Envelope surface

Another technique, capillary flow porometry has been developed by Porous Materials Inc. ° to characterize battery separators.The instrument can measure a number of characteristics of battery separators such as size of the pore at its most constricted part, the largest pore size, pore size distribution, permeability, and envelope surface... 

Noise measurement at machines measurement of airborne noise, enveloping surface methods. Part 13 - Compressors, including vacuum pumps, ... 

Only then a correlation of the LII results with the iodine number is to be expected if different specific surfaces are caused by variations in the primary particle size and not in porosity. The assumption that LII determines a measure for the enveloping surface without consideration of small porosities has been examined in further measurements at a test reactor of the Degussa AG with finer parameter variations. The aim was to manufacture carbon blacks of same primary particle size, but different surface structure. 

The extension of Eq. (3-32) is straightforward for a discretized enveloping surface (S) with the boundary element method (BEM) the final result can be expressed in a set of linear equations [124] ... 

When the axial base ligand was replaced with the other amines or phosphines, several types of racemization and different reaction rates were observed [15]. In order to explain the different types and reaction rates, we defined the reaction cavity for the reactive group as shown in Fig. 1 [14,16]. The reaction cavity is represented by the concave space limited by the envelope surface of the spheres, whose centers are positions of intra- and intermolecular atoms in the neighborhood of the reactive 1-cyanoethyl group, the radius of each sphere being... 

A black-and-white felt rub-down test is performed to demonstrate adequate cleanliness of the interior clean-envelope surfaces. This test consists of both black-and-white felt being wiped over any surface for 1 m linear distance with a firm hand pressure. No residue should be visible on the cloth. Each cloth should be 60cm square black or white static-free natural hber felt folded with cut edges inside to a 25-cm square. The cut edges should be sealed with an approved latex sealant. 

Another family of superimposed surfaces is used in the study of active sites of enzymes. By superimposing approximate molecular surfaces of several molecules showing similar activity with respect to the given enzyme, a part of their envelope surface, called their union surface, can be taken as an object that approximately fills out the cavity of the enzyme [167,311,338]. The shape of the union surface (in fact, the shape of its complement) is expected to provide more information on the shape of the enzyme cavity than a surface of a single active molecule. 

Fused sphere surfaces, such as fused sphere Van der Waals surfaces (VDWS ) are simple approximations to molecular contour surfaces. By specifying the locations of the centers and the radii of formal atomic spheres in a molecule, the fused sphere surface is fully defined as the envelope surface of the fused spheres and can be easily generated by a computer. Although fused sphere VDW surfaces are not capable of representing the fine details of molecular shape, such surfaces are very useful for an approximate shape representation. 

Fortuitously, for most molecules, the MIDCO s G(a) of the chemically most important small density threshold values a are those where the deviations are small from the simple fused sphere model surfaces. The usual Van der Waals surfaces fall within this range. For a molecule containing N nuclei, these VDWS s are obtained as the envelope surfaces of N interpenetrating spheres... 

Three ramilies of spheres and their envelope surfaces for H,0... 

Figure 7.1 Illustration of the principle of the Fused Spheres Guided Homotopy Method (FSGH), applied for the generation of dot representations of density scalable MIDCO surfaces for the water molecule. Three families of atomic spheres (thin lines) and their envelope surfaces (heavy lines) are shown in the upper part of the figure. In the lower part of the figure, the selected point sets on the innermost family of spheres are connected by interpolating lines to the exposed points (black dots) on the envelope surfaces of two enlarged families of spheres. Linear interpolation along the lines for two selected density values leads to two families of white dots, generating approximations of two MIDCO s (heavy lines in the lower figure).

However, this sequence of envelope surfaces of gradually enlarged fused spheres will not, in general, approximate the MIDCO s adequately for some practical applications in particular, at the seams of interpenetrating spheres this representation does not follow the corresponding MIDCO G(a) well. 

If the above rule is applied to the entire sequence of envelope surfaces, then one obtains a collection of at most (n x m x N) line segments generating a set of piecewise linear broken lines of approximately uniform distribution and approximately perpendicular to the tangent plane of each local spherical domain where the lines cross the envelope surfaces. Some of these lines may merge and possibly separate again as some of the selected points get buried and possibly reappear in the enlargement process of the spheres. 

Each of these lines is composed of straight line segments s(ftu, rt+ u ), connecting subsequent envelope surfaces. We assume that function values of the electronic charge density p(r) are available at each rty point of each envelope surface Fj. One can use linear interpolation between the endpoints r y and rt+>u of each line segment s(rtu, rt+ly ) in order to find points with a desired electronic charge density value a. 

All of the permeametry methods are based on the Carman-Kozeny equation given in Fig. 4 which relates the approach velocity u to the porosity of the powder e and the specific surface of the sample Sw. The specific surface calculated involves only the walls of the pores of the bed which are swept by the flow and it does not take into account the pores within the particles which do not contribute to the flow. The surface measured, therefore, is an envelope surface area and it can be very much smaller than the total surface area of the particles as measured, say, by gas adsorption. 

HIV-1 gene coding for the Envelope surface and transmembrane proteins ETS-1 transcription factor feline immunodeficiency vims HIV-1 gene coding for the capsid and matrix stmctural proteins... 

The envelope surface (12.2.3.1) gives a better correlation with (PPE) than the simple molecular surface, as expected, and an even better fit is obtained when the size effect is corrected for the shape effect using Cjeif (see 12.2.3.4), especially for larger molecules [8] ... 

The word shape is loaded with strong personal intuitions of what each of us thinks defines an object in three-dimensional (3D) space. Sometimes, we may view an object as a distribution of points in space and conceive its shape in terms of distances and angles, that is, local geometrical measures. More often, we associate the notion of shape with a solid object defined by an envelope surface. In this case, a precise geometrical characterization may lose its relevance, and it may be sufficient to characterize shape in a more qualitative fashion. Global topological measures are better suited here. Therefore, we... 

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