Fuller curves

Figure 6. Gradation curves of different aggregate blends. Lines 2 and 4 correspond closely to the upper and lower Fuller curve limits, respectively.

Mixes with a very low proportion of fine particles which fall below the lower Fuller curve appear to have reduced strength. The required sulphur content is low. 

Mixes falling within the Fuller curves at the fine end appear to be best because they require a low sulphur content and have reasonable strength. 

Fuller parabola for aggregates 0/8 is represented by sieve line 4 in Figure 3. Sulfur concrete mixtures whose aggregates corresponded to the grain size distribution of the Fuller curve no longer separated and were plastic... 

Equation (42) is valid for the extreme case of the Fuller curve. Therefore, calculations can be carried out for two extreme cases. For practical purposes the approximation A —7r/e is sufficiently accurate. 

Figure 6J Fuller curves of various degrees, after Popovics (1979).

Figure 18.14 The diffraction pattern of helices in fiber crystallites can be simulated by the diffraction pattern of a single slit with the shape of a sine curve (representing the projection of a helix). Two such simulations are given in (a) and (b), with the helix shown to the left of its diffraction pattern. The spacing between the layer lines is inversely related to the helix pitch, P and the angle of the cross arms in the diffraction pattern is related to the angle of climb of the helix, 6. The helix in (b) has a smaller pitch and angle of climb than the helix in (a). (Courtesy of W. Fuller.)...

As of this time, no one has solved the problem of the effect of asperities on a curved surface nor has anyone addressed the issue of crystalline facets. Needless to say, the problem of asperities on an irregular surface has not been addressed. However, Fuller and Tabor [118] have proposed a model that addresses the effects of variations of asperity size on adhesion for the case of planar surfaces. Assuming elastic response to the adhesion-induced stresses, they treated surface roughness as a random series of asperities having a Gaussian height distribution (f> z) and standard deviation o. Accordingly,... 

Carbon tubules (or nanotubes) are a new form of elemental carbon recently isolated from the soot obtained during the arc-discharge synthesis of fuller-enes[I]. High-resolution electron micrographs do not favor a scroll-like heUcal structure, but rather concentric tubular shells of 2 to 50 layers, with tips closed by curved, cone-shaped, or even polygonal caps. Later work[2] has shown the possibility of obtaining singleshell seamless nanotubes. 

To expand on the last remark, the simulation results from Fuller and Newman are shown in Figure 17. The curves clearly show a nonuniform current distribution that is mainly due to the change in the gas concentrations and the membrane hydration. In the simulation, the initial decrease in the current density is due to the change in the oxygen concentration. However, once enough water is generated to hydrate the membrane, the increased conductivity yields higher local current densities. What... 

Fuller, F.B. (1971) The writhing number of a space curve. Proc. Natl. Acad. Sci. USA 68, 815-819. Crick, F.H.C. (1976) Linking numbers and nucleosomes. Proc. Natl. Acad. Sci. USA 73,... 

Aggregates from a different source were blended using the mathematical technique to obtain five curves as before. The grading curves are shown in Figure 6. Mix 2 is almost coincident with the upper Fuller limit and mix 4 with the lower limit. Strengths, voids in the mineral aggregate (VMA), and densities are given in Table 1. 

These data are derived from the Marshall design curves (10) the "optimum" contents meet all the criteria established for asphaltic mixtures. The optimum Sulphlex-233 content is at a slightly higher than equal volume replacement of the optimum AC-20 content. Reference (10) presents a fuller discussion of this topic. 

System Model. The equilibrium model (model a) did not properly represent the observed rate curve because the predicted peak maximum, using this model, always occurred at least an order of magnitude earlier in time than was actually observed when measured values for all parameters were substituted into the equilibrium model. Thus a mass transfer influence—e.g.j intracrystalline diffusional limitations or product desorption limitations—must be invoked to explain the data. The diffusional limitations model might fit the data qualitatively as Tan and Fuller (6) show for their system. However, this model contains three fitting constants and should be applied only when there is sufficient evidence of diffusional limitations. 

