimental data in defining the parameters of the method. Indeed, semi-empirical methods can sometimes be more accurate than some poorer ab initio methods, which require much longer computation times. 

Each observation in any branch of scientific investigation is inaccurate to some degree. Often the accurate value for the concentration of some particular constituent in the analyte cannot be determined. However, it is reasonable to assume the accurate value exists, and it is important to estimate the limits between which this value lies. It must be understood that the statistical approach is concerned with the appraisal of experimental design and data. Statistical techniques can neither detect nor evaluate constant errors (bias) the detection and elimination of inaccuracy are analytical problems. Nevertheless, statistical techniques can assist considerably in determining whether or not inaccuracies exist and in indicating when procedural modifications have reduced them. 

In using the table for pore size calculations, it is necessary to read off the values of the uptake from the experimental isotherm for the values of p/p° corresponding to the different r values given in the table. Unfortunately, these values of relative pressure do not correspond to division marks on the scale of abscissae, so that care is needed if inaccuracy is to be avoided. This difficulty can be circumvented by basing the standard table on even intervals of relative pressure rather than of r but this then leads to uneven spacings of r . Table 3.6 illustrates the application of the standard table to a specific example—the desorption branch of the silica isotherm already referred to. The resultant distribution curve appears as Curve C in Fig. 3.18. 

Section 6.13.2 and illustrated in Figure 6.5. The possible inaccuracies of the method were made clear and it was stressed that these are reduced by obtaining term values near to the dissociation limit. Whether this can be done depends very much on the relative dispositions of the various potential curves in a particular molecule and whether electronic transitions between them are allowed. How many ground state vibrational term values can be obtained from an emission spectrum is determined by the Franck-Condon principle. If r c r" then progressions in emission are very short and few term values result but if r is very different from r", as in the A U — system of carbon monoxide discussed in Section 7.2.5.4, long progressions are observed in emission and a more accurate value of Dq can be obtained. 

It is likely that volumetric measures were used for quantity deterrnination when commodities were first bartered however, it has been established with certainty that weighing scales or balances have been in use for at least 7,000 years (1). Measuring by weight instead of by volume eliminates some very considerable inaccuracies from, for example, changes in specific gravity of liquids with temperature, or changes in density of solids owing to voids. 

Accuracies of the flow meters discussed herein are specified as either a percentage of the full-scale flow or as a percentage of the actual flow rate. It may be convenient in some appHcations to compare the potential inaccuracies in actual volumetric flow rates. For example, in reading two Hters per minute (LPM) on a flow meter rated for five LPM, the maximum error for a 1% of full-scale accuracy specification would be 0.01 x 5 = 0.05 LPM. If another flow meter of similar range, but having 1% of actual flow rate specification, were used, the maximum error would be 0.01 x 2 = 0.02 LPM. To minimize errors, meters having full-scale accuracy specifications are normally not used at the lower end of their range. Whenever possible, performance parameters should be assessed for the expected installation conditions, not the reference conditions that are the basis of nominal product performance specifications. 

The SSG procedure assumes absence of voids (or constant void content). Voids depress the values of the measured specific gravity. The inaccuracies that result from voids can be corrected by applying ir techniques (63). 

In most process plant situations where feedforward control is appropriate, a combination of the feedforward and feedback control is usually used. The feedforward portion reduces the impact of measured disturbances on the controlled variable while the feedback portion compensates for model inaccuracies and unmeasured disturbances. This control strategy is referred to as feedforward control with feedback trim. 

Mathematical Models for Distribution Curves Mathematical models have been developed to fit the various distribution cur ves. It is most unlikely that any frequency distribution cur ve obtained in practice will exactly fit a cur ve plotted from any of these mathematical models. Nevertheless, the approximations are extremely useful, particularly in view of the inherent inaccuracies of practical data. The most common are the binomial, Poisson, and normal, or gaussian, distributions. 

In addition to understanding the principles of accountancy and obtaining a working knowledge of its practical techniques, engineers should be aware of possible inaccuracies of accounting information in the same way that they allow for errors in any technic data. 

In the Verband Deutscher Elektrotechniker (VDE) regulations [1,4], no demands are made on the accuracy of the measured or calculated voltage drops in a rail network. An inaccuracy of 10% and, in difficult cases, up to 20%, should be permitted. A calculation of the annual mean values is required. If the necessary equipment is not available, a calculation is permitted over a shorter period (e.g., an average day). Voltage drops in the rail network only indicate the trend of the interference of buried installations. Assessment of the risk of corrosion of an installation can only be made by measuring the object/soil potential. A change in potential of 0.1 V can be taken as an indication of an inadmissible corrosion risk [5]. 

Loose casing and support Pressure pulsations Vibration transmission Gear inaccuracy Valve vibration Dry whirl Blade passage... 

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