Penetration error

Cubic form see Table 5.4 for penetration error. Extrapolated. 

The point multipoles can give the accurate description of the electrostatic interactions between Gay-Berne particles separated with a certain distance (independent of the particle sizes). As the two particles are getting too close to each other, the point multipoles are not able to accurately describe the overlap of their charge density, causing the so-called penetration error [59]. An effective solution to avoid the penetration error would be to seek a proper damping function [60]. In current GBEMP model, we employed the damping function defined as... 

Attention should be given in the fact, that penetration of eddy currents in residual austenite will be slightly deeper than in the martensite structure of steel, as austenite shows low electrical conductivity. The signal originatimg from the austenite structure will be amplified in effect of the influence of the structure found at greater depth. There will be no error as the method of measurement is compartable and the samples made for reference purposes will have the same structure as the studied part. 

Projections of market penetrations and contributions to primary consumption of energy from biomass are subject to much criticism and contain significant errors. However, even though these projections may be incorrect, they are necessary to assess the future role and impact of renewable energy resources, and to help in deciding whether a potential renewable energy resource should be developed. 

Precoat Procedure Precoat filtration tests are run in exactly the same manner as bottom-feed tests except that the leaf must first be precoated with a bed of diatomaceous earth, perhte, or other shave-able inert sohds. Some trial and error is involved in selecting a grade of precoat material which will retain the filtered solids to be removed on the surface of the bed without any significant penetration. During this selection process, relatively thin precoat beds of I to 2 cm are satisfactory. After a grade has been selected, bench-scale tests should be... 

Since the Wenner formula [Eq. (24-41)] was deduced for hemispherical electrodes, measuring errors appear for spike electrodes. To avoid errors in excess of 5%, the depth of penetration must be less than a 5. Soil resistivity increases greatly under frost conditions. While electrodes can be driven through thin layers of frost, soil resistivity measurements deeper than 20 cm in frozen ground are virtually impossible. 

Thus either the penetration theory or the film theory (equation 10.144 or 10.145) respectively can be used to describe the mass transfer process. The error will not exceed some 9 per cent provided that the appropriate equation is used, equation 10.144 for L2 jDt > n and equation 10.145 for L2/Dt < n. Equation 10.145 will frequently apply quite closely in a wetted-wall column or in a packed tower with large packings. Equation 10.144 will apply when one of the phases is dispersed in the form of droplets, as in a spray tower, or in a packed tower with small packing elements. 

An alternative to the measurement of the dimensions of the indentation by means of a microscope is the direct reading method, of which the Rockwell method is an example. The Rockwell hardness is based on indentation into the sample under the action of two consecutively applied loads - a minor load (initial) and a standardised major load (final). In order to eliminate zero error and possible surface effects due to roughness or scale, the initial or minor load is first applied and produce an initial indentation. The Rockwell hardness is based on the increment in the indentation depth produced by the major load over that produced by the minor load. Rockwell hardness scales are divided into a number of groups, each one of these corresponding to a specified penetrator and a specified value of the major load. The different combinations are designated by different subscripts used to express the Rockwell hardness number. Thus, when the test is performed with 150 kg load and a diamond cone indentor, the resulting hardness number is called the Rockwell C (Rc) hardness. If the applied load is 100 kg and the indentor used is a 1.58 mm diameter hardened steel ball, a Rockwell B (RB) hardness number is obtained. The facts that the dial has several scales and that different indentation tools can be filled, enable Rockwell machine to be used equally well for hard and soft materials and for small and thin specimens. Rockwell hardness number is dimensionless. The test is easy to carry out and rapidly accomplished. As a result it is used widely in industrial applications, particularly in quality situations. 

In practice, the application of x-ray measurement techniques to thin films involves some special problems. Typical films are much thinner than the penetration depth of commonly used x-rays, so the diffracted intensity is much lower than that from bulk materials. Thin films are often strongly textured this, on the other hand, results in improved intensity for suitable experimental conditions but complicates the measurement problem. Measurements at other than ambient temperature, not usually attempted with bulk materials, constitutes additional complexity. Since typical strains are on the order of 1 X 10 , measurements of interplanar spacing with a precision of the order of 1 X 10 are needed for reasonably accurate results hence, potential sources of error must be kept to a low level. In particular, the sample displacement error can be a major source of difficulty with a heated sample. The sample surface must remain accurately on the axis of the instrument during heating. 

---