The applicability of relation (9.71) to a real polymer system was discussed in works by Pokrovskii et al. (1973) Pokrovskii and Kruchinin (1980) Pyshno-grai et al. (1994). Figure 19 represents the experimental values of the ratio A/77 depending on the invariant D for the polymer systems, listed in Table 3, in comparison with the universal theoretical curve calculated according to equation (9.71). The experimental results can be seen to have a definite scatter relative to the theoretical curve this can be ascribed to both natural experimental errors and the necessity of improving the theoretical calculation by appealing to the fuller set of constitutive relations (9.48)-(9.49). In the former case a variation of [3 in (9.49) leads to a set of A/77 vs D curves (Pyshnograi et al. 1994). 

FIG. 15.44 Schematic representation of the bulk structure of an LCP during shear flow in the respective regions of the three-region flow curve, as proposed by Onogi and Asada (1980) and by Beekmans (1997). The lower cartoon in region II is in agreement with newer ideas of the structure obtained in the 1990 s by Burghardt. Fuller, 1991, Vermant et al., 1994, Walker et al., 1995. 

Around 1985, Kroto, Smalley, and Curl (Rice University) isolated a molecule of formula Cf,cj from the soot produced by using a laser (or an electric arc) to vaporize graphite. Molecular spectra showed that G , is unusually symmetrical It has only one type of carbon atom by 13C NMR (5143 ppm), and there are only two types of bonds (1.39 A and 1.45 A). Figure 16-16 shows the structure of C(1, which was named buckminsterfiillerene in honor of the American architect R. Buckminster Fuller, whose geodesic domes used similar five- and six-membered rings to form a curved roof. The Cg0 molecules are sometimes called buckyballs, and these types of compounds (Cgo and similar carbon clusters) are called fullerenes. 

Figure 3.17 Birefringence as a function of the eigenvalue of the velocity gradient tensor, G, for planar flows generated in a four-roll mill, for dilute solutions of polystyrenes of three different molecular weights in polychlorinated biphenyl solvent. Here G is the strain rate and a the flow type parameter. For planar extension, a — 1 and G = is the extension rate for simple shear, a = 0 and G = y is the shear rate. The different symbols correspond to a values of 1.0 (0)> 0.8 (A), 0.5 (-1-), and 0.25 (diamonds). The curves are theoretical predictions from the FENE dumbbell model, including conformation-dependent drag (discussed in Section 3.6.2.2.2). (From Fuller and Leal 1980, reprinted with permission from Steinkopff Publishers.)...

The manufacture of molded articles is usually carried out with mixtures of aluminum oxides with different particle size distributions. This is particularly important when pore-free end-products are required, because this enables a higher volume concentration of aluminum oxide to be obtained than the 74% of ideally cubic close packed spheres by filling the gaps with smaller particles. The particle size distributions used in practice are usually determined using empirically determined approximate formulae (Andreasen or Fuller distribution curves) which take into account the morphology of the individual particles. 

In initial studies in which substance P was administered to subjects by intravenous infusion, no effect on airway caliber could be demonstrated. It is possible that potent cardiovascular side effects resulted in homeostatic reflexes with secondary effects on the airways that masked the effects of substance P (Fuller et al., 1987). However, when changes in the partial flow volume curve, a highly sensitive index of airway caliber, were used as the index of airway obstruction, inhaled NkA - and, to a lesser extent, inhaled substance P - caused airway obstruction in healthy people (Joos et al., 1987). NkA is approximately 10-100 times more potent as a bronchocon-strictor in asthmatic than in non-asthmatic subjects (Cheung et al., 1992, 1993) this ratio of potency is similar to that observed for other agonists. 

Zhou L, Vandersteen J, Wang L, Fuller T, Taylor M, Palais B, Wittwer CT. High-resolution DNA melting curve analysis to establish HLA genotypic identity. Tissue Antigens 2004 64 156-64. 

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