Accuracy high degree

The potential fiinctions for the mteractions between pairs of rare-gas atoms are known to a high degree of accuracy [125]. Flowever, many of them use ad hoc fiinctional fonns parametrized to give the best possible fit to a wide range of experimental data. They will not be considered because it is more instmctive to consider representations that are more finnly rooted in theory and could be used for a wide range of interactions with confidence. 

With the advent of quantum mechanics, quite early attempts were made to obtain methods to predict chemical reactivity quantitatively. This endeavor has now matured to a point where details of the geometric and energetic changes in the course of a reaction can be calculated to a high degree of accuracy, albeit still with quite some demand on computational resources. 

Part of the answer is that, unless we require a high degree of accuracy, it does not matter very much. This is illustrated by the values for Tq and for and N2, given in Table... 

The equations given predict vapor behavior to high degrees of accuracy but tend to give poor results near and within the Hquid region. The compressibihty factor can be used to accurately determine gas volumes when used in conjunction with a virial expansion or an equation such as equation 53 (77). However, the prediction of saturated Hquid volume and density requires another technique. A correlation was found in 1958 between the critical compressibihty factor and reduced density, based on inert gases. From this correlation an equation for normal and polar substances was developed (78) ... 

When a process is continuous, nucleation frequently occurs in the presence of a seeded solution by the combined effec ts of mechanical stimulus and nucleation caused by supersaturation (heterogeneous nucleation). If such a system is completely and uniformly mixed (i.e., the product stream represents the typical magma circulated within the system) and if the system is operating at steady state, the particle-size distribution has definite hmits which can be predic ted mathematically with a high degree of accuracy, as will be shown later in this section. 

Thus, to third order in strain, the entropy along the Hugoniot is constant, and weak shock waves are nearly isentropic. For small strains, the Hugoniot can be replaced with the isentrope to a high degree of accuracy. At the initial state, the Hugoniot and isentrope have the same slope and curvature in the P-V plane. 

Computational methods have played an exceedingly important role in understanding the fundamental aspects of shock compression and in solving complex shock-wave problems. Major advances in the numerical algorithms used for solving dynamic problems, coupled with the tremendous increase in computational capabilities, have made many problems tractable that only a few years ago could not have been solved. It is now possible to perform two-dimensional molecular dynamics simulations with a high degree of accuracy, and three-dimensional problems can also be solved with moderate accuracy. 

To determine the pipeline potentials, the resultant induced field strengths have to be included in the equations in Section 23.3.2. Such calculations can be carried out with computers that allow detailed subdivision of the sections subject to interference. A high degree of accuracy is thus achieved because in the calculation with complex numbers, the phase angle will be exactly allowed for. Such calculations usually lead to lower field strengths than simplified calculations. Computer programs for these calculations are to be found in Ref. 16. 

Computer simulation techniques offer the ability to study the potential energy surfaces of chemical reactions to a high degree of quantitative accuracy [4]. Theoretical studies of chemical reactions in the gas phase are a major field and can provide detailed insights into a variety of processes of fundamental interest in atmospheric and combustion chemistry. In the past decade theoretical methods were extended to the study of reaction processes in mesoscopic systems such as enzymatic reactions in solution, albeit to a more approximate level than the most accurate gas-phase studies. 

X-ray structures are determined at different levels of resolution. At low resolution only the shape of the molecule is obtained, whereas at high resolution most atomic positions can be determined to a high degree of accuracy. At medium resolution the fold of the polypeptide chain is usually correctly revealed as well as the approximate positions of the side chains, including those at the active site. The quality of the final three-dimensional model of the protein depends on the resolution of the x-ray data and on the degree of refinement. In a highly refined structure, with an R value less than 0.20 at a resolution around 2.0 A, the estimated errors in atomic positions are around 0.1 A to 0.2 A, provided the amino acid sequence is known. 

Every analytical result forms the basis for a subsequent decision process. So the result should be subject to a high degree of precision and accuracy. This is also true of chromatographic methods. The physical detection methods described until now are frequently not sufficient on their own. If this is the case they have to be complemented by specific chemical reactions (derivatization). 

Apart from the degree of novelty of a process event, its complexity (e.g., the range of operations to be carried out), the interrelationships of the process variables involved and the required accuracy, will affect performance. Startup and shutdown operations are examples of tasks which, although are not entirely unfamiliar, involve a high degree of complexity. 

Precision tools are used in the manufacture of roller chains, and a high degree of accuracy is maintained. The chain is made up of links, pins, and bushings, all fabricated from a high grade of steel, with the pins and the bushings ground to ensure accuracy of pitch. 

Several methods for the evaluation of the MDF have been put forward, notably that processed by Tchebycheff, which gives a high degree of accuracy in the case of large cooling ranges. In the form in which it is most commonly used, it reads ... 

The most usual forms of platinum or, more frequently, of the platinum alloys containing 5 or 10% of rhodium, are thin protective sheaths contoured to conform with the shape of the underlying refractory. Sheaths of this type, generally 0-25 mm to 0-65 mm thick, are widely employed to protect tank lips, skimmer blocks, stirrers, thermocouple pockets, etc. More substantial —thicknesses-up to 2-5 mm thick —are used to protect orifices whose dimensional accuracy must be maintained to a high degree. 

Precision may be defined as the concordance of a series of measurements of the same quantity. Accuracy expresses the correctness of a measurement, and precision the reproducibility of a measurement (the latter definition will be modified later). Precision always accompanies accuracy, but a high degree of precision does not imply accuracy. This may be illustrated by the following example. 

This method is particularly useful where a high degree of accuracy is not required. 

Since a small quantity of electricity can be readily measured with a high degree of accuracy, the method has high sensitivity. Coulometric titrimetry has several important advantages. 

De Tar and Day [498] considered problems which arise in applying the first-order expression [eqn. (15)] to kinetic data of limited accuracy. If a is known to a high degree of accuracy (e.g. 0.1%), then small components (5—10%) of higher or lower order behaviour are detectable. When the accuracy of a is reduced to 1%, a second-order component of 25% could escape detection, and perhaps an even larger contribution might be missed within a limited a interval. Using exact values of a from known kinetic behaviour, the apparent rate coefficient, ft, was found to depend on both the proportion of the non-first-order component and on the extent of reaction considered. 

The development of methods and instrumentation, especially in the high field range, will already open up quite new areas of uses already in the near future. These may at least partly replace and complete solid-state vibration spectroscopy in the polymer field in cases where the amount of material is not the limiting factor. As far as we are able to predict the future, the development of exact quantitative methods of analysis, in particular, will rapidly develop to a high degree of accuracy. 

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